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

Percentage Accurate: 96.9% → 99.7%

Time: 15.1s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. sub-neg 97.3%

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

   2. +-commutative 97.3%

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

   3. associate-/r/ 98.8%

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

   4. distribute-lft-neg-in 98.8%

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

   5. fma-define 98.9%

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

   6. distribute-neg-frac2 98.9%

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

   7. distribute-neg-in 98.9%

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

   8. sub-neg 98.9%

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

   9. distribute-neg-in 98.9%

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

   10. remove-double-neg 98.9%

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

   11. +-commutative 98.9%

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

   12. sub-neg 98.9%

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

   13. metadata-eval 98.9%

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

3. Simplified 98.9%

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

5. Final simplification 98.9%

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

Alternative 2: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(z - y\right)\\ t_2 := x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -0.305:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-138}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (- z y)))) (t_2 (+ x (* (/ a t) (- z y)))))
   (if (<= t -0.305)
     t_2
     (if (<= t -3.3e-191)
       t_1
       (if (<= t 1.22e-138)
         (- x a)
         (if (<= t 2e-37) t_1 (if (<= t 2e-7) (- x a) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z - y));
	double t_2 = x + ((a / t) * (z - y));
	double tmp;
	if (t <= -0.305) {
		tmp = t_2;
	} else if (t <= -3.3e-191) {
		tmp = t_1;
	} else if (t <= 1.22e-138) {
		tmp = x - a;
	} else if (t <= 2e-37) {
		tmp = t_1;
	} else if (t <= 2e-7) {
		tmp = x - a;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (z - y))
    t_2 = x + ((a / t) * (z - y))
    if (t <= (-0.305d0)) then
        tmp = t_2
    else if (t <= (-3.3d-191)) then
        tmp = t_1
    else if (t <= 1.22d-138) then
        tmp = x - a
    else if (t <= 2d-37) then
        tmp = t_1
    else if (t <= 2d-7) then
        tmp = x - a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z - y));
	double t_2 = x + ((a / t) * (z - y));
	double tmp;
	if (t <= -0.305) {
		tmp = t_2;
	} else if (t <= -3.3e-191) {
		tmp = t_1;
	} else if (t <= 1.22e-138) {
		tmp = x - a;
	} else if (t <= 2e-37) {
		tmp = t_1;
	} else if (t <= 2e-7) {
		tmp = x - a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z - y))
	t_2 = x + ((a / t) * (z - y))
	tmp = 0
	if t <= -0.305:
		tmp = t_2
	elif t <= -3.3e-191:
		tmp = t_1
	elif t <= 1.22e-138:
		tmp = x - a
	elif t <= 2e-37:
		tmp = t_1
	elif t <= 2e-7:
		tmp = x - a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z - y)))
	t_2 = Float64(x + Float64(Float64(a / t) * Float64(z - y)))
	tmp = 0.0
	if (t <= -0.305)
		tmp = t_2;
	elseif (t <= -3.3e-191)
		tmp = t_1;
	elseif (t <= 1.22e-138)
		tmp = Float64(x - a);
	elseif (t <= 2e-37)
		tmp = t_1;
	elseif (t <= 2e-7)
		tmp = Float64(x - a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * (z - y));
	t_2 = x + ((a / t) * (z - y));
	tmp = 0.0;
	if (t <= -0.305)
		tmp = t_2;
	elseif (t <= -3.3e-191)
		tmp = t_1;
	elseif (t <= 1.22e-138)
		tmp = x - a;
	elseif (t <= 2e-37)
		tmp = t_1;
	elseif (t <= 2e-7)
		tmp = x - a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.305], t$95$2, If[LessEqual[t, -3.3e-191], t$95$1, If[LessEqual[t, 1.22e-138], N[(x - a), $MachinePrecision], If[LessEqual[t, 2e-37], t$95$1, If[LessEqual[t, 2e-7], N[(x - a), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.304999999999999993 or 1.9999999999999999e-7 < t

   1. Initial program 99.1%

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

      1. associate-/r/ 97.8%

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

   3. Simplified 97.8%

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

      1. *-commutative 97.8%

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

      2. clear-num 97.7%

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

      3. un-div-inv 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in t around inf 85.0%

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

      1. associate-/r/ 87.9%

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

   9. Applied egg-rr 87.9%

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

   if -0.304999999999999993 < t < -3.29999999999999981e-191 or 1.22e-138 < t < 2.00000000000000013e-37

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 71.7%

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

   4. Taylor expanded in t around 0 71.7%

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

   if -3.29999999999999981e-191 < t < 1.22e-138 or 2.00000000000000013e-37 < t < 1.9999999999999999e-7

