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

Percentage Accurate: 96.8% → 99.7%

Time: 13.5s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% 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 98.8%

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

   1. sub-neg 98.8%

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

   2. +-commutative 98.8%

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

   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. Final simplification 99.9%

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

Alternative 2: 75.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{a}{z + -1}\\ t_2 := x - a \cdot \frac{y}{t}\\ t_3 := x - a \cdot \frac{z}{z + -1}\\ \mathbf{if}\;t \leq -1350:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.06 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-266}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-94}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ a (+ z -1.0)))))
        (t_2 (- x (* a (/ y t))))
        (t_3 (- x (* a (/ z (+ z -1.0))))))
   (if (<= t -1350.0)
     t_2
     (if (<= t -2.06e-209)
       t_1
       (if (<= t -9.2e-266)
         t_3
         (if (<= t 3.9e-181)
           t_1
           (if (<= t 1.2e-94) t_3 (if (<= t 2.4e+14) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (a / (z + -1.0)));
	double t_2 = x - (a * (y / t));
	double t_3 = x - (a * (z / (z + -1.0)));
	double tmp;
	if (t <= -1350.0) {
		tmp = t_2;
	} else if (t <= -2.06e-209) {
		tmp = t_1;
	} else if (t <= -9.2e-266) {
		tmp = t_3;
	} else if (t <= 3.9e-181) {
		tmp = t_1;
	} else if (t <= 1.2e-94) {
		tmp = t_3;
	} else if (t <= 2.4e+14) {
		tmp = t_1;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x + (y * (a / (z + (-1.0d0))))
    t_2 = x - (a * (y / t))
    t_3 = x - (a * (z / (z + (-1.0d0))))
    if (t <= (-1350.0d0)) then
        tmp = t_2
    else if (t <= (-2.06d-209)) then
        tmp = t_1
    else if (t <= (-9.2d-266)) then
        tmp = t_3
    else if (t <= 3.9d-181) then
        tmp = t_1
    else if (t <= 1.2d-94) then
        tmp = t_3
    else if (t <= 2.4d+14) then
        tmp = t_1
    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 + (y * (a / (z + -1.0)));
	double t_2 = x - (a * (y / t));
	double t_3 = x - (a * (z / (z + -1.0)));
	double tmp;
	if (t <= -1350.0) {
		tmp = t_2;
	} else if (t <= -2.06e-209) {
		tmp = t_1;
	} else if (t <= -9.2e-266) {
		tmp = t_3;
	} else if (t <= 3.9e-181) {
		tmp = t_1;
	} else if (t <= 1.2e-94) {
		tmp = t_3;
	} else if (t <= 2.4e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (a / (z + -1.0)))
	t_2 = x - (a * (y / t))
	t_3 = x - (a * (z / (z + -1.0)))
	tmp = 0
	if t <= -1350.0:
		tmp = t_2
	elif t <= -2.06e-209:
		tmp = t_1
	elif t <= -9.2e-266:
		tmp = t_3
	elif t <= 3.9e-181:
		tmp = t_1
	elif t <= 1.2e-94:
		tmp = t_3
	elif t <= 2.4e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(a / Float64(z + -1.0))))
	t_2 = Float64(x - Float64(a * Float64(y / t)))
	t_3 = Float64(x - Float64(a * Float64(z / Float64(z + -1.0))))
	tmp = 0.0
	if (t <= -1350.0)
		tmp = t_2;
	elseif (t <= -2.06e-209)
		tmp = t_1;
	elseif (t <= -9.2e-266)
		tmp = t_3;
	elseif (t <= 3.9e-181)
		tmp = t_1;
	elseif (t <= 1.2e-94)
		tmp = t_3;
	elseif (t <= 2.4e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (a / (z + -1.0)));
	t_2 = x - (a * (y / t));
	t_3 = x - (a * (z / (z + -1.0)));
	tmp = 0.0;
	if (t <= -1350.0)
		tmp = t_2;
	elseif (t <= -2.06e-209)
		tmp = t_1;
	elseif (t <= -9.2e-266)
		tmp = t_3;
	elseif (t <= 3.9e-181)
		tmp = t_1;
	elseif (t <= 1.2e-94)
		tmp = t_3;
	elseif (t <= 2.4e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(a / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(a * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1350.0], t$95$2, If[LessEqual[t, -2.06e-209], t$95$1, If[LessEqual[t, -9.2e-266], t$95$3, If[LessEqual[t, 3.9e-181], t$95$1, If[LessEqual[t, 1.2e-94], t$95$3, If[LessEqual[t, 2.4e+14], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1350 or 2.4e14 < 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/ 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 t around inf 90.4%

