Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.6% → 90.4%

Time: 18.3s

Alternatives: 17

Speedup: 1.0×

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: 66.6% 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: 90.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \left(t\_3 + \frac{y}{z} \cdot \frac{x}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 10^{+308}:\\ \;\;\;\;\left(\frac{z \cdot t}{t\_1} + \frac{x \cdot y}{t\_1}\right) - \frac{z \cdot a}{t\_1}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} - \frac{z \cdot \frac{t - a}{z + -1} + \frac{z \cdot \left(x \cdot b\right)}{{\left(z + -1\right)}^{2}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3 (/ (- t a) (- b y)))
        (t_4
         (+
          (+ t_3 (* (/ y z) (/ x (- b y))))
          (* y (/ (- a t) (* z (pow (- b y) 2.0)))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-205)
       (/ (+ (* x y) (- (* z t) (* z a))) t_1)
       (if (<= t_2 0.0)
         t_4
         (if (<= t_2 1e+308)
           (- (+ (/ (* z t) t_1) (/ (* x y) t_1)) (/ (* z a) t_1))
           (if (<= t_2 INFINITY)
             (-
              (/ x (- 1.0 z))
              (/
               (+
                (* z (/ (- t a) (+ z -1.0)))
                (/ (* z (* x b)) (pow (+ z -1.0) 2.0)))
               y))
             t_4)))))))

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 * y) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = (t_3 + ((y / z) * (x / (b - y)))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-205) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_4;
	} else if (t_2 <= 1e+308) {
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / pow((z + -1.0), 2.0))) / y);
	} else {
		tmp = t_4;
	}
	return tmp;
}

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 * y) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = (t_3 + ((y / z) * (x / (b - y)))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-205) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_4;
	} else if (t_2 <= 1e+308) {
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / Math.pow((z + -1.0), 2.0))) / y);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	t_3 = (t - a) / (b - y)
	t_4 = (t_3 + ((y / z) * (x / (b - y)))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-205:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	elif t_2 <= 0.0:
		tmp = t_4
	elif t_2 <= 1e+308:
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1)
	elif t_2 <= math.inf:
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / math.pow((z + -1.0), 2.0))) / y)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(Float64(t_3 + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-205)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = t_4;
	elseif (t_2 <= 1e+308)
		tmp = Float64(Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(x * y) / t_1)) - Float64(Float64(z * a) / t_1));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(x / Float64(1.0 - z)) - Float64(Float64(Float64(z * Float64(Float64(t - a) / Float64(z + -1.0))) + Float64(Float64(z * Float64(x * b)) / (Float64(z + -1.0) ^ 2.0))) / y));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((x * y) + (z * (t - a))) / t_1;
	t_3 = (t - a) / (b - y);
	t_4 = (t_3 + ((y / z) * (x / (b - y)))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-205)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = t_4;
	elseif (t_2 <= 1e+308)
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	elseif (t_2 <= Inf)
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / ((z + -1.0) ^ 2.0))) / y);
	else
		tmp = t_4;
	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[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-205], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], t$95$4, If[LessEqual[t$95$2, 1e+308], N[(N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * N[(N[(t - a), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(x * b), $MachinePrecision]), $MachinePrecision] / N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 27.3%

