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

Percentage Accurate: 96.8% → 99.6%

Time: 12.8s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

   1. sub-neg 98.7%

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

   2. +-commutative 98.7%

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

   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-def 99.9%

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

   6. distribute-neg-frac 99.9%

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

   7. sub-neg 99.9%

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

   8. distribute-neg-in 99.9%

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

   9. remove-double-neg 99.9%

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

   10. +-commutative 99.9%

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

   11. sub-neg 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 70.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a}{t}\\ \mathbf{if}\;t \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ a t)))))
   (if (<= t -1.0)
     t_1
     (if (<= t 7.1e-90)
       (- x (* y a))
       (if (<= t 6e+79) (+ x (/ a (/ (- 1.0 z) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (a / t));
	double tmp;
	if (t <= -1.0) {
		tmp = t_1;
	} else if (t <= 7.1e-90) {
		tmp = x - (y * a);
	} else if (t <= 6e+79) {
		tmp = x + (a / ((1.0 - z) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (a / t))
    if (t <= (-1.0d0)) then
        tmp = t_1
    else if (t <= 7.1d-90) then
        tmp = x - (y * a)
    else if (t <= 6d+79) then
        tmp = x + (a / ((1.0d0 - z) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (a / t));
	double tmp;
	if (t <= -1.0) {
		tmp = t_1;
	} else if (t <= 7.1e-90) {
		tmp = x - (y * a);
	} else if (t <= 6e+79) {
		tmp = x + (a / ((1.0 - z) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (a / t))
	tmp = 0
	if t <= -1.0:
		tmp = t_1
	elif t <= 7.1e-90:
		tmp = x - (y * a)
	elif t <= 6e+79:
		tmp = x + (a / ((1.0 - z) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(a / t)))
	tmp = 0.0
	if (t <= -1.0)
		tmp = t_1;
	elseif (t <= 7.1e-90)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 6e+79)
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (a / t));
	tmp = 0.0;
	if (t <= -1.0)
		tmp = t_1;
	elseif (t <= 7.1e-90)
		tmp = x - (y * a);
	elseif (t <= 6e+79)
		tmp = x + (a / ((1.0 - z) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.0], t$95$1, If[LessEqual[t, 7.1e-90], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+79], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1 or 5.99999999999999948e79 < t

   1. Initial program 98.9%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. associate--l+ 75.7%

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

      2. +-commutative 75.7%

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

      3. associate-*r/ 82.4%

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

      4. +-commutative 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in t around inf 80.8%

