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

Percentage Accurate: 97.1% → 99.7%

Time: 12.8s

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: 97.1% 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: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. sub-neg 97.6%

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

   2. +-commutative 97.6%

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

   3. associate-/r/ 99.1%

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

   4. distribute-lft-neg-in 99.1%

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

   5. fma-define 99.2%

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

   6. distribute-neg-frac2 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. sub-neg 99.2%

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

   9. distribute-neg-in 99.2%

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

   10. remove-double-neg 99.2%

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

   11. +-commutative 99.2%

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

   12. sub-neg 99.2%

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

   13. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-32}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+45}:\\ \;\;\;\;x + z \cdot \frac{a}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e-8)
   (+ x (/ a (+ -1.0 (/ t z))))
   (if (<= z 1.06e-32)
     (+ x (* a (/ y (- -1.0 t))))
     (if (<= z 2.6e+45)
       (+ x (* z (/ a (- (+ t 1.0) z))))
       (+ x (- (* a (/ y z)) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-8) {
		tmp = x + (a / (-1.0 + (t / z)));
	} else if (z <= 1.06e-32) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 2.6e+45) {
		tmp = x + (z * (a / ((t + 1.0) - z)));
	} else {
		tmp = x + ((a * (y / z)) - 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 <= (-2.2d-8)) then
        tmp = x + (a / ((-1.0d0) + (t / z)))
    else if (z <= 1.06d-32) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 2.6d+45) then
        tmp = x + (z * (a / ((t + 1.0d0) - z)))
    else
        tmp = x + ((a * (y / z)) - 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 <= -2.2e-8) {
		tmp = x + (a / (-1.0 + (t / z)));
	} else if (z <= 1.06e-32) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 2.6e+45) {
		tmp = x + (z * (a / ((t + 1.0) - z)));
	} else {
		tmp = x + ((a * (y / z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e-8:
		tmp = x + (a / (-1.0 + (t / z)))
	elif z <= 1.06e-32:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 2.6e+45:
		tmp = x + (z * (a / ((t + 1.0) - z)))
	else:
		tmp = x + ((a * (y / z)) - a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e-8)
		tmp = Float64(x + Float64(a / Float64(-1.0 + Float64(t / z))));
	elseif (z <= 1.06e-32)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 2.6e+45)
		tmp = Float64(x + Float64(z * Float64(a / Float64(Float64(t + 1.0) - z))));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(y / z)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e-8)
		tmp = x + (a / (-1.0 + (t / z)));
	elseif (z <= 1.06e-32)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 2.6e+45)
		tmp = x + (z * (a / ((t + 1.0) - z)));
	else
		tmp = x + ((a * (y / z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e-8], N[(x + N[(a / N[(-1.0 + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-32], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+45], N[(x + N[(z * N[(a / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1999999999999998e-8

   1. Initial program 93.9%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 91.2%

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

      1. associate--l+ 91.2%

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

      2. associate-*r/ 91.2%

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

      3. associate-*r/ 91.2%

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

      4. mul-1-neg 91.2%

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

      5. div-sub 91.2%

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

      6. sub-neg 91.2%

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

      7. distribute-lft-in 91.2%

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

      8. metadata-eval 91.2%

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

      9. mul-1-neg 91.2%

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

      10. unsub-neg 91.2%

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

      11. remove-double-neg 91.2%

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

   9. Simplified 91.2%

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

   10. Taylor expanded in t around inf 89.6%

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

       1. associate-*r/ 89.6%

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

       2. neg-mul-1 89.6%

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

   12. Simplified 89.6%

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

   if -2.1999999999999998e-8 < z < 1.05999999999999994e-32

   1. Initial program 99.8%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 94.5%

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

   if 1.05999999999999994e-32 < z < 2.60000000000000007e45

   1. Initial program 99.8%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 87.6%

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

      1. mul-1-neg 87.6%

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

      2. *-commutative 87.6%

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

      3. associate--l+ 87.6%

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

      4. +-commutative 87.6%

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

      5. associate-*r/ 87.7%

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

      6. distribute-rgt-neg-in 87.7%

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

      7. distribute-neg-frac2 87.7%

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

      8. associate-+l- 87.7%

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

      9. sub-neg 87.7%

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

      10. metadata-eval 87.7%

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

      11. +-commutative 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in a around 0 87.7%

