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

Percentage Accurate: 97.1% → 99.6%

Time: 10.3s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% 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 98.1%

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

   1. sub-neg 98.1%

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

   2. +-commutative 98.1%

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

   3. associate-/r/ 99.2%

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

   4. distribute-lft-neg-in 99.2%

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

   5. fma-define 99.2%

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

   6. distribute-neg-frac2 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. sub-neg 99.2%

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

   9. distribute-neg-in 99.2%

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

   10. remove-double-neg 99.2%

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

   11. +-commutative 99.2%

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

   12. sub-neg 99.2%

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

   13. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z}{1 - z}\\ t_2 := x + \frac{a}{t} \cdot \left(z - y\right)\\ t_3 := x - y \cdot a\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-275}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5000000000:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ z (- 1.0 z)))))
        (t_2 (+ x (* (/ a t) (- z y))))
        (t_3 (- x (* y a))))
   (if (<= t -6.5e+34)
     t_2
     (if (<= t -3.7e-154)
       t_1
       (if (<= t -2.1e-275)
         t_3
         (if (<= t 2.8e-232) t_1 (if (<= t 5000000000.0) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / (1.0 - z)));
	double t_2 = x + ((a / t) * (z - y));
	double t_3 = x - (y * a);
	double tmp;
	if (t <= -6.5e+34) {
		tmp = t_2;
	} else if (t <= -3.7e-154) {
		tmp = t_1;
	} else if (t <= -2.1e-275) {
		tmp = t_3;
	} else if (t <= 2.8e-232) {
		tmp = t_1;
	} else if (t <= 5000000000.0) {
		tmp = t_3;
	} 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 + (a * (z / (1.0d0 - z)))
    t_2 = x + ((a / t) * (z - y))
    t_3 = x - (y * a)
    if (t <= (-6.5d+34)) then
        tmp = t_2
    else if (t <= (-3.7d-154)) then
        tmp = t_1
    else if (t <= (-2.1d-275)) then
        tmp = t_3
    else if (t <= 2.8d-232) then
        tmp = t_1
    else if (t <= 5000000000.0d0) then
        tmp = t_3
    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 / (1.0 - z)));
	double t_2 = x + ((a / t) * (z - y));
	double t_3 = x - (y * a);
	double tmp;
	if (t <= -6.5e+34) {
		tmp = t_2;
	} else if (t <= -3.7e-154) {
		tmp = t_1;
	} else if (t <= -2.1e-275) {
		tmp = t_3;
	} else if (t <= 2.8e-232) {
		tmp = t_1;
	} else if (t <= 5000000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z / (1.0 - z)))
	t_2 = x + ((a / t) * (z - y))
	t_3 = x - (y * a)
	tmp = 0
	if t <= -6.5e+34:
		tmp = t_2
	elif t <= -3.7e-154:
		tmp = t_1
	elif t <= -2.1e-275:
		tmp = t_3
	elif t <= 2.8e-232:
		tmp = t_1
	elif t <= 5000000000.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z / Float64(1.0 - z))))
	t_2 = Float64(x + Float64(Float64(a / t) * Float64(z - y)))
	t_3 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (t <= -6.5e+34)
		tmp = t_2;
	elseif (t <= -3.7e-154)
		tmp = t_1;
	elseif (t <= -2.1e-275)
		tmp = t_3;
	elseif (t <= 2.8e-232)
		tmp = t_1;
	elseif (t <= 5000000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * (z / (1.0 - z)));
	t_2 = x + ((a / t) * (z - y));
	t_3 = x - (y * a);
	tmp = 0.0;
	if (t <= -6.5e+34)
		tmp = t_2;
	elseif (t <= -3.7e-154)
		tmp = t_1;
	elseif (t <= -2.1e-275)
		tmp = t_3;
	elseif (t <= 2.8e-232)
		tmp = t_1;
	elseif (t <= 5000000000.0)
		tmp = t_3;
	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 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+34], t$95$2, If[LessEqual[t, -3.7e-154], t$95$1, If[LessEqual[t, -2.1e-275], t$95$3, If[LessEqual[t, 2.8e-232], t$95$1, If[LessEqual[t, 5000000000.0], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.50000000000000017e34 or 5e9 < t

   1. Initial program 96.3%

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

      1. clear-num 96.2%

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

      2. associate-/r/ 96.3%

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

      3. clear-num 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in t around inf 87.2%

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

   if -6.50000000000000017e34 < t < -3.69999999999999987e-154 or -2.09999999999999988e-275 < t < 2.79999999999999993e-232