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

   3. Taylor expanded in z around inf 58.5%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-205

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.7%

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

   4. Applied egg-rr 99.7%

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

   if -2e-205 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 9.9%

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

   3. Taylor expanded in z around inf 54.3%

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

      1. associate--r+ 54.3%

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

      2. +-commutative 54.3%

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

      3. associate--l+ 54.3%

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

      4. *-commutative 54.3%

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

      5. times-frac 61.3%

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

      6. div-sub 61.3%

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

      7. associate-/l* 98.4%

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

   5. Simplified 98.4%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e308

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 99.6%

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

   if 1e308 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 21.9%

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

   3. Taylor expanded in x around 0 21.9%

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

   4. Taylor expanded in y around -inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

      3. associate-*r/ 65.1%

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

      4. mul-1-neg 65.1%

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

      5. sub-neg 65.1%

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

      6. metadata-eval 65.1%

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

   6. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{-x}{z + -1} - \frac{z \cdot \frac{t - a}{z + -1} + \frac{\left(b \cdot x\right) \cdot z}{{\left(z + -1\right)}^{2}}}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+308}:\\ \;\;\;\;\left(\frac{z \cdot t}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\right) - \frac{z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} - \frac{z \cdot \frac{t - a}{z + -1} + \frac{z \cdot \left(x \cdot b\right)}{{\left(z + -1\right)}^{2}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+308}:\\ \;\;\;\;\left(\frac{z \cdot t}{t\_1} + \frac{x \cdot y}{t\_1}\right) - \frac{z \cdot a}{t\_1}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} - \frac{z \cdot \frac{t - a}{z + -1} + \frac{z \cdot \left(x \cdot b\right)}{{\left(z + -1\right)}^{2}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3 (/ (- t a) (- b y))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-205)
       (/ (+ (* x y) (- (* z t) (* z a))) t_1)
       (if (<= t_2 0.0)
         t_3
         (if (<= t_2 1e+308)
           (- (+ (/ (* z t) t_1) (/ (* x y) t_1)) (/ (* z a) t_1))
           (if (<= t_2 INFINITY)
             (-
              (/ x (- 1.0 z))
              (/
               (+
                (* z (/ (- t a) (+ z -1.0)))
                (/ (* z (* x b)) (pow (+ z -1.0) 2.0)))
               y))
             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 * y) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-205) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_3;
	} else if (t_2 <= 1e+308) {
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / pow((z + -1.0), 2.0))) / y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

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 * y) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-205) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_3;
	} else if (t_2 <= 1e+308) {
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / Math.pow((z + -1.0), 2.0))) / y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	t_3 = (t - a) / (b - y)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-205:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	elif t_2 <= 0.0:
		tmp = t_3
	elif t_2 <= 1e+308:
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1)
	elif t_2 <= math.inf:
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / math.pow((z + -1.0), 2.0))) / y)
	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(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-205)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = t_3;
	elseif (t_2 <= 1e+308)
		tmp = Float64(Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(x * y) / t_1)) - Float64(Float64(z * a) / t_1));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(x / Float64(1.0 - z)) - Float64(Float64(Float64(z * Float64(Float64(t - a) / Float64(z + -1.0))) + Float64(Float64(z * Float64(x * b)) / (Float64(z + -1.0) ^ 2.0))) / y));
	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 * y) + (z * (t - a))) / t_1;
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-205)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = t_3;
	elseif (t_2 <= 1e+308)
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	elseif (t_2 <= Inf)
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / ((z + -1.0) ^ 2.0))) / y);
	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[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-205], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], t$95$3, If[LessEqual[t$95$2, 1e+308], N[(N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * N[(N[(t - a), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(x * b), $MachinePrecision]), $MachinePrecision] / N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

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)))) < -inf.0 or -2e-205 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.1%