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

   6. Taylor expanded in y around inf 85.4%

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

   if -1350 < t < -2.0600000000000001e-209 or -9.19999999999999986e-266 < t < 3.9e-181 or 1.2e-94 < t < 2.4e14

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 0 97.9%

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

   4. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*r/ 82.9%

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

   6. Simplified 82.9%

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

   if -2.0600000000000001e-209 < t < -9.19999999999999986e-266 or 3.9e-181 < t < 1.2e-94

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0 97.3%

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

   4. Taylor expanded in y around 0 62.0%

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

      1. mul-1-neg 62.0%

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

      2. associate-/l* 87.0%

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

      3. distribute-rgt-neg-in 87.0%

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

      4. distribute-frac-neg2 87.0%

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

      5. neg-sub0 87.0%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{0 - \left(1 - z\right)}} \]

      6. associate--r- 87.0%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{\left(0 - 1\right) + z}} \]

      7. metadata-eval 87.0%

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

   6. Simplified 87.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1350:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2.06 \cdot 10^{-209}:\\ \;\;\;\;x + y \cdot \frac{a}{z + -1}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-266}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-181}:\\ \;\;\;\;x + y \cdot \frac{a}{z + -1}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-94}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{a}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+28}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.0135:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \frac{a}{z + -1}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+74}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+28)
   (- x a)
   (if (<= z 0.0135)
     (+ x (* a (/ y (- -1.0 t))))
     (if (<= z 7.2e+45)
       (+ x (* y (/ a (+ z -1.0))))
       (if (<= z 2.4e+74) (+ x (* a (/ z t))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+28) {
		tmp = x - a;
	} else if (z <= 0.0135) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 7.2e+45) {
		tmp = x + (y * (a / (z + -1.0)));
	} else if (z <= 2.4e+74) {
		tmp = x + (a * (z / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.95d+28)) then
        tmp = x - a
    else if (z <= 0.0135d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 7.2d+45) then
        tmp = x + (y * (a / (z + (-1.0d0))))
    else if (z <= 2.4d+74) then
        tmp = x + (a * (z / t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+28) {
		tmp = x - a;
	} else if (z <= 0.0135) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 7.2e+45) {
		tmp = x + (y * (a / (z + -1.0)));
	} else if (z <= 2.4e+74) {
		tmp = x + (a * (z / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+28:
		tmp = x - a
	elif z <= 0.0135:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 7.2e+45:
		tmp = x + (y * (a / (z + -1.0)))
	elif z <= 2.4e+74:
		tmp = x + (a * (z / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+28)
		tmp = Float64(x - a);
	elseif (z <= 0.0135)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 7.2e+45)
		tmp = Float64(x + Float64(y * Float64(a / Float64(z + -1.0))));
	elseif (z <= 2.4e+74)
		tmp = Float64(x + Float64(a * Float64(z / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+28)
		tmp = x - a;
	elseif (z <= 0.0135)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 7.2e+45)
		tmp = x + (y * (a / (z + -1.0)));
	elseif (z <= 2.4e+74)
		tmp = x + (a * (z / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+28], N[(x - a), $MachinePrecision], If[LessEqual[z, 0.0135], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+45], N[(x + N[(y * N[(a / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+74], N[(x + N[(a * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9499999999999999e28 or 2.40000000000000008e74 < z