   1. Initial program 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 96.5%

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

   6. Taylor expanded in y around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. associate-/l* 77.5%

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

   8. Simplified 77.5%

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

   if -3.69999999999999987e-154 < t < -2.09999999999999988e-275 or 2.79999999999999993e-232 < t < 5e9

   1. Initial program 99.2%

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

      1. clear-num 99.1%

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

      2. associate-/r/ 99.2%

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

      3. clear-num 99.3%

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in t around 0 99.3%

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

   6. Taylor expanded in z around 0 80.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-154}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-275}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-232}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{elif}\;t \leq 5000000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{a}{1 - z}\\ t_2 := x + \frac{a}{t} \cdot \left(z - y\right)\\ t_3 := x - y \cdot a\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-275}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4500000000:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ a (- 1.0 z)))))
        (t_2 (+ x (* (/ a t) (- z y))))
        (t_3 (- x (* y a))))
   (if (<= t -6.5e+34)
     t_2
     (if (<= t -9e-152)
       t_1
       (if (<= t -3.8e-275)
         t_3
         (if (<= t 3.05e-232) t_1 (if (<= t 4500000000.0) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (a / (1.0 - z)));
	double t_2 = x + ((a / t) * (z - y));
	double t_3 = x - (y * a);
	double tmp;
	if (t <= -6.5e+34) {
		tmp = t_2;
	} else if (t <= -9e-152) {
		tmp = t_1;
	} else if (t <= -3.8e-275) {
		tmp = t_3;
	} else if (t <= 3.05e-232) {
		tmp = t_1;
	} else if (t <= 4500000000.0) {
		tmp = t_3;
	} 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 + (z * (a / (1.0d0 - z)))
    t_2 = x + ((a / t) * (z - y))
    t_3 = x - (y * a)
    if (t <= (-6.5d+34)) then
        tmp = t_2
    else if (t <= (-9d-152)) then
        tmp = t_1
    else if (t <= (-3.8d-275)) then
        tmp = t_3
    else if (t <= 3.05d-232) then
        tmp = t_1
    else if (t <= 4500000000.0d0) then
        tmp = t_3
    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 + (z * (a / (1.0 - z)));
	double t_2 = x + ((a / t) * (z - y));
	double t_3 = x - (y * a);
	double tmp;
	if (t <= -6.5e+34) {
		tmp = t_2;
	} else if (t <= -9e-152) {
		tmp = t_1;
	} else if (t <= -3.8e-275) {
		tmp = t_3;
	} else if (t <= 3.05e-232) {
		tmp = t_1;
	} else if (t <= 4500000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (a / (1.0 - z)))
	t_2 = x + ((a / t) * (z - y))
	t_3 = x - (y * a)
	tmp = 0
	if t <= -6.5e+34:
		tmp = t_2
	elif t <= -9e-152:
		tmp = t_1
	elif t <= -3.8e-275:
		tmp = t_3
	elif t <= 3.05e-232:
		tmp = t_1
	elif t <= 4500000000.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(a / Float64(1.0 - z))))
	t_2 = Float64(x + Float64(Float64(a / t) * Float64(z - y)))
	t_3 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (t <= -6.5e+34)
		tmp = t_2;
	elseif (t <= -9e-152)
		tmp = t_1;
	elseif (t <= -3.8e-275)
		tmp = t_3;
	elseif (t <= 3.05e-232)
		tmp = t_1;
	elseif (t <= 4500000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (a / (1.0 - z)));
	t_2 = x + ((a / t) * (z - y));
	t_3 = x - (y * a);
	tmp = 0.0;
	if (t <= -6.5e+34)
		tmp = t_2;
	elseif (t <= -9e-152)
		tmp = t_1;
	elseif (t <= -3.8e-275)
		tmp = t_3;
	elseif (t <= 3.05e-232)
		tmp = t_1;
	elseif (t <= 4500000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+34], t$95$2, If[LessEqual[t, -9e-152], t$95$1, If[LessEqual[t, -3.8e-275], t$95$3, If[LessEqual[t, 3.05e-232], t$95$1, If[LessEqual[t, 4500000000.0], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.50000000000000017e34 or 4.5e9 < t

   1. Initial program 96.3%

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

      1. clear-num 96.2%

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

      2. associate-/r/ 96.3%

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

      3. clear-num 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in t around inf 87.2%

