Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.7% → 95.5%

Time: 23.1s

Alternatives: 21

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-231}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\left(\left(\frac{t}{b - y} + \frac{\frac{x \cdot y}{z}}{b - y}\right) - \frac{a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;t_3 \leq 10^{+287}:\\ \;\;\;\;\frac{t_2}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y))))
        (t_2 (+ (* x y) (* z (- t a))))
        (t_3 (/ t_2 (+ y (* z (- b y))))))
   (if (<= t_3 -5e+233)
     t_1
     (if (<= t_3 -2e-231)
       t_3
       (if (<= t_3 0.0)
         (+
          (- (+ (/ t (- b y)) (/ (/ (* x y) z) (- b y))) (/ a (- b y)))
          (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))
         (if (<= t_3 1e+287) (/ t_2 (+ y (- (* z b) (* y z)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_2 = (x * y) + (z * (t - a));
	double t_3 = t_2 / (y + (z * (b - y)));
	double tmp;
	if (t_3 <= -5e+233) {
		tmp = t_1;
	} else if (t_3 <= -2e-231) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (((t / (b - y)) + (((x * y) / z) / (b - y))) - (a / (b - y))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	} else if (t_3 <= 1e+287) {
		tmp = t_2 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    t_2 = (x * y) + (z * (t - a))
    t_3 = t_2 / (y + (z * (b - y)))
    if (t_3 <= (-5d+233)) then
        tmp = t_1
    else if (t_3 <= (-2d-231)) then
        tmp = t_3
    else if (t_3 <= 0.0d0) then
        tmp = (((t / (b - y)) + (((x * y) / z) / (b - y))) - (a / (b - y))) + ((y / z) * ((a - t) / ((b - y) ** 2.0d0)))
    else if (t_3 <= 1d+287) then
        tmp = t_2 / (y + ((z * b) - (y * 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 b) {
	double t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_2 = (x * y) + (z * (t - a));
	double t_3 = t_2 / (y + (z * (b - y)));
	double tmp;
	if (t_3 <= -5e+233) {
		tmp = t_1;
	} else if (t_3 <= -2e-231) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (((t / (b - y)) + (((x * y) / z) / (b - y))) - (a / (b - y))) + ((y / z) * ((a - t) / Math.pow((b - y), 2.0)));
	} else if (t_3 <= 1e+287) {
		tmp = t_2 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (1.0 - z)) + ((t - a) / (b - y))
	t_2 = (x * y) + (z * (t - a))
	t_3 = t_2 / (y + (z * (b - y)))
	tmp = 0
	if t_3 <= -5e+233:
		tmp = t_1
	elif t_3 <= -2e-231:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (((t / (b - y)) + (((x * y) / z) / (b - y))) - (a / (b - y))) + ((y / z) * ((a - t) / math.pow((b - y), 2.0)))
	elif t_3 <= 1e+287:
		tmp = t_2 / (y + ((z * b) - (y * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_3 = Float64(t_2 / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_3 <= -5e+233)
		tmp = t_1;
	elseif (t_3 <= -2e-231)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(x * y) / z) / Float64(b - y))) - Float64(a / Float64(b - y))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))));
	elseif (t_3 <= 1e+287)
		tmp = Float64(t_2 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	t_2 = (x * y) + (z * (t - a));
	t_3 = t_2 / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_3 <= -5e+233)
		tmp = t_1;
	elseif (t_3 <= -2e-231)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (((t / (b - y)) + (((x * y) / z) / (b - y))) - (a / (b - y))) + ((y / z) * ((a - t) / ((b - y) ^ 2.0)));
	elseif (t_3 <= 1e+287)
		tmp = t_2 / (y + ((z * b) - (y * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+233], t$95$1, If[LessEqual[t$95$3, -2e-231], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+287], N[(t$95$2 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000009e233 or 1.0000000000000001e287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 25.0%

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

   2. Taylor expanded in x around 0 25.0%

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

   3. Taylor expanded in z around inf 62.5%

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

   4. Taylor expanded in y around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. unsub-neg 93.6%

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

   6. Simplified 93.6%

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

   if -5.00000000000000009e233 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-231

   1. Initial program 99.7%

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

   if -2e-231 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 25.0%

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

   2. Taylor expanded in z around inf 75.8%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right)} \]
   3. Step-by-step derivation

      1. associate--r+ 75.8%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}} \]

      2. associate-/r* 91.5%

         \[\leadsto \left(\left(\frac{t}{b - y} + \color{blue}{\frac{\frac{x \cdot y}{z}}{b - y}}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      3. *-commutative 91.5%

         \[\leadsto \left(\left(\frac{t}{b - y} + \frac{\frac{\color{blue}{y \cdot x}}{z}}{b - y}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      4. times-frac 99.8%

         \[\leadsto \left(\left(\frac{t}{b - y} + \frac{\frac{y \cdot x}{z}}{b - y}\right) - \frac{a}{b - y}\right) - \color{blue}{\frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}} \]

   4. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{\frac{y \cdot x}{z}}{b - y}\right) - \frac{a}{b - y}\right) - \frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}} \]

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e287

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.6%

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

   3. Applied egg-rr 99.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\left(\frac{t}{b - y} + \frac{\frac{x \cdot y}{z}}{b - y}\right) - \frac{a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 2: 95.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-231}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{\frac{y}{z} \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}} - \left(\frac{a - t}{b - y} - \frac{\frac{x \cdot y}{z}}{b - y}\right)\\ \mathbf{elif}\;t_3 \leq 10^{+287}:\\ \;\;\;\;\frac{t_2}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y))))
        (t_2 (+ (* x y) (* z (- t a))))
        (t_3 (/ t_2 (+ y (* z (- b y))))))
   (if (<= t_3 -5e+233)
     t_1
     (if (<= t_3 -2e-231)
       t_3
       (if (<= t_3 0.0)
         (-
          (/ (* (/ y z) (- a t)) (pow (- b y) 2.0))
          (- (/ (- a t) (- b y)) (/ (/ (* x y) z) (- b y))))
         (if (<= t_3 1e+287) (/ t_2 (+ y (- (* z b) (* y z)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_2 = (x * y) + (z * (t - a));
	double t_3 = t_2 / (y + (z * (b - y)));
	double tmp;
	if (t_3 <= -5e+233) {
		tmp = t_1;
	} else if (t_3 <= -2e-231) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (((y / z) * (a - t)) / pow((b - y), 2.0)) - (((a - t) / (b - y)) - (((x * y) / z) / (b - y)));
	} else if (t_3 <= 1e+287) {
		tmp = t_2 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    t_2 = (x * y) + (z * (t - a))
    t_3 = t_2 / (y + (z * (b - y)))
    if (t_3 <= (-5d+233)) then
        tmp = t_1
    else if (t_3 <= (-2d-231)) then
        tmp = t_3
    else if (t_3 <= 0.0d0) then
        tmp = (((y / z) * (a - t)) / ((b - y) ** 2.0d0)) - (((a - t) / (b - y)) - (((x * y) / z) / (b - y)))
    else if (t_3 <= 1d+287) then
        tmp = t_2 / (y + ((z * b) - (y * 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 b) {
	double t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_2 = (x * y) + (z * (t - a));
	double t_3 = t_2 / (y + (z * (b - y)));
	double tmp;
	if (t_3 <= -5e+233) {
		tmp = t_1;
	} else if (t_3 <= -2e-231) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (((y / z) * (a - t)) / Math.pow((b - y), 2.0)) - (((a - t) / (b - y)) - (((x * y) / z) / (b - y)));
	} else if (t_3 <= 1e+287) {
		tmp = t_2 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (1.0 - z)) + ((t - a) / (b - y))
	t_2 = (x * y) + (z * (t - a))
	t_3 = t_2 / (y + (z * (b - y)))
	tmp = 0
	if t_3 <= -5e+233:
		tmp = t_1
	elif t_3 <= -2e-231:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (((y / z) * (a - t)) / math.pow((b - y), 2.0)) - (((a - t) / (b - y)) - (((x * y) / z) / (b - y)))
	elif t_3 <= 1e+287:
		tmp = t_2 / (y + ((z * b) - (y * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_3 = Float64(t_2 / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_3 <= -5e+233)
		tmp = t_1;
	elseif (t_3 <= -2e-231)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(a - t)) / (Float64(b - y) ^ 2.0)) - Float64(Float64(Float64(a - t) / Float64(b - y)) - Float64(Float64(Float64(x * y) / z) / Float64(b - y))));
	elseif (t_3 <= 1e+287)
		tmp = Float64(t_2 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	t_2 = (x * y) + (z * (t - a));
	t_3 = t_2 / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_3 <= -5e+233)
		tmp = t_1;
	elseif (t_3 <= -2e-231)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (((y / z) * (a - t)) / ((b - y) ^ 2.0)) - (((a - t) / (b - y)) - (((x * y) / z) / (b - y)));
	elseif (t_3 <= 1e+287)
		tmp = t_2 / (y + ((z * b) - (y * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+233], t$95$1, If[LessEqual[t$95$3, -2e-231], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(N[(N[(y / z), $MachinePrecision] * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a - t), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+287], N[(t$95$2 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000009e233 or 1.0000000000000001e287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 25.0%