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

   if -1 < t < 7.1000000000000001e-90

   1. Initial program 99.0%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 71.4%

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

   5. Taylor expanded in t around 0 71.4%

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

      1. *-commutative 71.4%

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

   7. Simplified 71.4%

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

   if 7.1000000000000001e-90 < t < 5.99999999999999948e79

   1. Initial program 96.9%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 84.6%

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

   5. Taylor expanded in y around 0 63.2%

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

      1. sub-neg 63.2%

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

      2. mul-1-neg 63.2%

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

      3. remove-double-neg 63.2%

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

      4. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -1.1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 46000000000000:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ (- y z) t)))))
   (if (<= t -1.1)
     t_1
     (if (<= t 9.6e-90)
       (- x (* y a))
       (if (<= t 46000000000000.0) (+ x (/ a (/ (- 1.0 z) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * ((y - z) / t));
	double tmp;
	if (t <= -1.1) {
		tmp = t_1;
	} else if (t <= 9.6e-90) {
		tmp = x - (y * a);
	} else if (t <= 46000000000000.0) {
		tmp = x + (a / ((1.0 - z) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a * ((y - z) / t))
    if (t <= (-1.1d0)) then
        tmp = t_1
    else if (t <= 9.6d-90) then
        tmp = x - (y * a)
    else if (t <= 46000000000000.0d0) then
        tmp = x + (a / ((1.0d0 - z) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * ((y - z) / t));
	double tmp;
	if (t <= -1.1) {
		tmp = t_1;
	} else if (t <= 9.6e-90) {
		tmp = x - (y * a);
	} else if (t <= 46000000000000.0) {
		tmp = x + (a / ((1.0 - z) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * ((y - z) / t))
	tmp = 0
	if t <= -1.1:
		tmp = t_1
	elif t <= 9.6e-90:
		tmp = x - (y * a)
	elif t <= 46000000000000.0:
		tmp = x + (a / ((1.0 - z) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(Float64(y - z) / t)))
	tmp = 0.0
	if (t <= -1.1)
		tmp = t_1;
	elseif (t <= 9.6e-90)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 46000000000000.0)
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * ((y - z) / t));
	tmp = 0.0;
	if (t <= -1.1)
		tmp = t_1;
	elseif (t <= 9.6e-90)
		tmp = x - (y * a);
	elseif (t <= 46000000000000.0)
		tmp = x + (a / ((1.0 - z) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1], t$95$1, If[LessEqual[t, 9.6e-90], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 46000000000000.0], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1000000000000001 or 4.6e13 < t

   1. Initial program 98.2%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 87.3%

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

   if -1.1000000000000001 < t < 9.6000000000000006e-90

   1. Initial program 99.0%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 71.4%

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

   5. Taylor expanded in t around 0 71.4%

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

      1. *-commutative 71.4%

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

   7. Simplified 71.4%

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

   if 9.6000000000000006e-90 < t < 4.6e13

   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%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 93.6%

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

   5. Taylor expanded in y around 0 75.1%

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

      1. sub-neg 75.1%

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

      2. mul-1-neg 75.1%

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

      3. remove-double-neg 75.1%

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

      4. associate-/l* 75.1%

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

   7. Simplified 75.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 46000000000000:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 4: 90.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \lor \neg \left(t \leq 8.2 \cdot 10^{+79}\right):\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2) (not (<= t 8.2e+79)))
   (- x (* a (/ (- y z) t)))
   (+ x (* a (/ (- z y) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2) || !(t <= 8.2e+79)) {
		tmp = x - (a * ((y - z) / t));
	} else {
		tmp = x + (a * ((z - y) / (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 ((t <= (-3.2d0)) .or. (.not. (t <= 8.2d+79))) then
        tmp = x - (a * ((y - z) / t))
    else
        tmp = x + (a * ((z - y) / (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 ((t <= -3.2) || !(t <= 8.2e+79)) {
		tmp = x - (a * ((y - z) / t));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2) or not (t <= 8.2e+79):
		tmp = x - (a * ((y - z) / t))
	else:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2) || !(t <= 8.2e+79))
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / t)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.2) || ~((t <= 8.2e+79)))
		tmp = x - (a * ((y - z) / t));
	else
		tmp = x + (a * ((z - y) / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.2], N[Not[LessEqual[t, 8.2e+79]], $MachinePrecision]], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000002 or 8.2e79 < t

   1. Initial program 98.9%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 90.4%

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

   if -3.2000000000000002 < t < 8.2e79

   1. Initial program 98.5%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 96.5%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \lor \neg \left(t \leq 8.2 \cdot 10^{+79}\right):\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \]

Alternative 5: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+46} \lor \neg \left(z \leq 4 \cdot 10^{-8}\right):\\ \;\;\;\;x - \frac{y - z}{-\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+46) (not (<= z 4e-8)))
   (- x (/ (- y z) (- (/ z a))))
   (- x (/ (* y a) (+ t 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+46) || !(z <= 4e-8)) {
		tmp = x - ((y - z) / -(z / a));
	} else {
		tmp = x - ((y * a) / (t + 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 ((z <= (-8d+46)) .or. (.not. (z <= 4d-8))) then
        tmp = x - ((y - z) / -(z / a))
    else
        tmp = x - ((y * a) / (t + 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 ((z <= -8e+46) || !(z <= 4e-8)) {
		tmp = x - ((y - z) / -(z / a));
	} else {
		tmp = x - ((y * a) / (t + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+46) or not (z <= 4e-8):
		tmp = x - ((y - z) / -(z / a))
	else:
		tmp = x - ((y * a) / (t + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+46) || !(z <= 4e-8))
		tmp = Float64(x - Float64(Float64(y - z) / Float64(-Float64(z / a))));
	else
		tmp = Float64(x - Float64(Float64(y * a) / Float64(t + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+46) || ~((z <= 4e-8)))
		tmp = x - ((y - z) / -(z / a));
	else
		tmp = x - ((y * a) / (t + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+46], N[Not[LessEqual[z, 4e-8]], $MachinePrecision]], N[(x - N[(N[(y - z), $MachinePrecision] / (-N[(z / a), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * a), $MachinePrecision] / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999999e46 or 4.0000000000000001e-8 < z