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

   if -6.50000000000000017e34 < t < -9.0000000000000008e-152 or -3.79999999999999972e-275 < t < 3.0500000000000001e-232

   1. Initial program 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 96.5%

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

   6. Taylor expanded in y around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. *-commutative 68.3%

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

      3. associate-*r/ 77.4%

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

      4. distribute-rgt-neg-in 77.4%

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

      5. distribute-frac-neg2 77.4%

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

      6. neg-sub0 77.4%

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

      7. associate--r- 77.4%

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

      8. metadata-eval 77.4%

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

   8. Simplified 77.4%

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

   if -9.0000000000000008e-152 < t < -3.79999999999999972e-275 or 3.0500000000000001e-232 < t < 4.5e9

   1. Initial program 99.2%

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

      1. clear-num 99.1%

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

      2. associate-/r/ 99.2%

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

      3. clear-num 99.3%

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in t around 0 99.3%

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

   6. Taylor expanded in z around 0 80.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-152}:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-275}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-232}:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;t \leq 4500000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -19:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-164}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1420000000000:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ a z)))))
   (if (<= z -19.0)
     t_1
     (if (<= z 6e-164)
       (- x (* y a))
       (if (<= z 1420000000000.0) (+ x (* (/ a t) (- z y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -19.0) {
		tmp = t_1;
	} else if (z <= 6e-164) {
		tmp = x - (y * a);
	} else if (z <= 1420000000000.0) {
		tmp = x + ((a / t) * (z - y));
	} 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 + ((y - z) * (a / z))
    if (z <= (-19.0d0)) then
        tmp = t_1
    else if (z <= 6d-164) then
        tmp = x - (y * a)
    else if (z <= 1420000000000.0d0) then
        tmp = x + ((a / t) * (z - y))
    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 + ((y - z) * (a / z));
	double tmp;
	if (z <= -19.0) {
		tmp = t_1;
	} else if (z <= 6e-164) {
		tmp = x - (y * a);
	} else if (z <= 1420000000000.0) {
		tmp = x + ((a / t) * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (a / z))
	tmp = 0
	if z <= -19.0:
		tmp = t_1
	elif z <= 6e-164:
		tmp = x - (y * a)
	elif z <= 1420000000000.0:
		tmp = x + ((a / t) * (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(a / z)))
	tmp = 0.0
	if (z <= -19.0)
		tmp = t_1;
	elseif (z <= 6e-164)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 1420000000000.0)
		tmp = Float64(x + Float64(Float64(a / t) * Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (a / z));
	tmp = 0.0;
	if (z <= -19.0)
		tmp = t_1;
	elseif (z <= 6e-164)
		tmp = x - (y * a);
	elseif (z <= 1420000000000.0)
		tmp = x + ((a / t) * (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -19.0], t$95$1, If[LessEqual[z, 6e-164], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1420000000000.0], N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -19 or 1.42e12 < z

   1. Initial program 97.1%

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

      1. clear-num 96.9%

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

      2. associate-/r/ 97.0%

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

      3. clear-num 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in t around 0 88.6%

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

   6. Taylor expanded in z around inf 88.2%

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

      1. associate-*r/ 88.2%

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

      2. neg-mul-1 88.2%

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

   8. Simplified 88.2%

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

   if -19 < z < 6.0000000000000002e-164

   1. Initial program 98.8%

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

      1. clear-num 98.7%

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

      2. associate-/r/ 98.9%

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

      3. clear-num 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around 0 75.7%

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

   6. Taylor expanded in z around 0 71.9%

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

   if 6.0000000000000002e-164 < z < 1.42e12

   1. Initial program 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 78.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-164}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1420000000000:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-8}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-96}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+38}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e-8)
   (- x a)
   (if (<= z 8e-96)
     (- x (* y a))
     (if (<= z 3.5e+38) (+ x (* a (/ z t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e-8) {
		tmp = x - a;
	} else if (z <= 8e-96) {
		tmp = x - (y * a);
	} else if (z <= 3.5e+38) {
		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 <= (-8d-8)) then
        tmp = x - a
    else if (z <= 8d-96) then
        tmp = x - (y * a)
    else if (z <= 3.5d+38) 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 <= -8e-8) {
		tmp = x - a;
	} else if (z <= 8e-96) {
		tmp = x - (y * a);
	} else if (z <= 3.5e+38) {
		tmp = x + (a * (z / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e-8:
		tmp = x - a
	elif z <= 8e-96:
		tmp = x - (y * a)
	elif z <= 3.5e+38:
		tmp = x + (a * (z / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e-8)
		tmp = Float64(x - a);
	elseif (z <= 8e-96)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 3.5e+38)
		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 <= -8e-8)
		tmp = x - a;
	elseif (z <= 8e-96)
		tmp = x - (y * a);
	elseif (z <= 3.5e+38)
		tmp = x + (a * (z / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e-8], N[(x - a), $MachinePrecision], If[LessEqual[z, 8e-96], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+38], N[(x + N[(a * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000002e-8 or 3.50000000000000002e38 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 79.1%