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

   2. Taylor expanded in x around 0 25.0%

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

   3. Taylor expanded in z around inf 62.5%

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

   4. Taylor expanded in y around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. unsub-neg 93.6%

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

   6. Simplified 93.6%

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

   if -5.00000000000000009e233 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-231

   1. Initial program 99.7%

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

   if -2e-231 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 25.0%

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

   2. Taylor expanded in z around inf 75.8%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right)} \]
   3. Step-by-step derivation

      1. associate--r+ 75.8%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}} \]

      2. +-commutative 75.8%

         \[\leadsto \left(\color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right)} - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      3. associate--l+ 75.8%

         \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right)} - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      4. associate-/r* 91.5%

         \[\leadsto \left(\color{blue}{\frac{\frac{x \cdot y}{z}}{b - y}} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      5. *-commutative 91.5%

         \[\leadsto \left(\frac{\frac{\color{blue}{y \cdot x}}{z}}{b - y} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      6. div-sub 91.4%

         \[\leadsto \left(\frac{\frac{y \cdot x}{z}}{b - y} + \color{blue}{\frac{t - a}{b - y}}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      7. times-frac 99.7%

         \[\leadsto \left(\frac{\frac{y \cdot x}{z}}{b - y} + \frac{t - a}{b - y}\right) - \color{blue}{\frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}} \]

      8. associate-*r/ 91.4%

         \[\leadsto \left(\frac{\frac{y \cdot x}{z}}{b - y} + \frac{t - a}{b - y}\right) - \color{blue}{\frac{\frac{y}{z} \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}} \]

   4. Simplified 91.4%

      \[\leadsto \color{blue}{\left(\frac{\frac{y \cdot x}{z}}{b - y} + \frac{t - a}{b - y}\right) - \frac{\frac{y}{z} \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}} \]

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e287

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.6%

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

   3. Applied egg-rr 99.6%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{y}{z} \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}} - \left(\frac{a - t}{b - y} - \frac{\frac{x \cdot y}{z}}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 95.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{x}{1 - z} + t_3\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+233}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3 + \frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z}\\ \mathbf{elif}\;t_2 \leq 10^{+287}:\\ \;\;\;\;\frac{t_1}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a))))
        (t_2 (/ t_1 (+ y (* z (- b y)))))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (+ (/ x (- 1.0 z)) t_3)))
   (if (<= t_2 -5e+233)
     t_4
     (if (<= t_2 -2e-231)
       t_2
       (if (<= t_2 0.0)
         (+
          t_3
          (/ (- (/ x (/ (- b y) y)) (/ y (/ (pow (- b y) 2.0) (- t a)))) z))
         (if (<= t_2 1e+287) (/ t_1 (+ y (- (* z b) (* y z)))) t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + (z * (b - y)));
	double t_3 = (t - a) / (b - y);
	double t_4 = (x / (1.0 - z)) + t_3;
	double tmp;
	if (t_2 <= -5e+233) {
		tmp = t_4;
	} else if (t_2 <= -2e-231) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_3 + (((x / ((b - y) / y)) - (y / (pow((b - y), 2.0) / (t - a)))) / z);
	} else if (t_2 <= 1e+287) {
		tmp = t_1 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x * y) + (z * (t - a))
    t_2 = t_1 / (y + (z * (b - y)))
    t_3 = (t - a) / (b - y)
    t_4 = (x / (1.0d0 - z)) + t_3
    if (t_2 <= (-5d+233)) then
        tmp = t_4
    else if (t_2 <= (-2d-231)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = t_3 + (((x / ((b - y) / y)) - (y / (((b - y) ** 2.0d0) / (t - a)))) / z)
    else if (t_2 <= 1d+287) then
        tmp = t_1 / (y + ((z * b) - (y * z)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + (z * (b - y)));
	double t_3 = (t - a) / (b - y);
	double t_4 = (x / (1.0 - z)) + t_3;
	double tmp;
	if (t_2 <= -5e+233) {
		tmp = t_4;
	} else if (t_2 <= -2e-231) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_3 + (((x / ((b - y) / y)) - (y / (Math.pow((b - y), 2.0) / (t - a)))) / z);
	} else if (t_2 <= 1e+287) {
		tmp = t_1 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * (t - a))
	t_2 = t_1 / (y + (z * (b - y)))
	t_3 = (t - a) / (b - y)
	t_4 = (x / (1.0 - z)) + t_3
	tmp = 0
	if t_2 <= -5e+233:
		tmp = t_4
	elif t_2 <= -2e-231:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_3 + (((x / ((b - y) / y)) - (y / (math.pow((b - y), 2.0) / (t - a)))) / z)
	elif t_2 <= 1e+287:
		tmp = t_1 / (y + ((z * b) - (y * z)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(Float64(x / Float64(1.0 - z)) + t_3)
	tmp = 0.0
	if (t_2 <= -5e+233)
		tmp = t_4;
	elseif (t_2 <= -2e-231)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t_3 + Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(t - a)))) / z));
	elseif (t_2 <= 1e+287)
		tmp = Float64(t_1 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * (t - a));
	t_2 = t_1 / (y + (z * (b - y)));
	t_3 = (t - a) / (b - y);
	t_4 = (x / (1.0 - z)) + t_3;
	tmp = 0.0;
	if (t_2 <= -5e+233)
		tmp = t_4;
	elseif (t_2 <= -2e-231)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_3 + (((x / ((b - y) / y)) - (y / (((b - y) ^ 2.0) / (t - a)))) / z);
	elseif (t_2 <= 1e+287)
		tmp = t_1 / (y + ((z * b) - (y * z)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+233], t$95$4, If[LessEqual[t$95$2, -2e-231], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t$95$3 + N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+287], N[(t$95$1 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000009e233 or 1.0000000000000001e287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 25.0%

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

   2. Taylor expanded in x around 0 25.0%

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

   3. Taylor expanded in z around inf 62.5%

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

   4. Taylor expanded in y around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. unsub-neg 93.6%

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

   6. Simplified 93.6%

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

   if -5.00000000000000009e233 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-231

   1. Initial program 99.7%

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

   if -2e-231 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 25.0%

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

   2. Taylor expanded in z around -inf 91.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. associate--l+ 91.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 91.6%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 91.6%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 91.5%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{\frac{x}{\frac{b - y}{y}}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 99.8%

         \[\leadsto \left(-\frac{-1 \cdot \left(\frac{x}{\frac{b - y}{y}} - \color{blue}{\frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 99.7%

         \[\leadsto \left(-\frac{-1 \cdot \left(\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   4. Simplified 99.7%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e287