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. mul-1-neg 88.8%

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

      2. distribute-neg-frac 88.8%

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

   4. Simplified 88.8%

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

   if -7.9999999999999999e46 < z < 4.0000000000000001e-8

   1. Initial program 99.2%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 85.4%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+46} \lor \neg \left(z \leq 4 \cdot 10^{-8}\right):\\ \;\;\;\;x - \frac{y - z}{-\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \]

Alternative 6: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a}{t}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+79}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ a t)))))
   (if (<= t -6.8e-10)
     t_1
     (if (<= t 2.6e-89) (- x (* y a)) (if (<= t 7e+79) (- x a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (a / t));
	double tmp;
	if (t <= -6.8e-10) {
		tmp = t_1;
	} else if (t <= 2.6e-89) {
		tmp = x - (y * a);
	} else if (t <= 7e+79) {
		tmp = x - a;
	} 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 * (a / t))
    if (t <= (-6.8d-10)) then
        tmp = t_1
    else if (t <= 2.6d-89) then
        tmp = x - (y * a)
    else if (t <= 7d+79) then
        tmp = x - a
    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 * (a / t));
	double tmp;
	if (t <= -6.8e-10) {
		tmp = t_1;
	} else if (t <= 2.6e-89) {
		tmp = x - (y * a);
	} else if (t <= 7e+79) {
		tmp = x - a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (a / t))
	tmp = 0
	if t <= -6.8e-10:
		tmp = t_1
	elif t <= 2.6e-89:
		tmp = x - (y * a)
	elif t <= 7e+79:
		tmp = x - a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(a / t)))
	tmp = 0.0
	if (t <= -6.8e-10)
		tmp = t_1;
	elseif (t <= 2.6e-89)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 7e+79)
		tmp = Float64(x - a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (a / t));
	tmp = 0.0;
	if (t <= -6.8e-10)
		tmp = t_1;
	elseif (t <= 2.6e-89)
		tmp = x - (y * a);
	elseif (t <= 7e+79)
		tmp = x - a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-10], t$95$1, If[LessEqual[t, 2.6e-89], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+79], N[(x - a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.8000000000000003e-10 or 6.99999999999999961e79 < t

   1. Initial program 98.9%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. associate--l+ 75.7%

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

      2. +-commutative 75.7%

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

      3. associate-*r/ 82.4%

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

      4. +-commutative 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in t around inf 80.8%

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

   if -6.8000000000000003e-10 < t < 2.5999999999999999e-89

   1. Initial program 99.0%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 71.4%

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

   5. Taylor expanded in t around 0 71.4%

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

      1. *-commutative 71.4%

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

   7. Simplified 71.4%

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

   if 2.5999999999999999e-89 < t < 6.99999999999999961e79

   1. Initial program 96.9%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 63.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-10}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+79}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \end{array} \]