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

   3. Taylor expanded in z around inf 78.5%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-205

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.7%

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

   4. Applied egg-rr 99.7%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e308

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 99.6%

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

   if 1e308 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 21.9%

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

   3. Taylor expanded in x around 0 21.9%

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

   4. Taylor expanded in y around -inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

      3. associate-*r/ 65.1%

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

      4. mul-1-neg 65.1%

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

      5. sub-neg 65.1%

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

      6. metadata-eval 65.1%

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

   6. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{-x}{z + -1} - \frac{z \cdot \frac{t - a}{z + -1} + \frac{\left(b \cdot x\right) \cdot z}{{\left(z + -1\right)}^{2}}}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+308}:\\ \;\;\;\;\left(\frac{z \cdot t}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\right) - \frac{z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} - \frac{z \cdot \frac{t - a}{z + -1} + \frac{z \cdot \left(x \cdot b\right)}{{\left(z + -1\right)}^{2}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-278}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 140000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (- (* z t) (* z a))) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -7.2e+58)
     t_2
     (if (<= z -4.5e-187)
       t_1
       (if (<= z -2.65e-278)
         (+ x (* t (/ z y)))
         (if (<= z 140000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.2e+58) {
		tmp = t_2;
	} else if (z <= -4.5e-187) {
		tmp = t_1;
	} else if (z <= -2.65e-278) {
		tmp = x + (t * (z / y));
	} else if (z <= 140000000000.0) {
		tmp = t_1;
	} 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 = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-7.2d+58)) then
        tmp = t_2
    else if (z <= (-4.5d-187)) then
        tmp = t_1
    else if (z <= (-2.65d-278)) then
        tmp = x + (t * (z / y))
    else if (z <= 140000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.2e+58) {
		tmp = t_2;
	} else if (z <= -4.5e-187) {
		tmp = t_1;
	} else if (z <= -2.65e-278) {
		tmp = x + (t * (z / y));
	} else if (z <= 140000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.2e+58:
		tmp = t_2
	elif z <= -4.5e-187:
		tmp = t_1
	elif z <= -2.65e-278:
		tmp = x + (t * (z / y))
	elif z <= 140000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.2e+58)
		tmp = t_2;
	elseif (z <= -4.5e-187)
		tmp = t_1;
	elseif (z <= -2.65e-278)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (z <= 140000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.2e+58)
		tmp = t_2;
	elseif (z <= -4.5e-187)
		tmp = t_1;
	elseif (z <= -2.65e-278)
		tmp = x + (t * (z / y));
	elseif (z <= 140000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * 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]}, If[LessEqual[z, -7.2e+58], t$95$2, If[LessEqual[z, -4.5e-187], t$95$1, If[LessEqual[z, -2.65e-278], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 140000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999993e58 or 1.4e11 < z

   1. Initial program 34.3%

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

   3. Taylor expanded in z around inf 88.2%

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

   if -7.19999999999999993e58 < z < -4.4999999999999998e-187 or -2.65e-278 < z < 1.4e11

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. distribute-lft-in 86.8%

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

   4. Applied egg-rr 86.8%

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

   if -4.4999999999999998e-187 < z < -2.65e-278

   1. Initial program 54.7%

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

   3. Taylor expanded in z around 0 29.8%

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

      1. *-commutative 29.8%

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

   5. Simplified 29.8%

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

   6. Taylor expanded in t around inf 81.9%

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

      1. associate-/l* 82.1%

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

   8. Simplified 82.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-278}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 140000000000:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-277}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 140000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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))))
   (if (<= z -1.22e+59)
     t_2
     (if (<= z -4.5e-187)
       t_1
       (if (<= z -1.4e-277)
         (+ x (* t (/ z y)))
         (if (<= z 140000000000.0) t_1 t_2))))))

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 tmp;
	if (z <= -1.22e+59) {
		tmp = t_2;
	} else if (z <= -4.5e-187) {
		tmp = t_1;
	} else if (z <= -1.4e-277) {
		tmp = x + (t * (z / y));
	} else if (z <= 140000000000.0) {
		tmp = t_1;
	} 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 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.22d+59)) then
        tmp = t_2
    else if (z <= (-4.5d-187)) then
        tmp = t_1
    else if (z <= (-1.4d-277)) then
        tmp = x + (t * (z / y))
    else if (z <= 140000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.22e+59) {
		tmp = t_2;
	} else if (z <= -4.5e-187) {
		tmp = t_1;
	} else if (z <= -1.4e-277) {
		tmp = x + (t * (z / y));
	} else if (z <= 140000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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)
	tmp = 0
	if z <= -1.22e+59:
		tmp = t_2
	elif z <= -4.5e-187:
		tmp = t_1
	elif z <= -1.4e-277:
		tmp = x + (t * (z / y))
	elif z <= 140000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	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))
	tmp = 0.0
	if (z <= -1.22e+59)
		tmp = t_2;
	elseif (z <= -4.5e-187)
		tmp = t_1;
	elseif (z <= -1.4e-277)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (z <= 140000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	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);
	tmp = 0.0;
	if (z <= -1.22e+59)
		tmp = t_2;
	elseif (z <= -4.5e-187)
		tmp = t_1;
	elseif (z <= -1.4e-277)
		tmp = x + (t * (z / y));
	elseif (z <= 140000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, If[LessEqual[z, -1.22e+59], t$95$2, If[LessEqual[z, -4.5e-187], t$95$1, If[LessEqual[z, -1.4e-277], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 140000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.22e59 or 1.4e11 < z