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.6%

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

   3. Applied egg-rr 99.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 93.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{x}{1 - z} + t_3\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+233}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{+287}:\\ \;\;\;\;\frac{t_1}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a))))
        (t_2 (/ t_1 (+ y (* z (- b y)))))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (+ (/ x (- 1.0 z)) t_3)))
   (if (<= t_2 -5e+233)
     t_4
     (if (<= t_2 -2e-231)
       t_2
       (if (<= t_2 0.0)
         t_3
         (if (<= t_2 1e+287) (/ t_1 (+ y (- (* z b) (* y z)))) t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + (z * (b - y)));
	double t_3 = (t - a) / (b - y);
	double t_4 = (x / (1.0 - z)) + t_3;
	double tmp;
	if (t_2 <= -5e+233) {
		tmp = t_4;
	} else if (t_2 <= -2e-231) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_3;
	} else if (t_2 <= 1e+287) {
		tmp = t_1 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x * y) + (z * (t - a))
    t_2 = t_1 / (y + (z * (b - y)))
    t_3 = (t - a) / (b - y)
    t_4 = (x / (1.0d0 - z)) + t_3
    if (t_2 <= (-5d+233)) then
        tmp = t_4
    else if (t_2 <= (-2d-231)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = t_3
    else if (t_2 <= 1d+287) then
        tmp = t_1 / (y + ((z * b) - (y * z)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + (z * (b - y)));
	double t_3 = (t - a) / (b - y);
	double t_4 = (x / (1.0 - z)) + t_3;
	double tmp;
	if (t_2 <= -5e+233) {
		tmp = t_4;
	} else if (t_2 <= -2e-231) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_3;
	} else if (t_2 <= 1e+287) {
		tmp = t_1 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * (t - a))
	t_2 = t_1 / (y + (z * (b - y)))
	t_3 = (t - a) / (b - y)
	t_4 = (x / (1.0 - z)) + t_3
	tmp = 0
	if t_2 <= -5e+233:
		tmp = t_4
	elif t_2 <= -2e-231:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_3
	elif t_2 <= 1e+287:
		tmp = t_1 / (y + ((z * b) - (y * z)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(Float64(x / Float64(1.0 - z)) + t_3)
	tmp = 0.0
	if (t_2 <= -5e+233)
		tmp = t_4;
	elseif (t_2 <= -2e-231)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_3;
	elseif (t_2 <= 1e+287)
		tmp = Float64(t_1 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * (t - a));
	t_2 = t_1 / (y + (z * (b - y)));
	t_3 = (t - a) / (b - y);
	t_4 = (x / (1.0 - z)) + t_3;
	tmp = 0.0;
	if (t_2 <= -5e+233)
		tmp = t_4;
	elseif (t_2 <= -2e-231)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_3;
	elseif (t_2 <= 1e+287)
		tmp = t_1 / (y + ((z * b) - (y * z)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+233], t$95$4, If[LessEqual[t$95$2, -2e-231], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$3, If[LessEqual[t$95$2, 1e+287], N[(t$95$1 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000009e233 or 1.0000000000000001e287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 25.0%

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

   2. Taylor expanded in x around 0 25.0%

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

   3. Taylor expanded in z around inf 62.5%

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

   4. Taylor expanded in y around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. unsub-neg 93.6%

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

   6. Simplified 93.6%

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

   if -5.00000000000000009e233 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-231

   1. Initial program 99.7%

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

   if -2e-231 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 25.0%

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

   2. Taylor expanded in z around inf 80.3%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e287

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.6%

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

   3. Applied egg-rr 99.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 93.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x}{1 - z} + t_2\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+233}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (+ (/ x (- 1.0 z)) t_2)))
   (if (<= t_1 -5e+233)
     t_3
     (if (<= t_1 -2e-231)
       t_1
       (if (<= t_1 0.0) t_2 (if (<= t_1 1e+287) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_1 <= -5e+233) {
		tmp = t_3;
	} else if (t_1 <= -2e-231) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+287) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    t_3 = (x / (1.0d0 - z)) + t_2
    if (t_1 <= (-5d+233)) then
        tmp = t_3
    else if (t_1 <= (-2d-231)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t_2
    else if (t_1 <= 1d+287) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_1 <= -5e+233) {
		tmp = t_3;
	} else if (t_1 <= -2e-231) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+287) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	t_3 = (x / (1.0 - z)) + t_2
	tmp = 0
	if t_1 <= -5e+233:
		tmp = t_3
	elif t_1 <= -2e-231:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t_2
	elif t_1 <= 1e+287:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	tmp = 0.0
	if (t_1 <= -5e+233)
		tmp = t_3;
	elseif (t_1 <= -2e-231)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 1e+287)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	t_3 = (x / (1.0 - z)) + t_2;
	tmp = 0.0;
	if (t_1 <= -5e+233)
		tmp = t_3;
	elseif (t_1 <= -2e-231)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 1e+287)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+233], t$95$3, If[LessEqual[t$95$1, -2e-231], t$95$1, If[LessEqual[t$95$1, 0.0], t$95$2, If[LessEqual[t$95$1, 1e+287], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000009e233 or 1.0000000000000001e287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 25.0%

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

   2. Taylor expanded in x around 0 25.0%

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

   3. Taylor expanded in z around inf 62.5%

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

   4. Taylor expanded in y around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. unsub-neg 93.6%

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

   6. Simplified 93.6%

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

   if -5.00000000000000009e233 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-231 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e287

   1. Initial program 99.6%

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

   if -2e-231 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 25.0%

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

   2. Taylor expanded in z around inf 80.3%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := x + \frac{z}{\frac{t_1}{t}}\\ t_3 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ t_4 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -8600:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{t_4}{t_1}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-234}:\\ \;\;\;\;\frac{t_4}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-244}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.09:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ x (/ z (/ t_1 t))))
        (t_3 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y))))
        (t_4 (* z (- t a))))
   (if (<= z -8600.0)
     t_3
     (if (<= z -5.8e-75)
       (/ t_4 t_1)
       (if (<= z -5e-222)
         t_2
         (if (<= z -2.25e-234)
           (/ t_4 (+ y (* z b)))
           (if (<= z 6.8e-244) x (if (<= z 0.09) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = x + (z / (t_1 / t));
	double t_3 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_4 = z * (t - a);
	double tmp;
	if (z <= -8600.0) {
		tmp = t_3;
	} else if (z <= -5.8e-75) {
		tmp = t_4 / t_1;
	} else if (z <= -5e-222) {
		tmp = t_2;
	} else if (z <= -2.25e-234) {
		tmp = t_4 / (y + (z * b));
	} else if (z <= 6.8e-244) {
		tmp = x;
	} else if (z <= 0.09) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = x + (z / (t_1 / t))
    t_3 = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    t_4 = z * (t - a)
    if (z <= (-8600.0d0)) then
        tmp = t_3
    else if (z <= (-5.8d-75)) then
        tmp = t_4 / t_1
    else if (z <= (-5d-222)) then
        tmp = t_2
    else if (z <= (-2.25d-234)) then
        tmp = t_4 / (y + (z * b))
    else if (z <= 6.8d-244) then
        tmp = x
    else if (z <= 0.09d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = x + (z / (t_1 / t));
	double t_3 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_4 = z * (t - a);
	double tmp;
	if (z <= -8600.0) {
		tmp = t_3;
	} else if (z <= -5.8e-75) {
		tmp = t_4 / t_1;
	} else if (z <= -5e-222) {
		tmp = t_2;
	} else if (z <= -2.25e-234) {
		tmp = t_4 / (y + (z * b));
	} else if (z <= 6.8e-244) {
		tmp = x;
	} else if (z <= 0.09) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = x + (z / (t_1 / t))
	t_3 = (x / (1.0 - z)) + ((t - a) / (b - y))
	t_4 = z * (t - a)
	tmp = 0
	if z <= -8600.0:
		tmp = t_3
	elif z <= -5.8e-75:
		tmp = t_4 / t_1
	elif z <= -5e-222:
		tmp = t_2
	elif z <= -2.25e-234:
		tmp = t_4 / (y + (z * b))
	elif z <= 6.8e-244:
		tmp = x
	elif z <= 0.09:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(x + Float64(z / Float64(t_1 / t)))
	t_3 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	t_4 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -8600.0)
		tmp = t_3;
	elseif (z <= -5.8e-75)
		tmp = Float64(t_4 / t_1);
	elseif (z <= -5e-222)
		tmp = t_2;
	elseif (z <= -2.25e-234)
		tmp = Float64(t_4 / Float64(y + Float64(z * b)));
	elseif (z <= 6.8e-244)
		tmp = x;
	elseif (z <= 0.09)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = x + (z / (t_1 / t));
	t_3 = (x / (1.0 - z)) + ((t - a) / (b - y));
	t_4 = z * (t - a);
	tmp = 0.0;
	if (z <= -8600.0)
		tmp = t_3;
	elseif (z <= -5.8e-75)
		tmp = t_4 / t_1;
	elseif (z <= -5e-222)
		tmp = t_2;
	elseif (z <= -2.25e-234)
		tmp = t_4 / (y + (z * b));
	elseif (z <= 6.8e-244)
		tmp = x;
	elseif (z <= 0.09)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8600.0], t$95$3, If[LessEqual[z, -5.8e-75], N[(t$95$4 / t$95$1), $MachinePrecision], If[LessEqual[z, -5e-222], t$95$2, If[LessEqual[z, -2.25e-234], N[(t$95$4 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-244], x, If[LessEqual[z, 0.09], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8600 or 0.089999999999999997 < z

   1. Initial program 47.8%

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

   2. Taylor expanded in x around 0 47.8%

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

   3. Taylor expanded in z around inf 80.7%

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

   4. Taylor expanded in y around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   6. Simplified 86.6%

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

   if -8600 < z < -5.8000000000000003e-75

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0 76.0%

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

   if -5.8000000000000003e-75 < z < -5.00000000000000008e-222 or 6.80000000000000018e-244 < z < 0.089999999999999997