   1. Initial program 98.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 81.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.305:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-191}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-138}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-37}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+96}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-223}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (- z y)))))
   (if (<= z -6.4e+96)
     (- x a)
     (if (<= z -9.5e-271)
       t_1
       (if (<= z 6.5e-223)
         (- x (* a (/ y t)))
         (if (<= z 2.1e-6) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z - y));
	double tmp;
	if (z <= -6.4e+96) {
		tmp = x - a;
	} else if (z <= -9.5e-271) {
		tmp = t_1;
	} else if (z <= 6.5e-223) {
		tmp = x - (a * (y / t));
	} else if (z <= 2.1e-6) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (a * (z - y))
    if (z <= (-6.4d+96)) then
        tmp = x - a
    else if (z <= (-9.5d-271)) then
        tmp = t_1
    else if (z <= 6.5d-223) then
        tmp = x - (a * (y / t))
    else if (z <= 2.1d-6) then
        tmp = t_1
    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 t_1 = x + (a * (z - y));
	double tmp;
	if (z <= -6.4e+96) {
		tmp = x - a;
	} else if (z <= -9.5e-271) {
		tmp = t_1;
	} else if (z <= 6.5e-223) {
		tmp = x - (a * (y / t));
	} else if (z <= 2.1e-6) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z - y))
	tmp = 0
	if z <= -6.4e+96:
		tmp = x - a
	elif z <= -9.5e-271:
		tmp = t_1
	elif z <= 6.5e-223:
		tmp = x - (a * (y / t))
	elif z <= 2.1e-6:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z - y)))
	tmp = 0.0
	if (z <= -6.4e+96)
		tmp = Float64(x - a);
	elseif (z <= -9.5e-271)
		tmp = t_1;
	elseif (z <= 6.5e-223)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 2.1e-6)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * (z - y));
	tmp = 0.0;
	if (z <= -6.4e+96)
		tmp = x - a;
	elseif (z <= -9.5e-271)
		tmp = t_1;
	elseif (z <= 6.5e-223)
		tmp = x - (a * (y / t));
	elseif (z <= 2.1e-6)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+96], N[(x - a), $MachinePrecision], If[LessEqual[z, -9.5e-271], t$95$1, If[LessEqual[z, 6.5e-223], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-6], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.40000000000000013e96 or 2.0999999999999998e-6 < z

   1. Initial program 94.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.5%

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

   if -6.40000000000000013e96 < z < -9.50000000000000103e-271 or 6.4999999999999996e-223 < z < 2.0999999999999998e-6

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 97.3%

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

   4. Taylor expanded in t around 0 76.3%

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

   if -9.50000000000000103e-271 < z < 6.4999999999999996e-223

   1. Initial program 99.9%

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

      1. associate-/r/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 69.1%

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

   6. Taylor expanded in y around inf 66.4%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+96}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-271}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-223}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-6}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{y - z}{z}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- y z) z)))))
   (if (<= z -9.2e+63)
     t_1
     (if (<= z 2.2)
       (+ x (/ (- y z) (/ (- -1.0 t) a)))
       (if (<= z 4.5e+119) t_1 (+ x (* a (/ z (+ (- t z) 1.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((y - z) / z));
	double tmp;
	if (z <= -9.2e+63) {
		tmp = t_1;
	} else if (z <= 2.2) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else if (z <= 4.5e+119) {
		tmp = t_1;
	} else {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + (a * ((y - z) / z))
    if (z <= (-9.2d+63)) then
        tmp = t_1
    else if (z <= 2.2d0) then
        tmp = x + ((y - z) / (((-1.0d0) - t) / a))
    else if (z <= 4.5d+119) then
        tmp = t_1
    else
        tmp = x + (a * (z / ((t - z) + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((y - z) / z));
	double tmp;
	if (z <= -9.2e+63) {
		tmp = t_1;
	} else if (z <= 2.2) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else if (z <= 4.5e+119) {
		tmp = t_1;
	} else {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * ((y - z) / z))
	tmp = 0
	if z <= -9.2e+63:
		tmp = t_1
	elif z <= 2.2:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	elif z <= 4.5e+119:
		tmp = t_1
	else:
		tmp = x + (a * (z / ((t - z) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(Float64(y - z) / z)))
	tmp = 0.0
	if (z <= -9.2e+63)
		tmp = t_1;
	elseif (z <= 2.2)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(-1.0 - t) / a)));
	elseif (z <= 4.5e+119)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * ((y - z) / z));
	tmp = 0.0;
	if (z <= -9.2e+63)
		tmp = t_1;
	elseif (z <= 2.2)
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	elseif (z <= 4.5e+119)
		tmp = t_1;
	else
		tmp = x + (a * (z / ((t - z) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+63], t$95$1, If[LessEqual[z, 2.2], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+119], t$95$1, N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.19999999999999973e63 or 2.2000000000000002 < z < 4.5000000000000002e119