   1. Initial program 98.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 84.7%

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

   if -1.9499999999999999e28 < z < 0.0134999999999999998

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 93.4%

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

   if 0.0134999999999999998 < z < 7.2e45

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 86.8%

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

   4. Taylor expanded in y around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-*r/ 80.1%

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

   6. Simplified 80.1%

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

   if 7.2e45 < z < 2.40000000000000008e74

   1. Initial program 88.4%

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

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

   6. Taylor expanded in y around 0 75.6%

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

      1. sub-neg 75.6%

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

      2. mul-1-neg 75.6%

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

      3. remove-double-neg 75.6%

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

      4. associate-/l* 75.6%

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

   8. Simplified 75.6%

      \[\leadsto \color{blue}{x + a \cdot \frac{z}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+28}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.0135:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \frac{a}{z + -1}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+74}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -215000000000:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 0.85:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+175}:\\ \;\;\;\;x + \frac{z \cdot a}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -215000000000.0)
   (- x (/ (- z y) (/ z a)))
   (if (<= z 0.85)
     (+ x (* a (/ y (- -1.0 t))))
     (if (<= z 2.75e+175) (+ x (/ (* z a) (- (+ t 1.0) z))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -215000000000.0) {
		tmp = x - ((z - y) / (z / a));
	} else if (z <= 0.85) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 2.75e+175) {
		tmp = x + ((z * a) / ((t + 1.0) - z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-215000000000.0d0)) then
        tmp = x - ((z - y) / (z / a))
    else if (z <= 0.85d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 2.75d+175) then
        tmp = x + ((z * a) / ((t + 1.0d0) - z))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -215000000000.0) {
		tmp = x - ((z - y) / (z / a));
	} else if (z <= 0.85) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 2.75e+175) {
		tmp = x + ((z * a) / ((t + 1.0) - z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -215000000000.0:
		tmp = x - ((z - y) / (z / a))
	elif z <= 0.85:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 2.75e+175:
		tmp = x + ((z * a) / ((t + 1.0) - z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -215000000000.0)
		tmp = Float64(x - Float64(Float64(z - y) / Float64(z / a)));
	elseif (z <= 0.85)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 2.75e+175)
		tmp = Float64(x + Float64(Float64(z * a) / Float64(Float64(t + 1.0) - z)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -215000000000.0)
		tmp = x - ((z - y) / (z / a));
	elseif (z <= 0.85)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 2.75e+175)
		tmp = x + ((z * a) / ((t + 1.0) - z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -215000000000.0], N[(x - N[(N[(z - y), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.85], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e+175], N[(x + N[(N[(z * a), $MachinePrecision] / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.15e11

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 86.3%

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

      1. associate-*r/ 86.3%

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

      2. neg-mul-1 86.3%

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

   5. Simplified 86.3%

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

   if -2.15e11 < z < 0.849999999999999978

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 94.2%

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

   if 0.849999999999999978 < z < 2.75000000000000009e175

   1. Initial program 94.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 y around 0 81.6%

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

      1. sub-neg 81.6%

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

      2. mul-1-neg 81.6%

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

      3. *-commutative 81.6%

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

      4. associate--l+ 81.6%

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

      5. +-commutative 81.6%

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

      6. associate-*r/ 78.7%

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

      7. remove-double-neg 78.7%

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

      8. associate-*r/ 81.6%

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

      9. *-commutative 81.6%

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

      10. +-commutative 81.6%

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

      11. associate--l+ 81.6%

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

   7. Simplified 81.6%

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

   if 2.75000000000000009e175 < z

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 100.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -215000000000:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 0.85:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+175}:\\ \;\;\;\;x + \frac{z \cdot a}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+28}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+75}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+28)
   (- x a)
   (if (<= z 15.0)
     (+ x (* a (/ y (- -1.0 t))))
     (if (<= z 6.4e+75) (+ x (* a (/ (- z y) t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+28) {
		tmp = x - a;
	} else if (z <= 15.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 6.4e+75) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d+28)) then
        tmp = x - a
    else if (z <= 15.0d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 6.4d+75) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+28) {
		tmp = x - a;
	} else if (z <= 15.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 6.4e+75) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+28:
		tmp = x - a
	elif z <= 15.0:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 6.4e+75:
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+28)
		tmp = Float64(x - a);
	elseif (z <= 15.0)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 6.4e+75)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+28)
		tmp = x - a;
	elseif (z <= 15.0)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 6.4e+75)
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+28], N[(x - a), $MachinePrecision], If[LessEqual[z, 15.0], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+75], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6000000000000002e28 or 6.39999999999999969e75 < z