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0 87.0%

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

      1. expm1-log1p-u 73.6%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\right)\right)} \]

      2. expm1-udef 51.5%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\right)} - 1\right)} \]

      3. associate-/l* 49.2%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}\right)} - 1\right) \]

      4. +-commutative 49.2%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(e^{\mathsf{log1p}\left(\frac{z}{\frac{\color{blue}{z \cdot \left(b - y\right) + y}}{t - a}}\right)} - 1\right) \]

      5. fma-udef 49.2%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(e^{\mathsf{log1p}\left(\frac{z}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{t - a}}\right)} - 1\right) \]

   4. Applied egg-rr 49.2%

      \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 71.3%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}\right)\right)} \]

      2. expm1-log1p 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in t around inf 71.0%

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

   8. Taylor expanded in z around 0 70.6%

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

   if -5.00000000000000008e-222 < z < -2.25000000000000005e-234

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.4%

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

   3. Taylor expanded in b around inf 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   if -2.25000000000000005e-234 < z < 6.80000000000000018e-244

   1. Initial program 88.8%

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

   2. Taylor expanded in z around 0 86.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8600:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-222}:\\ \;\;\;\;x + \frac{z}{\frac{y + z \cdot \left(b - y\right)}{t}}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-234}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-244}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.09:\\ \;\;\;\;x + \frac{z}{\frac{y + z \cdot \left(b - y\right)}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 61.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -46000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-80}:\\ \;\;\;\;\frac{t_1}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ t_1 (+ y (* z b))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -46000.0)
     t_3
     (if (<= z -1.7e-80)
       (/ t_1 (* y (- 1.0 z)))
       (if (<= z -6.8e-107)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= z -3.8e-234)
           t_2
           (if (<= z 3.3e-173)
             x
             (if (<= z 1.8e-127)
               t_2
               (if (<= z 6e+18) (/ x (- 1.0 z)) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = t_1 / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -46000.0) {
		tmp = t_3;
	} else if (z <= -1.7e-80) {
		tmp = t_1 / (y * (1.0 - z));
	} else if (z <= -6.8e-107) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -3.8e-234) {
		tmp = t_2;
	} else if (z <= 3.3e-173) {
		tmp = x;
	} else if (z <= 1.8e-127) {
		tmp = t_2;
	} else if (z <= 6e+18) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = t_1 / (y + (z * b))
    t_3 = (t - a) / (b - y)
    if (z <= (-46000.0d0)) then
        tmp = t_3
    else if (z <= (-1.7d-80)) then
        tmp = t_1 / (y * (1.0d0 - z))
    else if (z <= (-6.8d-107)) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= (-3.8d-234)) then
        tmp = t_2
    else if (z <= 3.3d-173) then
        tmp = x
    else if (z <= 1.8d-127) then
        tmp = t_2
    else if (z <= 6d+18) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = t_1 / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -46000.0) {
		tmp = t_3;
	} else if (z <= -1.7e-80) {
		tmp = t_1 / (y * (1.0 - z));
	} else if (z <= -6.8e-107) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -3.8e-234) {
		tmp = t_2;
	} else if (z <= 3.3e-173) {
		tmp = x;
	} else if (z <= 1.8e-127) {
		tmp = t_2;
	} else if (z <= 6e+18) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = t_1 / (y + (z * b))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -46000.0:
		tmp = t_3
	elif z <= -1.7e-80:
		tmp = t_1 / (y * (1.0 - z))
	elif z <= -6.8e-107:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= -3.8e-234:
		tmp = t_2
	elif z <= 3.3e-173:
		tmp = x
	elif z <= 1.8e-127:
		tmp = t_2
	elif z <= 6e+18:
		tmp = x / (1.0 - z)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(t_1 / Float64(y + Float64(z * b)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -46000.0)
		tmp = t_3;
	elseif (z <= -1.7e-80)
		tmp = Float64(t_1 / Float64(y * Float64(1.0 - z)));
	elseif (z <= -6.8e-107)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= -3.8e-234)
		tmp = t_2;
	elseif (z <= 3.3e-173)
		tmp = x;
	elseif (z <= 1.8e-127)
		tmp = t_2;
	elseif (z <= 6e+18)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = t_1 / (y + (z * b));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -46000.0)
		tmp = t_3;
	elseif (z <= -1.7e-80)
		tmp = t_1 / (y * (1.0 - z));
	elseif (z <= -6.8e-107)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= -3.8e-234)
		tmp = t_2;
	elseif (z <= 3.3e-173)
		tmp = x;
	elseif (z <= 1.8e-127)
		tmp = t_2;
	elseif (z <= 6e+18)
		tmp = x / (1.0 - z);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -46000.0], t$95$3, If[LessEqual[z, -1.7e-80], N[(t$95$1 / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e-107], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-234], t$95$2, If[LessEqual[z, 3.3e-173], x, If[LessEqual[z, 1.8e-127], t$95$2, If[LessEqual[z, 6e+18], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -46000 or 6e18 < z

   1. Initial program 46.6%

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

   2. Taylor expanded in z around inf 80.0%

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

   if -46000 < z < -1.7e-80

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   5. Simplified 61.7%

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

   if -1.7e-80 < z < -6.79999999999999989e-107

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 94.8%

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

      1. *-commutative 94.8%

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

   4. Simplified 94.8%

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

   if -6.79999999999999989e-107 < z < -3.79999999999999984e-234 or 3.3000000000000003e-173 < z < 1.8e-127

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0 65.7%

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

   3. Taylor expanded in b around inf 65.7%

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

      1. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if -3.79999999999999984e-234 < z < 3.3000000000000003e-173

   1. Initial program 87.6%

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

   2. Taylor expanded in z around 0 81.8%

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

   if 1.8e-127 < z < 6e18

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

   4. Simplified 52.3%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -46000:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-80}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-234}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6700:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.75 \cdot 10^{-78}:\\ \;\;\;\;\frac{1}{1 - z} \cdot \frac{t_1}{y}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 40000000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ t_1 (+ y (* z b))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -6700.0)
     t_3
     (if (<= z -3.75e-78)
       (* (/ 1.0 (- 1.0 z)) (/ t_1 y))
       (if (<= z -4.2e-113)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= z -3.3e-234)
           t_2
           (if (<= z 2.35e-173)
             x
             (if (<= z 1.8e-127)
               t_2
               (if (<= z 40000000000000.0) (/ x (- 1.0 z)) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = t_1 / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -6700.0) {
		tmp = t_3;
	} else if (z <= -3.75e-78) {
		tmp = (1.0 / (1.0 - z)) * (t_1 / y);
	} else if (z <= -4.2e-113) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -3.3e-234) {
		tmp = t_2;
	} else if (z <= 2.35e-173) {
		tmp = x;
	} else if (z <= 1.8e-127) {
		tmp = t_2;
	} else if (z <= 40000000000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = t_1 / (y + (z * b))
    t_3 = (t - a) / (b - y)
    if (z <= (-6700.0d0)) then
        tmp = t_3
    else if (z <= (-3.75d-78)) then
        tmp = (1.0d0 / (1.0d0 - z)) * (t_1 / y)
    else if (z <= (-4.2d-113)) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= (-3.3d-234)) then
        tmp = t_2
    else if (z <= 2.35d-173) then
        tmp = x
    else if (z <= 1.8d-127) then
        tmp = t_2
    else if (z <= 40000000000000.0d0) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = t_1 / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -6700.0) {
		tmp = t_3;
	} else if (z <= -3.75e-78) {
		tmp = (1.0 / (1.0 - z)) * (t_1 / y);
	} else if (z <= -4.2e-113) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -3.3e-234) {
		tmp = t_2;
	} else if (z <= 2.35e-173) {
		tmp = x;
	} else if (z <= 1.8e-127) {
		tmp = t_2;
	} else if (z <= 40000000000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = t_1 / (y + (z * b))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -6700.0:
		tmp = t_3
	elif z <= -3.75e-78:
		tmp = (1.0 / (1.0 - z)) * (t_1 / y)
	elif z <= -4.2e-113:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= -3.3e-234:
		tmp = t_2
	elif z <= 2.35e-173:
		tmp = x
	elif z <= 1.8e-127:
		tmp = t_2
	elif z <= 40000000000000.0:
		tmp = x / (1.0 - z)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(t_1 / Float64(y + Float64(z * b)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -6700.0)
		tmp = t_3;
	elseif (z <= -3.75e-78)
		tmp = Float64(Float64(1.0 / Float64(1.0 - z)) * Float64(t_1 / y));
	elseif (z <= -4.2e-113)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= -3.3e-234)
		tmp = t_2;
	elseif (z <= 2.35e-173)
		tmp = x;
	elseif (z <= 1.8e-127)
		tmp = t_2;
	elseif (z <= 40000000000000.0)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = t_1 / (y + (z * b));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -6700.0)
		tmp = t_3;
	elseif (z <= -3.75e-78)
		tmp = (1.0 / (1.0 - z)) * (t_1 / y);
	elseif (z <= -4.2e-113)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= -3.3e-234)
		tmp = t_2;
	elseif (z <= 2.35e-173)
		tmp = x;
	elseif (z <= 1.8e-127)
		tmp = t_2;
	elseif (z <= 40000000000000.0)
		tmp = x / (1.0 - z);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6700.0], t$95$3, If[LessEqual[z, -3.75e-78], N[(N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-113], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-234], t$95$2, If[LessEqual[z, 2.35e-173], x, If[LessEqual[z, 1.8e-127], t$95$2, If[LessEqual[z, 40000000000000.0], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6700 or 4e13 < z