   1. Initial program 93.6%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 96.2%

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

      1. neg-mul-1 96.2%

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

   7. Simplified 96.2%

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

   if -9.19999999999999973e63 < z < 2.2000000000000002

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

   if 4.5000000000000002e119 < z

   1. Initial program 95.1%

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

      1. sub-neg 95.1%

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

      2. +-commutative 95.1%

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

      3. associate-/r/ 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

      5. fma-define 100.0%

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

      6. distribute-neg-frac2 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. sub-neg 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. remove-double-neg 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. associate-/l* 100.0%

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

      4. associate--r+ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. +-commutative 100.0%

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

      8. associate--l+ 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+63}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+119}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t + 1}{a}}{y}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+119}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ z (+ (- t z) 1.0))))))
   (if (<= z -4e+25)
     t_1
     (if (<= z 2.2)
       (+ x (/ -1.0 (/ (/ (+ t 1.0) a) y)))
       (if (<= z 2.7e+119) (+ x (* a (/ (- y z) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / ((t - z) + 1.0)));
	double tmp;
	if (z <= -4e+25) {
		tmp = t_1;
	} else if (z <= 2.2) {
		tmp = x + (-1.0 / (((t + 1.0) / a) / y));
	} else if (z <= 2.7e+119) {
		tmp = x + (a * ((y - z) / z));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + (a * (z / ((t - z) + 1.0d0)))
    if (z <= (-4d+25)) then
        tmp = t_1
    else if (z <= 2.2d0) then
        tmp = x + ((-1.0d0) / (((t + 1.0d0) / a) / y))
    else if (z <= 2.7d+119) then
        tmp = x + (a * ((y - z) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / ((t - z) + 1.0)));
	double tmp;
	if (z <= -4e+25) {
		tmp = t_1;
	} else if (z <= 2.2) {
		tmp = x + (-1.0 / (((t + 1.0) / a) / y));
	} else if (z <= 2.7e+119) {
		tmp = x + (a * ((y - z) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z / ((t - z) + 1.0)))
	tmp = 0
	if z <= -4e+25:
		tmp = t_1
	elif z <= 2.2:
		tmp = x + (-1.0 / (((t + 1.0) / a) / y))
	elif z <= 2.7e+119:
		tmp = x + (a * ((y - z) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))))
	tmp = 0.0
	if (z <= -4e+25)
		tmp = t_1;
	elseif (z <= 2.2)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(t + 1.0) / a) / y)));
	elseif (z <= 2.7e+119)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * (z / ((t - z) + 1.0)));
	tmp = 0.0;
	if (z <= -4e+25)
		tmp = t_1;
	elseif (z <= 2.2)
		tmp = x + (-1.0 / (((t + 1.0) / a) / y));
	elseif (z <= 2.7e+119)
		tmp = x + (a * ((y - z) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+25], t$95$1, If[LessEqual[z, 2.2], N[(x + N[(-1.0 / N[(N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+119], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000036e25 or 2.6999999999999998e119 < z

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. +-commutative 94.6%

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

      3. associate-/r/ 99.9%

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

      4. distribute-lft-neg-in 99.9%

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

      5. fma-define 99.9%

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

      6. distribute-neg-frac2 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. remove-double-neg 99.9%

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

      11. +-commutative 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. unsub-neg 68.0%