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

   if 2.60000000000000007e45 < z

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 88.8%

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

      1. neg-mul-1 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in y around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

      3. associate-/l* 90.3%

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

   8. Simplified 90.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-32}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+45}:\\ \;\;\;\;x + z \cdot \frac{a}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -48 \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -48.0) (not (<= z 2.4e-5)))
   (+ x (- (* a (/ y z)) a))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -48.0) || !(z <= 2.4e-5)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x + (a * (y / (-1.0 - 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 <= (-48.0d0)) .or. (.not. (z <= 2.4d-5))) then
        tmp = x + ((a * (y / z)) - a)
    else
        tmp = x + (a * (y / ((-1.0d0) - 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 <= -48.0) || !(z <= 2.4e-5)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -48.0) or not (z <= 2.4e-5):
		tmp = x + ((a * (y / z)) - a)
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -48.0) || !(z <= 2.4e-5))
		tmp = Float64(x + Float64(Float64(a * Float64(y / z)) - a));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -48.0) || ~((z <= 2.4e-5)))
		tmp = x + ((a * (y / z)) - a);
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -48.0], N[Not[LessEqual[z, 2.4e-5]], $MachinePrecision]], N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -48 or 2.4000000000000001e-5 < z

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. neg-mul-1 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in y around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. associate-/l* 82.1%

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

   8. Simplified 82.1%

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

   if -48 < z < 2.4000000000000001e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 93.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48 \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+52} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.15e+52) (not (<= z 2.4e-5)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+52) || !(z <= 2.4e-5)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - 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 <= (-2.15d+52)) .or. (.not. (z <= 2.4d-5))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - 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 <= -2.15e+52) || !(z <= 2.4e-5)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.15e+52) or not (z <= 2.4e-5):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.15e+52) || !(z <= 2.4e-5))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.15e+52) || ~((z <= 2.4e-5)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.15e+52], N[Not[LessEqual[z, 2.4e-5]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e52 or 2.4000000000000001e-5 < z

   1. Initial program 95.0%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 76.2%

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

   if -2.15e52 < z < 2.4000000000000001e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 89.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+52} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e-9)
   (+ x (/ a (+ -1.0 (/ t z))))
   (if (<= z 2.4e-5) (+ x (* a (/ y (- -1.0 t)))) (+ x (- (* a (/ y z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e-9) {
		tmp = x + (a / (-1.0 + (t / z)));
	} else if (z <= 2.4e-5) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((a * (y / z)) - 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 <= (-2.8d-9)) then
        tmp = x + (a / ((-1.0d0) + (t / z)))
    else if (z <= 2.4d-5) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + ((a * (y / z)) - 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 <= -2.8e-9) {
		tmp = x + (a / (-1.0 + (t / z)));
	} else if (z <= 2.4e-5) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((a * (y / z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e-9:
		tmp = x + (a / (-1.0 + (t / z)))
	elif z <= 2.4e-5:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + ((a * (y / z)) - a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e-9)
		tmp = Float64(x + Float64(a / Float64(-1.0 + Float64(t / z))));
	elseif (z <= 2.4e-5)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(y / z)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e-9)
		tmp = x + (a / (-1.0 + (t / z)));
	elseif (z <= 2.4e-5)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + ((a * (y / z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e-9], N[(x + N[(a / N[(-1.0 + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-5], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999984e-9