   1. Initial program 34.3%

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

   3. Taylor expanded in z around inf 88.2%

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

   if -1.22e59 < z < -4.4999999999999998e-187 or -1.39999999999999988e-277 < z < 1.4e11

   1. Initial program 86.8%

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

   if -4.4999999999999998e-187 < z < -1.39999999999999988e-277

   1. Initial program 54.7%

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

   3. Taylor expanded in z around 0 29.8%

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

      1. *-commutative 29.8%

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

   5. Simplified 29.8%

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

   6. Taylor expanded in t around inf 81.9%

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

      1. associate-/l* 82.1%

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

   8. Simplified 82.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-277}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 140000000000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot t}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-146}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z t) y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -9.5e-28)
     t_2
     (if (<= z 7.5e-232)
       t_1
       (if (<= z 9e-146) (- x (* z (/ a y))) (if (<= z 1.16e-36) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((z * t) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e-28) {
		tmp = t_2;
	} else if (z <= 7.5e-232) {
		tmp = t_1;
	} else if (z <= 9e-146) {
		tmp = x - (z * (a / y));
	} else if (z <= 1.16e-36) {
		tmp = t_1;
	} 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 = x + ((z * t) / y)
    t_2 = (t - a) / (b - y)
    if (z <= (-9.5d-28)) then
        tmp = t_2
    else if (z <= 7.5d-232) then
        tmp = t_1
    else if (z <= 9d-146) then
        tmp = x - (z * (a / y))
    else if (z <= 1.16d-36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((z * t) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e-28) {
		tmp = t_2;
	} else if (z <= 7.5e-232) {
		tmp = t_1;
	} else if (z <= 9e-146) {
		tmp = x - (z * (a / y));
	} else if (z <= 1.16e-36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((z * t) / y)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -9.5e-28:
		tmp = t_2
	elif z <= 7.5e-232:
		tmp = t_1
	elif z <= 9e-146:
		tmp = x - (z * (a / y))
	elif z <= 1.16e-36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(z * t) / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -9.5e-28)
		tmp = t_2;
	elseif (z <= 7.5e-232)
		tmp = t_1;
	elseif (z <= 9e-146)
		tmp = Float64(x - Float64(z * Float64(a / y)));
	elseif (z <= 1.16e-36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((z * t) / y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -9.5e-28)
		tmp = t_2;
	elseif (z <= 7.5e-232)
		tmp = t_1;
	elseif (z <= 9e-146)
		tmp = x - (z * (a / y));
	elseif (z <= 1.16e-36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-28], t$95$2, If[LessEqual[z, 7.5e-232], t$95$1, If[LessEqual[z, 9e-146], N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e-36], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.50000000000000001e-28 or 1.16000000000000002e-36 < z

   1. Initial program 43.6%

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

   3. Taylor expanded in z around inf 81.3%

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

   if -9.50000000000000001e-28 < z < 7.5000000000000006e-232 or 9.0000000000000001e-146 < z < 1.16000000000000002e-36

   1. Initial program 79.5%

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

   3. Taylor expanded in z around 0 46.0%

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

      1. *-commutative 46.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in t around inf 63.9%