   1. Initial program 46.6%

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

   2. Taylor expanded in z around inf 80.0%

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

   if -6700 < z < -3.75000000000000021e-78

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   5. Simplified 61.7%

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

      1. associate-/r* 61.8%

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

      2. div-inv 61.7%

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

      3. *-commutative 61.7%

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

   7. Applied egg-rr 61.7%

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

   if -3.75000000000000021e-78 < z < -4.2e-113

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 94.8%

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

      1. *-commutative 94.8%

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

   4. Simplified 94.8%

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

   if -4.2e-113 < z < -3.30000000000000014e-234 or 2.35e-173 < z < 1.8e-127

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0 65.7%

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

   3. Taylor expanded in b around inf 65.7%

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

      1. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if -3.30000000000000014e-234 < z < 2.35e-173

   1. Initial program 87.6%

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

   2. Taylor expanded in z around 0 81.8%

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

   if 1.8e-127 < z < 4e13

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

   4. Simplified 52.3%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6700:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.75 \cdot 10^{-78}:\\ \;\;\;\;\frac{1}{1 - z} \cdot \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-234}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 40000000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 9: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -12200:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-76}:\\ \;\;\;\;\frac{t_1}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 305000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ t_1 y)) (t_3 (/ (- t a) (- b y))))
   (if (<= z -12200.0)
     t_3
     (if (<= z -1.12e-76)
       (/ t_1 (* y (- 1.0 z)))
       (if (<= z -5e-222)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= z -3.8e-234)
           t_2
           (if (<= z 4e-166)
             x
             (if (<= z 2.3e-127)
               t_2
               (if (<= z 305000000.0) (/ x (- 1.0 z)) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = t_1 / y;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -12200.0) {
		tmp = t_3;
	} else if (z <= -1.12e-76) {
		tmp = t_1 / (y * (1.0 - z));
	} else if (z <= -5e-222) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -3.8e-234) {
		tmp = t_2;
	} else if (z <= 4e-166) {
		tmp = x;
	} else if (z <= 2.3e-127) {
		tmp = t_2;
	} else if (z <= 305000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = t_1 / y
    t_3 = (t - a) / (b - y)
    if (z <= (-12200.0d0)) then
        tmp = t_3
    else if (z <= (-1.12d-76)) then
        tmp = t_1 / (y * (1.0d0 - z))
    else if (z <= (-5d-222)) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= (-3.8d-234)) then
        tmp = t_2
    else if (z <= 4d-166) then
        tmp = x
    else if (z <= 2.3d-127) then
        tmp = t_2
    else if (z <= 305000000.0d0) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = t_1 / y;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -12200.0) {
		tmp = t_3;
	} else if (z <= -1.12e-76) {
		tmp = t_1 / (y * (1.0 - z));
	} else if (z <= -5e-222) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -3.8e-234) {
		tmp = t_2;
	} else if (z <= 4e-166) {
		tmp = x;
	} else if (z <= 2.3e-127) {
		tmp = t_2;
	} else if (z <= 305000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = t_1 / y
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -12200.0:
		tmp = t_3
	elif z <= -1.12e-76:
		tmp = t_1 / (y * (1.0 - z))
	elif z <= -5e-222:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= -3.8e-234:
		tmp = t_2
	elif z <= 4e-166:
		tmp = x
	elif z <= 2.3e-127:
		tmp = t_2
	elif z <= 305000000.0:
		tmp = x / (1.0 - z)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(t_1 / y)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -12200.0)
		tmp = t_3;
	elseif (z <= -1.12e-76)
		tmp = Float64(t_1 / Float64(y * Float64(1.0 - z)));
	elseif (z <= -5e-222)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= -3.8e-234)
		tmp = t_2;
	elseif (z <= 4e-166)
		tmp = x;
	elseif (z <= 2.3e-127)
		tmp = t_2;
	elseif (z <= 305000000.0)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = t_1 / y;
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -12200.0)
		tmp = t_3;
	elseif (z <= -1.12e-76)
		tmp = t_1 / (y * (1.0 - z));
	elseif (z <= -5e-222)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= -3.8e-234)
		tmp = t_2;
	elseif (z <= 4e-166)
		tmp = x;
	elseif (z <= 2.3e-127)
		tmp = t_2;
	elseif (z <= 305000000.0)
		tmp = x / (1.0 - z);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -12200.0], t$95$3, If[LessEqual[z, -1.12e-76], N[(t$95$1 / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-222], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-234], t$95$2, If[LessEqual[z, 4e-166], x, If[LessEqual[z, 2.3e-127], t$95$2, If[LessEqual[z, 305000000.0], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -12200 or 3.05e8 < z

   1. Initial program 46.6%

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

   2. Taylor expanded in z around inf 80.0%

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

   if -12200 < z < -1.12e-76

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   5. Simplified 61.7%

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

   if -1.12e-76 < z < -5.00000000000000008e-222

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 51.4%

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

      1. *-commutative 51.4%

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

   4. Simplified 51.4%

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

   if -5.00000000000000008e-222 < z < -3.79999999999999984e-234 or 4.00000000000000016e-166 < z < 2.30000000000000019e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 89.4%

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

   3. Taylor expanded in z around 0 71.5%

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

   if -3.79999999999999984e-234 < z < 4.00000000000000016e-166

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 79.8%

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

   if 2.30000000000000019e-127 < z < 3.05e8

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

   4. Simplified 52.3%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12200:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-76}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-234}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 305000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10: 68.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9500:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{1}{1 - z} \cdot \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-105}:\\ \;\;\;\;\frac{x \cdot y}{t_1}\\ \mathbf{elif}\;z \leq 0.8:\\ \;\;\;\;x + \frac{z}{\frac{t_1}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -9500.0)
     t_2
     (if (<= z -4.5e-80)
       (* (/ 1.0 (- 1.0 z)) (/ (* z (- t a)) y))
       (if (<= z -1.5e-105)
         (/ (* x y) t_1)
         (if (<= z 0.8) (+ x (/ z (/ t_1 t))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -9500.0) {
		tmp = t_2;
	} else if (z <= -4.5e-80) {
		tmp = (1.0 / (1.0 - z)) * ((z * (t - a)) / y);
	} else if (z <= -1.5e-105) {
		tmp = (x * y) / t_1;
	} else if (z <= 0.8) {
		tmp = x + (z / (t_1 / t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    if (z <= (-9500.0d0)) then
        tmp = t_2
    else if (z <= (-4.5d-80)) then
        tmp = (1.0d0 / (1.0d0 - z)) * ((z * (t - a)) / y)
    else if (z <= (-1.5d-105)) then
        tmp = (x * y) / t_1
    else if (z <= 0.8d0) then
        tmp = x + (z / (t_1 / t))
    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 b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -9500.0) {
		tmp = t_2;
	} else if (z <= -4.5e-80) {
		tmp = (1.0 / (1.0 - z)) * ((z * (t - a)) / y);
	} else if (z <= -1.5e-105) {
		tmp = (x * y) / t_1;
	} else if (z <= 0.8) {
		tmp = x + (z / (t_1 / t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -9500.0:
		tmp = t_2
	elif z <= -4.5e-80:
		tmp = (1.0 / (1.0 - z)) * ((z * (t - a)) / y)
	elif z <= -1.5e-105:
		tmp = (x * y) / t_1
	elif z <= 0.8:
		tmp = x + (z / (t_1 / t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -9500.0)
		tmp = t_2;
	elseif (z <= -4.5e-80)
		tmp = Float64(Float64(1.0 / Float64(1.0 - z)) * Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= -1.5e-105)
		tmp = Float64(Float64(x * y) / t_1);
	elseif (z <= 0.8)
		tmp = Float64(x + Float64(z / Float64(t_1 / t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -9500.0)
		tmp = t_2;
	elseif (z <= -4.5e-80)
		tmp = (1.0 / (1.0 - z)) * ((z * (t - a)) / y);
	elseif (z <= -1.5e-105)
		tmp = (x * y) / t_1;
	elseif (z <= 0.8)
		tmp = x + (z / (t_1 / t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9500.0], t$95$2, If[LessEqual[z, -4.5e-80], N[(N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-105], N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 0.8], N[(x + N[(z / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9500 or 0.80000000000000004 < z