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

   if -8.0000000000000002e-8 < z < 7.9999999999999993e-96

   1. Initial program 98.9%

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

      1. clear-num 98.8%

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

      2. associate-/r/ 99.0%

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

      3. clear-num 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around 0 75.9%

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

   6. Taylor expanded in z around 0 70.9%

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

   if 7.9999999999999993e-96 < z < 3.50000000000000002e38

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 79.1%

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

   6. Taylor expanded in y around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. associate-/l* 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

   8. Simplified 70.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-8}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-96}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+38}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+34} \lor \neg \left(t \leq 8000000000\right):\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.8e+34) (not (<= t 8000000000.0)))
   (+ x (* (/ a t) (- z y)))
   (+ x (* (- y z) (/ a (+ z -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.8e+34) || !(t <= 8000000000.0)) {
		tmp = x + ((a / t) * (z - y));
	} else {
		tmp = x + ((y - z) * (a / (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) :: tmp
    if ((t <= (-6.8d+34)) .or. (.not. (t <= 8000000000.0d0))) then
        tmp = x + ((a / t) * (z - y))
    else
        tmp = x + ((y - z) * (a / (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 tmp;
	if ((t <= -6.8e+34) || !(t <= 8000000000.0)) {
		tmp = x + ((a / t) * (z - y));
	} else {
		tmp = x + ((y - z) * (a / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.8e+34) or not (t <= 8000000000.0):
		tmp = x + ((a / t) * (z - y))
	else:
		tmp = x + ((y - z) * (a / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.8e+34) || !(t <= 8000000000.0))
		tmp = Float64(x + Float64(Float64(a / t) * Float64(z - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(a / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.8e+34) || ~((t <= 8000000000.0)))
		tmp = x + ((a / t) * (z - y));
	else
		tmp = x + ((y - z) * (a / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.8e+34], N[Not[LessEqual[t, 8000000000.0]], $MachinePrecision]], N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.7999999999999999e34 or 8e9 < t

   1. Initial program 96.3%

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

      1. clear-num 96.2%

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

      2. associate-/r/ 96.3%

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

      3. clear-num 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in t around inf 87.2%

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

   if -6.7999999999999999e34 < t < 8e9

   1. Initial program 99.5%

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

      1. clear-num 99.4%

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

      2. associate-/r/ 99.5%

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

      3. clear-num 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in t around 0 97.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+34} \lor \neg \left(t \leq 8000000000\right):\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-62}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e-6)
   (- x a)
   (if (<= z 1.3e-62) (- x (* y a)) (+ x (* z (/ a (- 1.0 z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e-6) {
		tmp = x - a;
	} else if (z <= 1.3e-62) {
		tmp = x - (y * a);
	} else {
		tmp = x + (z * (a / (1.0 - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.2d-6)) then
        tmp = x - a
    else if (z <= 1.3d-62) then
        tmp = x - (y * a)
    else
        tmp = x + (z * (a / (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e-6) {
		tmp = x - a;
	} else if (z <= 1.3e-62) {
		tmp = x - (y * a);
	} else {
		tmp = x + (z * (a / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e-6:
		tmp = x - a
	elif z <= 1.3e-62:
		tmp = x - (y * a)
	else:
		tmp = x + (z * (a / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e-6)
		tmp = Float64(x - a);
	elseif (z <= 1.3e-62)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x + Float64(z * Float64(a / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.2e-6)
		tmp = x - a;
	elseif (z <= 1.3e-62)
		tmp = x - (y * a);
	else
		tmp = x + (z * (a / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e-6], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.3e-62], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999999e-6