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

      3. associate-/l* 94.4%

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

      4. associate--r+ 94.4%

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

      5. sub-neg 94.4%

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

      6. metadata-eval 94.4%

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

      7. +-commutative 94.4%

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

      8. associate--l+ 94.4%

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

   7. Simplified 94.4%

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

   if -4.00000000000000036e25 < z < 2.2000000000000002

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

      2. +-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf 88.7%

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

      1. associate-/r* 92.9%

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

   10. Simplified 92.9%

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

   if 2.2000000000000002 < z < 2.6999999999999998e119

   1. Initial program 94.3%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 95.5%

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

      1. neg-mul-1 95.5%

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

   7. Simplified 95.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+25}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t + 1}{a}}{y}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+119}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+119}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ z (+ (- t z) 1.0))))))
   (if (<= z -4e+25)
     t_1
     (if (<= z 2.15)
       (+ x (* a (/ y (- -1.0 t))))
       (if (<= z 2.8e+119) (+ x (* a (/ (- y z) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / ((t - z) + 1.0)));
	double tmp;
	if (z <= -4e+25) {
		tmp = t_1;
	} else if (z <= 2.15) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 2.8e+119) {
		tmp = x + (a * ((y - z) / z));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + (a * (z / ((t - z) + 1.0d0)))
    if (z <= (-4d+25)) then
        tmp = t_1
    else if (z <= 2.15d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 2.8d+119) then
        tmp = x + (a * ((y - z) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / ((t - z) + 1.0)));
	double tmp;
	if (z <= -4e+25) {
		tmp = t_1;
	} else if (z <= 2.15) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 2.8e+119) {
		tmp = x + (a * ((y - z) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z / ((t - z) + 1.0)))
	tmp = 0
	if z <= -4e+25:
		tmp = t_1
	elif z <= 2.15:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 2.8e+119:
		tmp = x + (a * ((y - z) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))))
	tmp = 0.0
	if (z <= -4e+25)
		tmp = t_1;
	elseif (z <= 2.15)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 2.8e+119)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * (z / ((t - z) + 1.0)));
	tmp = 0.0;
	if (z <= -4e+25)
		tmp = t_1;
	elseif (z <= 2.15)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 2.8e+119)
		tmp = x + (a * ((y - z) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+25], t$95$1, If[LessEqual[z, 2.15], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+119], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000036e25 or 2.80000000000000013e119 < z

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. +-commutative 94.6%

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

      3. associate-/r/ 99.9%

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

      4. distribute-lft-neg-in 99.9%

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

      5. fma-define 99.9%

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

      6. distribute-neg-frac2 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. remove-double-neg 99.9%

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

      11. +-commutative 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. unsub-neg 68.0%

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

      3. associate-/l* 94.4%

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

      4. associate--r+ 94.4%

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

      5. sub-neg 94.4%

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

      6. metadata-eval 94.4%

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

      7. +-commutative 94.4%

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

      8. associate--l+ 94.4%

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

   7. Simplified 94.4%

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

   if -4.00000000000000036e25 < z < 2.14999999999999991

   1. Initial program 99.9%

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

      1. associate-/r/ 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around 0 91.6%

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

   if 2.14999999999999991 < z < 2.80000000000000013e119

   1. Initial program 94.3%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 95.5%

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

      1. neg-mul-1 95.5%

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

   7. Simplified 95.5%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+25}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{elif}\;z \leq 2.15:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+119}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+25} \lor \neg \left(z \leq 2.2\right):\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+25) (not (<= z 2.2)))
   (+ x (* a (/ (- y z) z)))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+25) || !(z <= 2.2)) {
		tmp = x + (a * ((y - z) / z));
	} 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 <= (-4d+25)) .or. (.not. (z <= 2.2d0))) then
        tmp = x + (a * ((y - z) / z))
    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 <= -4e+25) || !(z <= 2.2)) {
		tmp = x + (a * ((y - z) / z));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+25) or not (z <= 2.2):
		tmp = x + (a * ((y - z) / z))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+25) || !(z <= 2.2))
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / z)));
	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 <= -4e+25) || ~((z <= 2.2)))
		tmp = x + (a * ((y - z) / z));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+25], N[Not[LessEqual[z, 2.2]], $MachinePrecision]], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $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 < -4.00000000000000036e25 or 2.2000000000000002 < z

   1. Initial program 94.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 90.5%

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

      1. neg-mul-1 90.5%

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

   7. Simplified 90.5%

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

   if -4.00000000000000036e25 < z < 2.2000000000000002

   1. Initial program 99.9%

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

      1. associate-/r/ 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around 0 91.6%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+25} \lor \neg \left(z \leq 2.2\right):\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+96} \lor \neg \left(z \leq 8.2 \cdot 10^{+58}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.4e+96) (not (<= z 8.2e+58)))
   (- 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 <= -6.4e+96) || !(z <= 8.2e+58)) {
		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 <= (-6.4d+96)) .or. (.not. (z <= 8.2d+58))) 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 <= -6.4e+96) || !(z <= 8.2e+58)) {
		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 <= -6.4e+96) or not (z <= 8.2e+58):
		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 <= -6.4e+96) || !(z <= 8.2e+58))
		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 <= -6.4e+96) || ~((z <= 8.2e+58)))
		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, -6.4e+96], N[Not[LessEqual[z, 8.2e+58]], $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 < -6.40000000000000013e96 or 8.2e58 < z