   1. Initial program 47.8%

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

   2. Taylor expanded in z around inf 77.9%

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

   if -9500 < z < -4.5000000000000003e-80

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   5. Simplified 61.7%

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

      1. associate-/r* 61.8%

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

      2. div-inv 61.7%

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

      3. *-commutative 61.7%

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

   7. Applied egg-rr 61.7%

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

   if -4.5000000000000003e-80 < z < -1.5e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 94.8%

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

      1. *-commutative 94.8%

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

   4. Simplified 94.8%

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

   if -1.5e-105 < z < 0.80000000000000004

   1. Initial program 87.6%

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

   2. Taylor expanded in x around 0 87.6%

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

      1. expm1-log1p-u 75.7%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\right)\right)} \]

      2. expm1-udef 56.6%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\right)} - 1\right)} \]

      3. associate-/l* 52.1%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}\right)} - 1\right) \]

      4. +-commutative 52.1%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(e^{\mathsf{log1p}\left(\frac{z}{\frac{\color{blue}{z \cdot \left(b - y\right) + y}}{t - a}}\right)} - 1\right) \]

      5. fma-udef 52.1%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(e^{\mathsf{log1p}\left(\frac{z}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{t - a}}\right)} - 1\right) \]

   4. Applied egg-rr 52.1%

      \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 71.2%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}\right)\right)} \]

      2. expm1-log1p 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in t around inf 67.0%

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

   8. Taylor expanded in z around 0 71.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9500:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{1}{1 - z} \cdot \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-105}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 0.8:\\ \;\;\;\;x + \frac{z}{\frac{y + z \cdot \left(b - y\right)}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 11: 71.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-75}:\\ \;\;\;\;\frac{1}{1 - z} \cdot \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{x \cdot y}{t_1}\\ \mathbf{elif}\;z \leq 0.0116:\\ \;\;\;\;x + \frac{z}{\frac{t_1}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))))
   (if (<= z -7000.0)
     t_2
     (if (<= z -1.15e-75)
       (* (/ 1.0 (- 1.0 z)) (/ (* z (- t a)) y))
       (if (<= z -2.4e-102)
         (/ (* x y) t_1)
         (if (<= z 0.0116) (+ x (/ z (/ t_1 t))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (z <= -7000.0) {
		tmp = t_2;
	} else if (z <= -1.15e-75) {
		tmp = (1.0 / (1.0 - z)) * ((z * (t - a)) / y);
	} else if (z <= -2.4e-102) {
		tmp = (x * y) / t_1;
	} else if (z <= 0.0116) {
		tmp = x + (z / (t_1 / t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    if (z <= (-7000.0d0)) then
        tmp = t_2
    else if (z <= (-1.15d-75)) then
        tmp = (1.0d0 / (1.0d0 - z)) * ((z * (t - a)) / y)
    else if (z <= (-2.4d-102)) then
        tmp = (x * y) / t_1
    else if (z <= 0.0116d0) then
        tmp = x + (z / (t_1 / t))
    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 b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (z <= -7000.0) {
		tmp = t_2;
	} else if (z <= -1.15e-75) {
		tmp = (1.0 / (1.0 - z)) * ((z * (t - a)) / y);
	} else if (z <= -2.4e-102) {
		tmp = (x * y) / t_1;
	} else if (z <= 0.0116) {
		tmp = x + (z / (t_1 / t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y))
	tmp = 0
	if z <= -7000.0:
		tmp = t_2
	elif z <= -1.15e-75:
		tmp = (1.0 / (1.0 - z)) * ((z * (t - a)) / y)
	elif z <= -2.4e-102:
		tmp = (x * y) / t_1
	elif z <= 0.0116:
		tmp = x + (z / (t_1 / t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (z <= -7000.0)
		tmp = t_2;
	elseif (z <= -1.15e-75)
		tmp = Float64(Float64(1.0 / Float64(1.0 - z)) * Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= -2.4e-102)
		tmp = Float64(Float64(x * y) / t_1);
	elseif (z <= 0.0116)
		tmp = Float64(x + Float64(z / Float64(t_1 / t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	tmp = 0.0;
	if (z <= -7000.0)
		tmp = t_2;
	elseif (z <= -1.15e-75)
		tmp = (1.0 / (1.0 - z)) * ((z * (t - a)) / y);
	elseif (z <= -2.4e-102)
		tmp = (x * y) / t_1;
	elseif (z <= 0.0116)
		tmp = x + (z / (t_1 / t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7000.0], t$95$2, If[LessEqual[z, -1.15e-75], N[(N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-102], N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 0.0116], N[(x + N[(z / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7e3 or 0.0116 < z

   1. Initial program 47.8%

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

   2. Taylor expanded in x around 0 47.8%

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

   3. Taylor expanded in z around inf 80.7%

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

   4. Taylor expanded in y around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   6. Simplified 86.6%

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

   if -7e3 < z < -1.15e-75

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   5. Simplified 61.7%

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

      1. associate-/r* 61.8%

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

      2. div-inv 61.7%

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

      3. *-commutative 61.7%

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

   7. Applied egg-rr 61.7%

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

   if -1.15e-75 < z < -2.4e-102

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 93.5%

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

      1. *-commutative 93.5%

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

   4. Simplified 93.5%

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

   if -2.4e-102 < z < 0.0116

   1. Initial program 87.7%

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

   2. Taylor expanded in x around 0 87.7%

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

      1. expm1-log1p-u 75.0%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\right)\right)} \]

      2. expm1-udef 56.0%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\right)} - 1\right)} \]

      3. associate-/l* 51.5%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}\right)} - 1\right) \]

      4. +-commutative 51.5%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(e^{\mathsf{log1p}\left(\frac{z}{\frac{\color{blue}{z \cdot \left(b - y\right) + y}}{t - a}}\right)} - 1\right) \]

      5. fma-udef 51.5%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(e^{\mathsf{log1p}\left(\frac{z}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{t - a}}\right)} - 1\right) \]

   4. Applied egg-rr 51.5%

      \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 70.5%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}\right)\right)} \]

      2. expm1-log1p 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in t around inf 67.3%

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

   8. Taylor expanded in z around 0 71.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7000:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-75}:\\ \;\;\;\;\frac{1}{1 - z} \cdot \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 0.0116:\\ \;\;\;\;x + \frac{z}{\frac{y + z \cdot \left(b - y\right)}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 12: 84.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -520000 \lor \neg \left(z \leq 12.8\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -520000.0) (not (<= z 12.8)))
   (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))
   (+ x (/ (* z (- t a)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -520000.0) || !(z <= 12.8)) {
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y));
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-520000.0d0)) .or. (.not. (z <= 12.8d0))) then
        tmp = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    else
        tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -520000.0) || !(z <= 12.8)) {
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y));
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -520000.0) or not (z <= 12.8):
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y))
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -520000.0) || !(z <= 12.8))
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -520000.0) || ~((z <= 12.8)))
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y));
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -520000.0], N[Not[LessEqual[z, 12.8]], $MachinePrecision]], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e5 or 12.800000000000001 < z