   1. Initial program 98.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 84.7%

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

   if -2.6000000000000002e28 < z < 15

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 92.9%

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

   if 15 < z < 6.39999999999999969e75

   1. Initial program 95.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 81.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+28}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+75}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7400000:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 0.46:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+73}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7400000.0)
   (- x (/ (- z y) (/ z a)))
   (if (<= z 0.46)
     (+ x (* a (/ y (- -1.0 t))))
     (if (<= z 9e+73) (+ x (* a (/ (- z y) t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7400000.0) {
		tmp = x - ((z - y) / (z / a));
	} else if (z <= 0.46) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 9e+73) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7400000.0d0)) then
        tmp = x - ((z - y) / (z / a))
    else if (z <= 0.46d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 9d+73) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7400000.0) {
		tmp = x - ((z - y) / (z / a));
	} else if (z <= 0.46) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 9e+73) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7400000.0:
		tmp = x - ((z - y) / (z / a))
	elif z <= 0.46:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 9e+73:
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7400000.0)
		tmp = Float64(x - Float64(Float64(z - y) / Float64(z / a)));
	elseif (z <= 0.46)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 9e+73)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7400000.0)
		tmp = x - ((z - y) / (z / a));
	elseif (z <= 0.46)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 9e+73)
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7400000.0], N[(x - N[(N[(z - y), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.46], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+73], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.4e6

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 86.3%

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

      1. associate-*r/ 86.3%

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

      2. neg-mul-1 86.3%

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

   5. Simplified 86.3%

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

   if -7.4e6 < z < 0.46000000000000002

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 94.2%

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

   if 0.46000000000000002 < z < 8.99999999999999969e73

   1. Initial program 95.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 81.2%

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

   if 8.99999999999999969e73 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 91.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7400000:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 0.46:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+73}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+15}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-24}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+74}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+15)
   (- x a)
   (if (<= z 3.6e-24)
     (+ x (* a (- z y)))
     (if (<= z 1.45e+74) (- x (* a (/ y t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+15) {
		tmp = x - a;
	} else if (z <= 3.6e-24) {
		tmp = x + (a * (z - y));
	} else if (z <= 1.45e+74) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.2d+15)) then
        tmp = x - a
    else if (z <= 3.6d-24) then
        tmp = x + (a * (z - y))
    else if (z <= 1.45d+74) then
        tmp = x - (a * (y / t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+15) {
		tmp = x - a;
	} else if (z <= 3.6e-24) {
		tmp = x + (a * (z - y));
	} else if (z <= 1.45e+74) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+15:
		tmp = x - a
	elif z <= 3.6e-24:
		tmp = x + (a * (z - y))
	elif z <= 1.45e+74:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+15)
		tmp = Float64(x - a);
	elseif (z <= 3.6e-24)
		tmp = Float64(x + Float64(a * Float64(z - y)));
	elseif (z <= 1.45e+74)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+15)
		tmp = x - a;
	elseif (z <= 3.6e-24)
		tmp = x + (a * (z - y));
	elseif (z <= 1.45e+74)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+15], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.6e-24], N[(x + N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+74], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e15 or 1.4500000000000001e74 < z