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

   if 7.5000000000000006e-232 < z < 9.0000000000000001e-146

   1. Initial program 83.0%

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

   3. Taylor expanded in z around 0 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in a around inf 60.8%

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

      1. associate-*r/ 60.8%

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

      2. neg-mul-1 60.8%

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

   8. Simplified 60.8%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-232}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-146}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+23}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.8e-22)
     t_2
     (if (<= y 1.25e-17)
       t_1
       (if (<= y 8.2e+23) (+ x (* t (/ z y))) (if (<= y 2.95e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.8e-22) {
		tmp = t_2;
	} else if (y <= 1.25e-17) {
		tmp = t_1;
	} else if (y <= 8.2e+23) {
		tmp = x + (t * (z / y));
	} else if (y <= 2.95e+68) {
		tmp = t_1;
	} 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 = (t - a) / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.8d-22)) then
        tmp = t_2
    else if (y <= 1.25d-17) then
        tmp = t_1
    else if (y <= 8.2d+23) then
        tmp = x + (t * (z / y))
    else if (y <= 2.95d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.8e-22) {
		tmp = t_2;
	} else if (y <= 1.25e-17) {
		tmp = t_1;
	} else if (y <= 8.2e+23) {
		tmp = x + (t * (z / y));
	} else if (y <= 2.95e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.8e-22:
		tmp = t_2
	elif y <= 1.25e-17:
		tmp = t_1
	elif y <= 8.2e+23:
		tmp = x + (t * (z / y))
	elif y <= 2.95e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.8e-22)
		tmp = t_2;
	elseif (y <= 1.25e-17)
		tmp = t_1;
	elseif (y <= 8.2e+23)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (y <= 2.95e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.8e-22)
		tmp = t_2;
	elseif (y <= 1.25e-17)
		tmp = t_1;
	elseif (y <= 8.2e+23)
		tmp = x + (t * (z / y));
	elseif (y <= 2.95e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e-22], t$95$2, If[LessEqual[y, 1.25e-17], t$95$1, If[LessEqual[y, 8.2e+23], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999995e-22 or 2.94999999999999993e68 < y

   1. Initial program 46.1%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   if -2.79999999999999995e-22 < y < 1.25e-17 or 8.19999999999999992e23 < y < 2.94999999999999993e68

   1. Initial program 74.1%

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

   3. Taylor expanded in y around 0 60.4%

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

   if 1.25e-17 < y < 8.19999999999999992e23

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in t around inf 61.3%

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

      1. associate-/l* 61.3%

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

   8. Simplified 61.3%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+23}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+68}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+23}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -3.5e-22)
     t_2
     (if (<= y 3.3e-13)
       t_1
       (if (<= y 9.8e+23) (+ x (* z (/ t y))) (if (<= y 3e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -3.5e-22) {
		tmp = t_2;
	} else if (y <= 3.3e-13) {
		tmp = t_1;
	} else if (y <= 9.8e+23) {
		tmp = x + (z * (t / y));
	} else if (y <= 3e+68) {
		tmp = t_1;
	} 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 = (t - a) / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-3.5d-22)) then
        tmp = t_2
    else if (y <= 3.3d-13) then
        tmp = t_1
    else if (y <= 9.8d+23) then
        tmp = x + (z * (t / y))
    else if (y <= 3d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -3.5e-22) {
		tmp = t_2;
	} else if (y <= 3.3e-13) {
		tmp = t_1;
	} else if (y <= 9.8e+23) {
		tmp = x + (z * (t / y));
	} else if (y <= 3e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -3.5e-22:
		tmp = t_2
	elif y <= 3.3e-13:
		tmp = t_1
	elif y <= 9.8e+23:
		tmp = x + (z * (t / y))
	elif y <= 3e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.5e-22)
		tmp = t_2;
	elseif (y <= 3.3e-13)
		tmp = t_1;
	elseif (y <= 9.8e+23)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (y <= 3e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.5e-22)
		tmp = t_2;
	elseif (y <= 3.3e-13)
		tmp = t_1;
	elseif (y <= 9.8e+23)
		tmp = x + (z * (t / y));
	elseif (y <= 3e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-22], t$95$2, If[LessEqual[y, 3.3e-13], t$95$1, If[LessEqual[y, 9.8e+23], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000005e-22 or 3.0000000000000002e68 < y

   1. Initial program 46.1%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   if -3.50000000000000005e-22 < y < 3.3000000000000001e-13 or 9.8000000000000006e23 < y < 3.0000000000000002e68