   1. Initial program 47.5%

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

   2. Taylor expanded in x around 0 47.4%

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

   3. Taylor expanded in z around inf 81.2%

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

   4. Taylor expanded in y around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. unsub-neg 87.1%

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

   6. Simplified 87.1%

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

   if -5.2e5 < z < 12.800000000000001

   1. Initial program 87.9%

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

   2. Taylor expanded in x around 0 87.9%

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

   3. Taylor expanded in z around 0 89.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -520000 \lor \neg \left(z \leq 12.8\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 13: 62.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -20500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-83}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 270000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -20500.0)
     t_1
     (if (<= z -7e-83)
       (* (/ z y) (/ (- t a) (- 1.0 z)))
       (if (<= z 4e-166)
         x
         (if (<= z 1.9e-127)
           (/ (* z (- t a)) y)
           (if (<= z 270000000.0) (/ x (- 1.0 z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -20500.0) {
		tmp = t_1;
	} else if (z <= -7e-83) {
		tmp = (z / y) * ((t - a) / (1.0 - z));
	} else if (z <= 4e-166) {
		tmp = x;
	} else if (z <= 1.9e-127) {
		tmp = (z * (t - a)) / y;
	} else if (z <= 270000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-20500.0d0)) then
        tmp = t_1
    else if (z <= (-7d-83)) then
        tmp = (z / y) * ((t - a) / (1.0d0 - z))
    else if (z <= 4d-166) then
        tmp = x
    else if (z <= 1.9d-127) then
        tmp = (z * (t - a)) / y
    else if (z <= 270000000.0d0) then
        tmp = x / (1.0d0 - 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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -20500.0) {
		tmp = t_1;
	} else if (z <= -7e-83) {
		tmp = (z / y) * ((t - a) / (1.0 - z));
	} else if (z <= 4e-166) {
		tmp = x;
	} else if (z <= 1.9e-127) {
		tmp = (z * (t - a)) / y;
	} else if (z <= 270000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -20500.0:
		tmp = t_1
	elif z <= -7e-83:
		tmp = (z / y) * ((t - a) / (1.0 - z))
	elif z <= 4e-166:
		tmp = x
	elif z <= 1.9e-127:
		tmp = (z * (t - a)) / y
	elif z <= 270000000.0:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -20500.0)
		tmp = t_1;
	elseif (z <= -7e-83)
		tmp = Float64(Float64(z / y) * Float64(Float64(t - a) / Float64(1.0 - z)));
	elseif (z <= 4e-166)
		tmp = x;
	elseif (z <= 1.9e-127)
		tmp = Float64(Float64(z * Float64(t - a)) / y);
	elseif (z <= 270000000.0)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -20500.0)
		tmp = t_1;
	elseif (z <= -7e-83)
		tmp = (z / y) * ((t - a) / (1.0 - z));
	elseif (z <= 4e-166)
		tmp = x;
	elseif (z <= 1.9e-127)
		tmp = (z * (t - a)) / y;
	elseif (z <= 270000000.0)
		tmp = x / (1.0 - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -20500.0], t$95$1, If[LessEqual[z, -7e-83], N[(N[(z / y), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-166], x, If[LessEqual[z, 1.9e-127], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 270000000.0], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -20500 or 2.7e8 < z

   1. Initial program 46.6%

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

   2. Taylor expanded in z around inf 80.0%

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

   if -20500 < z < -7.00000000000000061e-83

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. times-frac 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   if -7.00000000000000061e-83 < z < 4.00000000000000016e-166

   1. Initial program 90.8%

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

   2. Taylor expanded in z around 0 62.2%

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

   if 4.00000000000000016e-166 < z < 1.90000000000000001e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.4%

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

   3. Taylor expanded in z around 0 78.6%

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

   if 1.90000000000000001e-127 < z < 2.7e8

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

   4. Simplified 52.3%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -20500:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-83}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 270000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 14: 63.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 270000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.65e-77)
     t_1
     (if (<= z 4e-166)
       x
       (if (<= z 1.75e-127)
         (/ (* z (- t a)) y)
         (if (<= z 270000000.0) (/ x (- 1.0 z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.65e-77) {
		tmp = t_1;
	} else if (z <= 4e-166) {
		tmp = x;
	} else if (z <= 1.75e-127) {
		tmp = (z * (t - a)) / y;
	} else if (z <= 270000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.65d-77)) then
        tmp = t_1
    else if (z <= 4d-166) then
        tmp = x
    else if (z <= 1.75d-127) then
        tmp = (z * (t - a)) / y
    else if (z <= 270000000.0d0) then
        tmp = x / (1.0d0 - 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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.65e-77) {
		tmp = t_1;
	} else if (z <= 4e-166) {
		tmp = x;
	} else if (z <= 1.75e-127) {
		tmp = (z * (t - a)) / y;
	} else if (z <= 270000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.65e-77:
		tmp = t_1
	elif z <= 4e-166:
		tmp = x
	elif z <= 1.75e-127:
		tmp = (z * (t - a)) / y
	elif z <= 270000000.0:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.65e-77)
		tmp = t_1;
	elseif (z <= 4e-166)
		tmp = x;
	elseif (z <= 1.75e-127)
		tmp = Float64(Float64(z * Float64(t - a)) / y);
	elseif (z <= 270000000.0)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.65e-77)
		tmp = t_1;
	elseif (z <= 4e-166)
		tmp = x;
	elseif (z <= 1.75e-127)
		tmp = (z * (t - a)) / y;
	elseif (z <= 270000000.0)
		tmp = x / (1.0 - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.65e-77], t$95$1, If[LessEqual[z, 4e-166], x, If[LessEqual[z, 1.75e-127], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 270000000.0], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.65000000000000007e-77 or 2.7e8 < z

   1. Initial program 50.0%

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

   2. Taylor expanded in z around inf 75.2%

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

   if -2.65000000000000007e-77 < z < 4.00000000000000016e-166

   1. Initial program 90.8%

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

   2. Taylor expanded in z around 0 62.2%

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

   if 4.00000000000000016e-166 < z < 1.74999999999999995e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.4%

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

   3. Taylor expanded in z around 0 78.6%

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

   if 1.74999999999999995e-127 < z < 2.7e8

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

   4. Simplified 52.3%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-77}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 270000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 15: 53.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+193} \lor \neg \left(y \leq 2.3 \cdot 10^{+223}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.95e-30)
     t_1
     (if (<= y 2.9e-47)
       (/ (- t a) b)
       (if (or (<= y 6.2e+193) (not (<= y 2.3e+223))) t_1 (/ t (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.95e-30) {
		tmp = t_1;
	} else if (y <= 2.9e-47) {
		tmp = (t - a) / b;
	} else if ((y <= 6.2e+193) || !(y <= 2.3e+223)) {
		tmp = t_1;
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-2.95d-30)) then
        tmp = t_1
    else if (y <= 2.9d-47) then
        tmp = (t - a) / b
    else if ((y <= 6.2d+193) .or. (.not. (y <= 2.3d+223))) then
        tmp = t_1
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.95e-30) {
		tmp = t_1;
	} else if (y <= 2.9e-47) {
		tmp = (t - a) / b;
	} else if ((y <= 6.2e+193) || !(y <= 2.3e+223)) {
		tmp = t_1;
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -2.95e-30:
		tmp = t_1
	elif y <= 2.9e-47:
		tmp = (t - a) / b
	elif (y <= 6.2e+193) or not (y <= 2.3e+223):
		tmp = t_1
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.95e-30)
		tmp = t_1;
	elseif (y <= 2.9e-47)
		tmp = Float64(Float64(t - a) / b);
	elseif ((y <= 6.2e+193) || !(y <= 2.3e+223))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.95e-30)
		tmp = t_1;
	elseif (y <= 2.9e-47)
		tmp = (t - a) / b;
	elseif ((y <= 6.2e+193) || ~((y <= 2.3e+223)))
		tmp = t_1;
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.95e-30], t$95$1, If[LessEqual[y, 2.9e-47], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[y, 6.2e+193], N[Not[LessEqual[y, 2.3e+223]], $MachinePrecision]], t$95$1, N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9499999999999999e-30 or 2.9e-47 < y < 6.19999999999999972e193 or 2.30000000000000004e223 < y