   1. Initial program 98.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 84.1%

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

   if -8.2e15 < z < 3.6000000000000001e-24

   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 99.2%

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

   4. Taylor expanded in t around 0 76.4%

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

   if 3.6000000000000001e-24 < z < 1.4500000000000001e74

   1. Initial program 96.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 80.7%

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

   6. Taylor expanded in y around inf 71.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+15}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-24}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+74}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-27}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+74}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e-27)
   (- x (+ a (/ a z)))
   (if (<= z 4.2e-24)
     (+ x (* a (- z y)))
     (if (<= z 2.1e+74) (- x (* a (/ y t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-27) {
		tmp = x - (a + (a / z));
	} else if (z <= 4.2e-24) {
		tmp = x + (a * (z - y));
	} else if (z <= 2.1e+74) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d-27)) then
        tmp = x - (a + (a / z))
    else if (z <= 4.2d-24) then
        tmp = x + (a * (z - y))
    else if (z <= 2.1d+74) then
        tmp = x - (a * (y / t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-27) {
		tmp = x - (a + (a / z));
	} else if (z <= 4.2e-24) {
		tmp = x + (a * (z - y));
	} else if (z <= 2.1e+74) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e-27:
		tmp = x - (a + (a / z))
	elif z <= 4.2e-24:
		tmp = x + (a * (z - y))
	elif z <= 2.1e+74:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e-27)
		tmp = Float64(x - Float64(a + Float64(a / z)));
	elseif (z <= 4.2e-24)
		tmp = Float64(x + Float64(a * Float64(z - y)));
	elseif (z <= 2.1e+74)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e-27)
		tmp = x - (a + (a / z));
	elseif (z <= 4.2e-24)
		tmp = x + (a * (z - y));
	elseif (z <= 2.1e+74)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e-27], N[(x - N[(a + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-24], N[(x + N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+74], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.34999999999999994e-27

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0 84.2%

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

   4. Taylor expanded in y around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-/l* 77.6%

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

      3. distribute-rgt-neg-in 77.6%

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

      4. distribute-frac-neg2 77.6%

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

      5. neg-sub0 77.6%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{0 - \left(1 - z\right)}} \]

      6. associate--r- 77.6%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{\left(0 - 1\right) + z}} \]

      7. metadata-eval 77.6%

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

   6. Simplified 77.6%

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

   7. Taylor expanded in z around inf 77.8%

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

   if -1.34999999999999994e-27 < z < 4.1999999999999999e-24

   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%

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

   4. Taylor expanded in t around 0 78.0%

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

   if 4.1999999999999999e-24 < z < 2.0999999999999999e74

   1. Initial program 96.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 80.7%

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

   6. Taylor expanded in y around inf 71.4%

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

   if 2.0999999999999999e74 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 91.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-27}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+74}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+28)
   (- x (/ (- z y) (/ z a)))
   (if (<= z 5e+76) (+ x (/ (- y z) (/ (- -1.0 t) a))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+28) {
		tmp = x - ((z - y) / (z / a));
	} else if (z <= 5e+76) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+28)) then
        tmp = x - ((z - y) / (z / a))
    else if (z <= 5d+76) then
        tmp = x + ((y - z) / (((-1.0d0) - t) / a))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+28) {
		tmp = x - ((z - y) / (z / a));
	} else if (z <= 5e+76) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+28:
		tmp = x - ((z - y) / (z / a))
	elif z <= 5e+76:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+28)
		tmp = Float64(x - Float64(Float64(z - y) / Float64(z / a)));
	elseif (z <= 5e+76)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(-1.0 - t) / a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+28)
		tmp = x - ((z - y) / (z / a));
	elseif (z <= 5e+76)
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+28], N[(x - N[(N[(z - y), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+76], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4500000000000001e28