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 80.3%

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

   if -6.1999999999999999e-6 < z < 1.3e-62

   1. Initial program 98.9%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 99.0%

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

      3. clear-num 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around 0 73.4%

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

   6. Taylor expanded in z around 0 69.5%

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

   if 1.3e-62 < z

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 81.1%

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

   6. Taylor expanded in y around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r/ 71.1%

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

      4. distribute-rgt-neg-in 71.1%

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

      5. distribute-frac-neg2 71.1%

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

      6. neg-sub0 71.1%

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

      7. associate--r- 71.1%

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

      8. metadata-eval 71.1%

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

   8. Simplified 71.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-62}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-6} \lor \neg \left(z \leq 11.5\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e-6) (not (<= z 11.5))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e-6) || !(z <= 11.5)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.8d-6)) .or. (.not. (z <= 11.5d0))) 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 <= -5.8e-6) || !(z <= 11.5)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e-6) or not (z <= 11.5):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e-6) || !(z <= 11.5))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.8e-6) || ~((z <= 11.5)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e-6], N[Not[LessEqual[z, 11.5]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000004e-6 or 11.5 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 76.4%

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

   if -5.8000000000000004e-6 < z < 11.5

   1. Initial program 99.0%

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

      1. clear-num 99.0%

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

      2. associate-/r/ 99.1%

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

      3. clear-num 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around 0 73.3%

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

   6. Taylor expanded in z around 0 68.3%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-6} \lor \neg \left(z \leq 11.5\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-32} \lor \neg \left(z \leq 370000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e-32) (not (<= z 370000000000.0))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e-32) || !(z <= 370000000000.0)) {
		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 <= (-1.35d-32)) .or. (.not. (z <= 370000000000.0d0))) 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 <= -1.35e-32) || !(z <= 370000000000.0)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e-32) or not (z <= 370000000000.0):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e-32) || !(z <= 370000000000.0))
		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 <= -1.35e-32) || ~((z <= 370000000000.0)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e-32], N[Not[LessEqual[z, 370000000000.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e-32 or 3.7e11 < z

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 75.6%

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

   if -1.3499999999999999e-32 < z < 3.7e11

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. +-commutative 99.0%

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

      3. associate-/r/ 98.4%

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

      4. distribute-lft-neg-in 98.4%

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

      5. fma-define 98.5%

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

      6. distribute-neg-frac2 98.5%

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

      7. distribute-neg-in 98.5%

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

      8. sub-neg 98.5%

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

      9. distribute-neg-in 98.5%

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

      10. remove-double-neg 98.5%

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

      11. +-commutative 98.5%

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

      12. sub-neg 98.5%

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

      13. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf 50.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-32} \lor \neg \left(z \leq 370000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.6% 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 98.1%

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

   1. associate-/r/ 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 11: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

   1. clear-num 98.1%

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

   2. associate-/r/ 98.2%

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

   3. clear-num 98.9%

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

4. Applied egg-rr 98.9%

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

5. Final simplification 98.9%

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

Alternative 12: 55.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-85}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.8e-238) x (if (<= x 2.9e-85) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.8e-238) {
		tmp = x;
	} else if (x <= 2.9e-85) {
		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 <= (-3.8d-238)) then
        tmp = x
    else if (x <= 2.9d-85) 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 <= -3.8e-238) {
		tmp = x;
	} else if (x <= 2.9e-85) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.8e-238:
		tmp = x
	elif x <= 2.9e-85:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.8e-238)
		tmp = x;
	elseif (x <= 2.9e-85)
		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 <= -3.8e-238)
		tmp = x;
	elseif (x <= 2.9e-85)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.8e-238], x, If[LessEqual[x, 2.9e-85], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999997e-238 or 2.9000000000000002e-85 < x

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. +-commutative 99.4%

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

      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 t around inf 65.4%

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

   if -3.7999999999999997e-238 < x < 2.9000000000000002e-85

   1. Initial program 94.3%

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

      1. associate-/r/ 96.8%

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

   3. Simplified 96.8%

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

      1. associate-/r/ 94.3%

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

      2. div-inv 94.2%

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

      3. associate-/r* 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in z around inf 30.9%

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

   8. Taylor expanded in x around 0 26.5%

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

      1. neg-mul-1 26.5%

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

   10. Simplified 26.5%

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

Alternative 13: 55.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

   1. sub-neg 98.1%

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

   2. +-commutative 98.1%

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

   3. associate-/r/ 99.2%

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

   4. distribute-lft-neg-in 99.2%

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

   5. fma-define 99.2%

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

   6. distribute-neg-frac2 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. sub-neg 99.2%

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

   9. distribute-neg-in 99.2%

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

   10. remove-double-neg 99.2%

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

   11. +-commutative 99.2%

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

   12. sub-neg 99.2%

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

   13. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in t around inf 52.5%

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

Developer target: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(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))))