   1. Initial program 93.9%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 91.2%

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

      1. associate--l+ 91.2%

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

      2. associate-*r/ 91.2%

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

      3. associate-*r/ 91.2%

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

      4. mul-1-neg 91.2%

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

      5. div-sub 91.2%

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

      6. sub-neg 91.2%

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

      7. distribute-lft-in 91.2%

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

      8. metadata-eval 91.2%

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

      9. mul-1-neg 91.2%

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

      10. unsub-neg 91.2%

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

      11. remove-double-neg 91.2%

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

   9. Simplified 91.2%

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

   10. Taylor expanded in t around inf 89.6%

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

       1. associate-*r/ 89.6%

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

       2. neg-mul-1 89.6%

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

   12. Simplified 89.6%

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

   if -2.79999999999999984e-9 < z < 2.4000000000000001e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 93.9%

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

   if 2.4000000000000001e-5 < z

   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 inf 82.4%

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

      1. neg-mul-1 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in y around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

      3. associate-/l* 83.7%

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

   8. Simplified 83.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-8} \lor \neg \left(z \leq 1.65 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.2e-8) (not (<= z 1.65e-5))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e-8) || !(z <= 1.65e-5)) {
		tmp = x - a;
	} else {
		tmp = x - (y * 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 <= (-2.2d-8)) .or. (.not. (z <= 1.65d-5))) then
        tmp = x - a
    else
        tmp = x - (y * 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 <= -2.2e-8) || !(z <= 1.65e-5)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.2e-8) or not (z <= 1.65e-5):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.2e-8) || !(z <= 1.65e-5))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.2e-8) || ~((z <= 1.65e-5)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.2e-8], N[Not[LessEqual[z, 1.65e-5]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999998e-8 or 1.6500000000000001e-5 < z

   1. Initial program 95.4%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.8%

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

   if -2.1999999999999998e-8 < z < 1.6500000000000001e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around 0 79.6%

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

   6. Taylor expanded in z around 0 76.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-8} \lor \neg \left(z \leq 1.65 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-25} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e-25) (not (<= z 2.4e-5))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e-25) || !(z <= 2.4e-5)) {
		tmp = x - a;
	} else {
		tmp = 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 <= (-4d-25)) .or. (.not. (z <= 2.4d-5))) then
        tmp = x - a
    else
        tmp = 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 <= -4e-25) || !(z <= 2.4e-5)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e-25) or not (z <= 2.4e-5):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e-25) || !(z <= 2.4e-5))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e-25) || ~((z <= 2.4e-5)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e-25], N[Not[LessEqual[z, 2.4e-5]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000015e-25 or 2.4000000000000001e-5 < z

   1. Initial program 95.5%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -4.00000000000000015e-25 < z < 2.4000000000000001e-5

   1. Initial program 99.8%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in x around inf 50.2%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-25} \lor \neg \left(z \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-/r/ 99.1%

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

3. Simplified 99.1%

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

5. Final simplification 99.1%

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

Alternative 9: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-174}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.3e-241) x (if (<= x 3.7e-174) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.3e-241) {
		tmp = x;
	} else if (x <= 3.7e-174) {
		tmp = -a;
	} else {
		tmp = 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 (x <= (-2.3d-241)) then
        tmp = x
    else if (x <= 3.7d-174) then
        tmp = -a
    else
        tmp = 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 (x <= -2.3e-241) {
		tmp = x;
	} else if (x <= 3.7e-174) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.3e-241:
		tmp = x
	elif x <= 3.7e-174:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.3e-241)
		tmp = x;
	elseif (x <= 3.7e-174)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.3e-241)
		tmp = x;
	elseif (x <= 3.7e-174)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.3e-241], x, If[LessEqual[x, 3.7e-174], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999999e-241 or 3.7000000000000001e-174 < x

   1. Initial program 98.9%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 58.5%

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

   if -2.2999999999999999e-241 < x < 3.7000000000000001e-174

   1. Initial program 92.2%

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

      1. associate-/r/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around inf 36.8%

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

   6. Taylor expanded in x around 0 36.8%

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

      1. neg-mul-1 36.8%

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

   8. Simplified 36.8%

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

Alternative 10: 54.3% 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 97.6%

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

   1. associate-/r/ 99.1%

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

3. Simplified 99.1%

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

5. Taylor expanded in x around inf 48.3%

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

Developer Target 1: 99.7% 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 2024137 
(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))))