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. associate-*r/ 87.2%

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

      2. neg-mul-1 87.2%

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

   5. Simplified 87.2%

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

   if -1.4500000000000001e28 < z < 4.99999999999999991e76

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 94.3%

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

   if 4.99999999999999991e76 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 91.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -950000:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;x - \frac{y - z}{\frac{1 - z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -950000.0)
   (+ x (/ (- y z) (/ (- -1.0 t) a)))
   (if (<= t 2.6e+23)
     (- x (/ (- y z) (/ (- 1.0 z) a)))
     (+ x (* a (/ (- z y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -950000.0) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else if (t <= 2.6e+23) {
		tmp = x - ((y - z) / ((1.0 - z) / a));
	} else {
		tmp = x + (a * ((z - y) / 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 (t <= (-950000.0d0)) then
        tmp = x + ((y - z) / (((-1.0d0) - t) / a))
    else if (t <= 2.6d+23) then
        tmp = x - ((y - z) / ((1.0d0 - z) / a))
    else
        tmp = x + (a * ((z - y) / 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 (t <= -950000.0) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else if (t <= 2.6e+23) {
		tmp = x - ((y - z) / ((1.0 - z) / a));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -950000.0:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	elif t <= 2.6e+23:
		tmp = x - ((y - z) / ((1.0 - z) / a))
	else:
		tmp = x + (a * ((z - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -950000.0)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(-1.0 - t) / a)));
	elseif (t <= 2.6e+23)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(1.0 - z) / a)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -950000.0)
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	elseif (t <= 2.6e+23)
		tmp = x - ((y - z) / ((1.0 - z) / a));
	else
		tmp = x + (a * ((z - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -950000.0], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+23], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(1.0 - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5e5

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 90.5%

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

   if -9.5e5 < t < 2.59999999999999992e23

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0 97.8%

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

   if 2.59999999999999992e23 < t

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   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 t around inf 91.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -950000:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;x - \frac{y - z}{\frac{1 - z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+16} \lor \neg \left(z \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+16) (not (<= z 5e-24))) (- x a) (+ x (* a (- z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+16) || !(z <= 5e-24)) {
		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 <= (-2d+16)) .or. (.not. (z <= 5d-24))) 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 <= -2e+16) || !(z <= 5e-24)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+16) or not (z <= 5e-24):
		tmp = x - a
	else:
		tmp = x + (a * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+16) || !(z <= 5e-24))
		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 <= -2e+16) || ~((z <= 5e-24)))
		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, -2e+16], N[Not[LessEqual[z, 5e-24]], $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 < -2e16 or 4.9999999999999998e-24 < z

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 78.1%

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

   if -2e16 < z < 4.9999999999999998e-24

   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 99.2%

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

   4. Taylor expanded in t around 0 76.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+16} \lor \neg \left(z \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+28} \lor \neg \left(z \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e+28) (not (<= z 5e-24))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e+28) || !(z <= 5e-24)) {
		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 <= (-1d+28)) .or. (.not. (z <= 5d-24))) 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 <= -1e+28) || !(z <= 5e-24)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e+28) or not (z <= 5e-24):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e+28) || !(z <= 5e-24))
		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 <= -1e+28) || ~((z <= 5e-24)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e+28], N[Not[LessEqual[z, 5e-24]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999958e27 or 4.9999999999999998e-24 < z

   1. Initial program 97.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 78.5%

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

   if -9.99999999999999958e27 < z < 4.9999999999999998e-24

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 76.7%

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

   4. Taylor expanded in z around 0 73.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+28} \lor \neg \left(z \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+28} \lor \neg \left(z \leq 5 \cdot 10^{-22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e+28) (not (<= z 5e-22))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+28) || !(z <= 5e-22)) {
		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 <= (-1.7d+28)) .or. (.not. (z <= 5d-22))) 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 <= -1.7e+28) || !(z <= 5e-22)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e+28) or not (z <= 5e-22):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e+28) || !(z <= 5e-22))
		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 <= -1.7e+28) || ~((z <= 5e-22)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e+28], N[Not[LessEqual[z, 5e-22]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e28 or 4.99999999999999954e-22 < z

   1. Initial program 97.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 79.1%

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

   if -1.7e28 < z < 4.99999999999999954e-22

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 x around inf 57.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+28} \lor \neg \left(z \leq 5 \cdot 10^{-22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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 98.8%

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

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

Alternative 15: 54.4% 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 98.8%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 x around inf 56.3%

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

6. Final simplification 56.3%

   \[\leadsto x \]
7. 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 2024066 
(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))))