   1. Initial program 94.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 88.7%

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

   if -6.40000000000000013e96 < z < 8.2e58

   1. Initial program 98.7%

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

      1. associate-/r/ 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around 0 86.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+96} \lor \neg \left(z \leq 8.2 \cdot 10^{+58}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+96} \lor \neg \left(z \leq 2.3 \cdot 10^{-6}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.4e+96) (not (<= z 2.3e-6))) (- x a) (+ x (* a (- z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e+96) || !(z <= 2.3e-6)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (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 <= (-6.4d+96)) .or. (.not. (z <= 2.3d-6))) then
        tmp = x - a
    else
        tmp = x + (a * (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 <= -6.4e+96) || !(z <= 2.3e-6)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.4e+96) or not (z <= 2.3e-6):
		tmp = x - a
	else:
		tmp = x + (a * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.4e+96) || !(z <= 2.3e-6))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.4e+96) || ~((z <= 2.3e-6)))
		tmp = x - a;
	else
		tmp = x + (a * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.4e+96], N[Not[LessEqual[z, 2.3e-6]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.40000000000000013e96 or 2.3e-6 < z

   1. Initial program 94.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.5%

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

   if -6.40000000000000013e96 < z < 2.3e-6

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 97.9%

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

   4. Taylor expanded in t around 0 70.6%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+96} \lor \neg \left(z \leq 2.3 \cdot 10^{-6}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -56000000000 \lor \neg \left(z \leq 2.45 \cdot 10^{+60}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -56000000000.0) (not (<= z 2.45e+60))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -56000000000.0) || !(z <= 2.45e+60)) {
		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 <= (-56000000000.0d0)) .or. (.not. (z <= 2.45d+60))) 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 <= -56000000000.0) || !(z <= 2.45e+60)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -56000000000.0) or not (z <= 2.45e+60):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -56000000000.0) || !(z <= 2.45e+60))
		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 <= -56000000000.0) || ~((z <= 2.45e+60)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -56000000000.0], N[Not[LessEqual[z, 2.45e+60]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.6e10 or 2.4500000000000001e60 < z

   1. Initial program 94.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 82.6%

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

   if -5.6e10 < z < 2.4500000000000001e60

   1. Initial program 99.2%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in x around inf 60.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -56000000000 \lor \neg \left(z \leq 2.45 \cdot 10^{+60}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (a * ((y - z) / (-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 + (a * ((y - z) / ((-1.0d0) + (z - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-/r/ 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 12: 54.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-186}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.8e-211) x (if (<= x 2.9e-186) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.8e-211) {
		tmp = x;
	} else if (x <= 2.9e-186) {
		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 <= (-4.8d-211)) then
        tmp = x
    else if (x <= 2.9d-186) 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 <= -4.8e-211) {
		tmp = x;
	} else if (x <= 2.9e-186) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.8e-211:
		tmp = x
	elif x <= 2.9e-186:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.8e-211)
		tmp = x;
	elseif (x <= 2.9e-186)
		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 <= -4.8e-211)
		tmp = x;
	elseif (x <= 2.9e-186)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.8e-211], x, If[LessEqual[x, 2.9e-186], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000004e-211 or 2.90000000000000019e-186 < x

   1. Initial program 99.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 64.8%

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

   if -4.8000000000000004e-211 < x < 2.90000000000000019e-186

   1. Initial program 90.0%

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

      1. associate-/r/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around inf 50.8%

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

   6. Taylor expanded in x around 0 44.2%

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

      1. neg-mul-1 44.2%

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

   8. Simplified 44.2%

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

Alternative 13: 53.0% 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 97.3%

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

   1. associate-/r/ 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in x around inf 54.5%

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

Alternative 14: 3.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-/r/ 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in z around inf 63.8%

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

6. Taylor expanded in x around 0 18.3%

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

   1. neg-mul-1 18.3%

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

8. Simplified 18.3%

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

   1. neg-sub0 18.3%

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

   2. sub-neg 18.3%

      \[\leadsto \color{blue}{0 + \left(-a\right)} \]

   3. add-sqr-sqrt 8.6%

      \[\leadsto 0 + \color{blue}{\sqrt{-a} \cdot \sqrt{-a}} \]

   4. sqrt-unprod 7.6%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \]

   5. sqr-neg 7.6%

      \[\leadsto 0 + \sqrt{\color{blue}{a \cdot a}} \]

   6. sqrt-unprod 1.5%

      \[\leadsto 0 + \color{blue}{\sqrt{a} \cdot \sqrt{a}} \]

   7. add-sqr-sqrt 3.0%

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

10. Applied egg-rr 3.0%

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

    1. +-lft-identity 3.0%

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

12. Simplified 3.0%

    \[\leadsto \color{blue}{a} \]
13. Add Preprocessing

Developer target: 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 2024110 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

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