Alternative 7: 81.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+76}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+76)
   (- x a)
   (if (<= z 3.1e-10)
     (- x (/ (* y a) (+ t 1.0)))
     (+ x (/ a (/ (- 1.0 z) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+76) {
		tmp = x - a;
	} else if (z <= 3.1e-10) {
		tmp = x - ((y * a) / (t + 1.0));
	} else {
		tmp = x + (a / ((1.0 - z) / 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 <= (-9.8d+76)) then
        tmp = x - a
    else if (z <= 3.1d-10) then
        tmp = x - ((y * a) / (t + 1.0d0))
    else
        tmp = x + (a / ((1.0d0 - z) / 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 <= -9.8e+76) {
		tmp = x - a;
	} else if (z <= 3.1e-10) {
		tmp = x - ((y * a) / (t + 1.0));
	} else {
		tmp = x + (a / ((1.0 - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.8e+76:
		tmp = x - a
	elif z <= 3.1e-10:
		tmp = x - ((y * a) / (t + 1.0))
	else:
		tmp = x + (a / ((1.0 - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+76)
		tmp = Float64(x - a);
	elseif (z <= 3.1e-10)
		tmp = Float64(x - Float64(Float64(y * a) / Float64(t + 1.0)));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.8e+76)
		tmp = x - a;
	elseif (z <= 3.1e-10)
		tmp = x - ((y * a) / (t + 1.0));
	else
		tmp = x + (a / ((1.0 - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+76], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.1e-10], N[(x - N[(N[(y * a), $MachinePrecision] / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.80000000000000053e76

   1. Initial program 97.5%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 87.2%

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

   if -9.80000000000000053e76 < z < 3.10000000000000015e-10

   1. Initial program 99.2%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 84.8%

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

   if 3.10000000000000015e-10 < 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/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 86.1%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. sub-neg 70.6%

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

      2. mul-1-neg 70.6%

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

      3. remove-double-neg 70.6%

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

      4. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+76}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \end{array} \]

Alternative 8: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

   1. associate-/r/ 99.9%

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

   2. *-commutative 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 9: 72.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+71}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+71) (- x a) (if (<= z 1.2e-8) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+71) {
		tmp = x - a;
	} else if (z <= 1.2e-8) {
		tmp = x - (y * 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 <= (-2.5d+71)) then
        tmp = x - a
    else if (z <= 1.2d-8) then
        tmp = x - (y * 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 <= -2.5e+71) {
		tmp = x - a;
	} else if (z <= 1.2e-8) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+71:
		tmp = x - a
	elif z <= 1.2e-8:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+71)
		tmp = Float64(x - a);
	elseif (z <= 1.2e-8)
		tmp = Float64(x - Float64(y * 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 <= -2.5e+71)
		tmp = x - a;
	elseif (z <= 1.2e-8)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+71], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.2e-8], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999986e71 or 1.19999999999999999e-8 < z

   1. Initial program 97.8%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 82.5%

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

   if -2.49999999999999986e71 < z < 1.19999999999999999e-8

   1. Initial program 99.2%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 84.8%

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

   5. Taylor expanded in t around 0 63.8%

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

      1. *-commutative 63.8%

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

   7. Simplified 63.8%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+71}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 10: 66.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+52}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+52) (- x a) (if (<= z 9.6e-13) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+52) {
		tmp = x - a;
	} else if (z <= 9.6e-13) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.4d+52)) then
        tmp = x - a
    else if (z <= 9.6d-13) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+52) {
		tmp = x - a;
	} else if (z <= 9.6e-13) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+52:
		tmp = x - a
	elif z <= 9.6e-13:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+52)
		tmp = Float64(x - a);
	elseif (z <= 9.6e-13)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+52)
		tmp = x - a;
	elseif (z <= 9.6e-13)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+52], N[(x - a), $MachinePrecision], If[LessEqual[z, 9.6e-13], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e52 or 9.5999999999999995e-13 < z

   1. Initial program 97.9%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 81.5%

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

   if -2.4e52 < z < 9.5999999999999995e-13

   1. Initial program 99.2%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 51.4%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+52}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 53.4% 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 98.7%

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

   1. associate-/r/ 99.9%

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

   2. *-commutative 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 50.4%

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

5. Final simplification 50.4%

   \[\leadsto x \]

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 2023274 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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