   1. Initial program 56.6%

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

   2. Taylor expanded in y around inf 47.5%

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

      1. mul-1-neg 47.5%

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

      2. unsub-neg 47.5%

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

   4. Simplified 47.5%

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

   if -2.9499999999999999e-30 < y < 2.9e-47

   1. Initial program 83.2%

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

   2. Taylor expanded in y around 0 58.9%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]

   if 6.19999999999999972e193 < y < 2.30000000000000004e223

   1. Initial program 51.8%

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

   2. Taylor expanded in t around inf 50.6%

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

      1. associate-/l* 39.8%

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

      2. +-commutative 39.8%

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

      3. fma-def 39.6%

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

   4. Simplified 39.6%

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

   5. Taylor expanded in z around inf 67.2%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+193} \lor \neg \left(y \leq 2.3 \cdot 10^{+223}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 16: 35.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{y}\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -13000000:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.082:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t) y)))
   (if (<= z -1.56e+236)
     t_1
     (if (<= z -13000000.0) (/ t b) (if (<= z 0.082) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t / y;
	double tmp;
	if (z <= -1.56e+236) {
		tmp = t_1;
	} else if (z <= -13000000.0) {
		tmp = t / b;
	} else if (z <= 0.082) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / y
    if (z <= (-1.56d+236)) then
        tmp = t_1
    else if (z <= (-13000000.0d0)) then
        tmp = t / b
    else if (z <= 0.082d0) then
        tmp = x
    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 b) {
	double t_1 = -t / y;
	double tmp;
	if (z <= -1.56e+236) {
		tmp = t_1;
	} else if (z <= -13000000.0) {
		tmp = t / b;
	} else if (z <= 0.082) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t / y
	tmp = 0
	if z <= -1.56e+236:
		tmp = t_1
	elif z <= -13000000.0:
		tmp = t / b
	elif z <= 0.082:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) / y)
	tmp = 0.0
	if (z <= -1.56e+236)
		tmp = t_1;
	elseif (z <= -13000000.0)
		tmp = Float64(t / b);
	elseif (z <= 0.082)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t / y;
	tmp = 0.0;
	if (z <= -1.56e+236)
		tmp = t_1;
	elseif (z <= -13000000.0)
		tmp = t / b;
	elseif (z <= 0.082)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) / y), $MachinePrecision]}, If[LessEqual[z, -1.56e+236], t$95$1, If[LessEqual[z, -13000000.0], N[(t / b), $MachinePrecision], If[LessEqual[z, 0.082], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5600000000000001e236 or 0.0820000000000000034 < z

   1. Initial program 37.6%

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

   2. Taylor expanded in t around inf 18.7%

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

      1. associate-/l* 23.6%

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

      2. +-commutative 23.6%

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

      3. fma-def 23.6%

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

   4. Simplified 23.6%

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

   5. Taylor expanded in b around 0 17.4%

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

      1. mul-1-neg 17.4%

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

      2. *-rgt-identity 17.4%

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

      3. distribute-rgt-neg-in 17.4%

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

      4. mul-1-neg 17.4%

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

      5. distribute-lft-in 17.4%

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

      6. times-frac 27.0%

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

      7. mul-1-neg 27.0%

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

      8. unsub-neg 27.0%

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

   7. Simplified 27.0%

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

   8. Taylor expanded in z around inf 27.0%

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

      1. associate-*r/ 27.0%

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

      2. neg-mul-1 27.0%

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

   10. Simplified 27.0%

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

   if -1.5600000000000001e236 < z < -1.3e7

   1. Initial program 64.2%

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

   2. Taylor expanded in t around inf 42.9%

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

      1. associate-/l* 43.2%

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

      2. +-commutative 43.2%

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

      3. fma-def 43.2%

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

   4. Simplified 43.2%

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

   5. Taylor expanded in b around inf 35.2%

      \[\leadsto \frac{t}{\color{blue}{b}} \]

   if -1.3e7 < z < 0.0820000000000000034

   1. Initial program 87.0%

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

   2. Taylor expanded in z around 0 51.3%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+236}:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{elif}\;z \leq -13000000:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.082:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \]

Alternative 17: 45.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-33} \lor \neg \left(z \leq 6.2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7e-33) (not (<= z 6.2e-6))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e-33) || !(z <= 6.2e-6)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7d-33)) .or. (.not. (z <= 6.2d-6))) then
        tmp = t / (b - y)
    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 b) {
	double tmp;
	if ((z <= -7e-33) || !(z <= 6.2e-6)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7e-33) or not (z <= 6.2e-6):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7e-33) || !(z <= 6.2e-6))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7e-33) || ~((z <= 6.2e-6)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7e-33], N[Not[LessEqual[z, 6.2e-6]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999997e-33 or 6.1999999999999999e-6 < z

   1. Initial program 50.0%

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

   2. Taylor expanded in t around inf 28.5%

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

      1. associate-/l* 31.4%

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

      2. +-commutative 31.4%

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

      3. fma-def 31.4%

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

   4. Simplified 31.4%

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

   5. Taylor expanded in z around inf 40.2%

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   if -6.9999999999999997e-33 < z < 6.1999999999999999e-6

   1. Initial program 87.2%

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

   2. Taylor expanded in z around 0 54.2%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-33} \lor \neg \left(z \leq 6.2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 42.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+129} \lor \neg \left(t \leq 3.5 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.8e+129) (not (<= t 3.5e+138)))
   (/ t (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.8e+129) || !(t <= 3.5e+138)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.8d+129)) .or. (.not. (t <= 3.5d+138))) then
        tmp = t / (b - y)
    else
        tmp = x / (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 b) {
	double tmp;
	if ((t <= -2.8e+129) || !(t <= 3.5e+138)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.8e+129) or not (t <= 3.5e+138):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.8e+129) || !(t <= 3.5e+138))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.8e+129) || ~((t <= 3.5e+138)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.8e+129], N[Not[LessEqual[t, 3.5e+138]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999975e129 or 3.4999999999999998e138 < t

   1. Initial program 70.7%

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

   2. Taylor expanded in t around inf 54.6%

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

      1. associate-/l* 55.9%

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

      2. +-commutative 55.9%

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

      3. fma-def 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in z around inf 61.2%

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   if -2.79999999999999975e129 < t < 3.4999999999999998e138

   1. Initial program 64.4%

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

   2. Taylor expanded in y around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. unsub-neg 40.3%

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

   4. Simplified 40.3%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+129} \lor \neg \left(t \leq 3.5 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 19: 37.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -57000000:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 12.8:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -57000000.0) (/ t b) (if (<= z 12.8) x (/ (- a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -57000000.0) {
		tmp = t / b;
	} else if (z <= 12.8) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-57000000.0d0)) then
        tmp = t / b
    else if (z <= 12.8d0) then
        tmp = x
    else
        tmp = -a / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -57000000.0) {
		tmp = t / b;
	} else if (z <= 12.8) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -57000000.0:
		tmp = t / b
	elif z <= 12.8:
		tmp = x
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -57000000.0)
		tmp = Float64(t / b);
	elseif (z <= 12.8)
		tmp = x;
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -57000000.0)
		tmp = t / b;
	elseif (z <= 12.8)
		tmp = x;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -57000000.0], N[(t / b), $MachinePrecision], If[LessEqual[z, 12.8], x, N[((-a) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7e7

   1. Initial program 55.5%

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

   2. Taylor expanded in t around inf 35.4%

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

      1. associate-/l* 38.1%

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

      2. +-commutative 38.1%

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

      3. fma-def 38.1%

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

   4. Simplified 38.1%

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

   5. Taylor expanded in b around inf 28.7%

      \[\leadsto \frac{t}{\color{blue}{b}} \]

   if -5.7e7 < z < 12.800000000000001

   1. Initial program 87.1%

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

   2. Taylor expanded in z around 0 50.9%

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

   if 12.800000000000001 < z

   1. Initial program 38.0%

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

   2. Taylor expanded in b around inf 10.5%

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

   3. Taylor expanded in a around inf 14.3%

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

      1. associate-*r/ 14.3%

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

      2. neg-mul-1 14.3%

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

   5. Simplified 14.3%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -57000000:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 12.8:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 20: 36.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13000000 \lor \neg \left(z \leq 1.35 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -13000000.0) (not (<= z 1.35e+44))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -13000000.0) || !(z <= 1.35e+44)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-13000000.0d0)) .or. (.not. (z <= 1.35d+44))) then
        tmp = t / b
    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 b) {
	double tmp;
	if ((z <= -13000000.0) || !(z <= 1.35e+44)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -13000000.0) or not (z <= 1.35e+44):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -13000000.0) || !(z <= 1.35e+44))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -13000000.0) || ~((z <= 1.35e+44)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -13000000.0], N[Not[LessEqual[z, 1.35e+44]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e7 or 1.35e44 < z

   1. Initial program 46.1%

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

   2. Taylor expanded in t around inf 29.2%

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

      1. associate-/l* 32.5%

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

      2. +-commutative 32.5%

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

      3. fma-def 32.5%

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

   4. Simplified 32.5%

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

   5. Taylor expanded in b around inf 22.7%

      \[\leadsto \frac{t}{\color{blue}{b}} \]

   if -1.3e7 < z < 1.35e44

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0 47.9%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13000000 \lor \neg \left(z \leq 1.35 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 25.5% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.1%

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

2. Taylor expanded in z around 0 25.4%

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

3. Final simplification 25.4%

   \[\leadsto x \]

Developer target: 73.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))