   1. Initial program 74.1%

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

   3. Taylor expanded in y around 0 60.4%

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

   if 3.3000000000000001e-13 < y < 9.8000000000000006e23

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in t around inf 61.3%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+23}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+68}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;y \leq 4.05 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -3.5e-22)
     t_2
     (if (<= y 7.6e-23)
       t_1
       (if (<= y 2.4e+23) (/ (* z (- t a)) y) (if (<= y 4.05e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -3.5e-22) {
		tmp = t_2;
	} else if (y <= 7.6e-23) {
		tmp = t_1;
	} else if (y <= 2.4e+23) {
		tmp = (z * (t - a)) / y;
	} else if (y <= 4.05e+68) {
		tmp = t_1;
	} 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 = (t - a) / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-3.5d-22)) then
        tmp = t_2
    else if (y <= 7.6d-23) then
        tmp = t_1
    else if (y <= 2.4d+23) then
        tmp = (z * (t - a)) / y
    else if (y <= 4.05d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -3.5e-22) {
		tmp = t_2;
	} else if (y <= 7.6e-23) {
		tmp = t_1;
	} else if (y <= 2.4e+23) {
		tmp = (z * (t - a)) / y;
	} else if (y <= 4.05e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -3.5e-22:
		tmp = t_2
	elif y <= 7.6e-23:
		tmp = t_1
	elif y <= 2.4e+23:
		tmp = (z * (t - a)) / y
	elif y <= 4.05e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.5e-22)
		tmp = t_2;
	elseif (y <= 7.6e-23)
		tmp = t_1;
	elseif (y <= 2.4e+23)
		tmp = Float64(Float64(z * Float64(t - a)) / y);
	elseif (y <= 4.05e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.5e-22)
		tmp = t_2;
	elseif (y <= 7.6e-23)
		tmp = t_1;
	elseif (y <= 2.4e+23)
		tmp = (z * (t - a)) / y;
	elseif (y <= 4.05e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-22], t$95$2, If[LessEqual[y, 7.6e-23], t$95$1, If[LessEqual[y, 2.4e+23], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 4.05e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000005e-22 or 4.0500000000000001e68 < y

   1. Initial program 46.1%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   if -3.50000000000000005e-22 < y < 7.60000000000000023e-23 or 2.4e23 < y < 4.0500000000000001e68

   1. Initial program 73.9%

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

   3. Taylor expanded in y around 0 60.8%

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

   if 7.60000000000000023e-23 < y < 2.4e23

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 78.1%

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

   4. Taylor expanded in x around 0 63.6%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;y \leq 4.05 \cdot 10^{+68}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-246}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-55}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.4e-29)
     t_1
     (if (<= z -4.8e-246)
       (+ x (/ (* z t) y))
       (if (<= z 1.75e-55) (- x (/ (* z a) y)) 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 <= -2.4e-29) {
		tmp = t_1;
	} else if (z <= -4.8e-246) {
		tmp = x + ((z * t) / y);
	} else if (z <= 1.75e-55) {
		tmp = x - ((z * a) / y);
	} 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 <= (-2.4d-29)) then
        tmp = t_1
    else if (z <= (-4.8d-246)) then
        tmp = x + ((z * t) / y)
    else if (z <= 1.75d-55) then
        tmp = x - ((z * a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.4e-29) {
		tmp = t_1;
	} else if (z <= -4.8e-246) {
		tmp = x + ((z * t) / y);
	} else if (z <= 1.75e-55) {
		tmp = x - ((z * a) / y);
	} 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 <= -2.4e-29:
		tmp = t_1
	elif z <= -4.8e-246:
		tmp = x + ((z * t) / y)
	elif z <= 1.75e-55:
		tmp = x - ((z * a) / y)
	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 <= -2.4e-29)
		tmp = t_1;
	elseif (z <= -4.8e-246)
		tmp = Float64(x + Float64(Float64(z * t) / y));
	elseif (z <= 1.75e-55)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	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 <= -2.4e-29)
		tmp = t_1;
	elseif (z <= -4.8e-246)
		tmp = x + ((z * t) / y);
	elseif (z <= 1.75e-55)
		tmp = x - ((z * a) / y);
	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, -2.4e-29], t$95$1, If[LessEqual[z, -4.8e-246], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-55], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999992e-29 or 1.75000000000000013e-55 < z

   1. Initial program 45.2%

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

   3. Taylor expanded in z around inf 79.7%

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

   if -2.39999999999999992e-29 < z < -4.7999999999999996e-246

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 52.5%

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

      1. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in t around inf 63.9%

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

   if -4.7999999999999996e-246 < z < 1.75000000000000013e-55

   1. Initial program 77.8%

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

   3. Taylor expanded in z around 0 40.7%

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

      1. *-commutative 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in a around inf 64.7%

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

      1. associate-*r/ 64.7%

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

      2. associate-*r* 64.7%

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

      3. neg-mul-1 64.7%

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

      4. *-commutative 64.7%

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

   8. Simplified 64.7%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-246}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-55}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-192}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-51}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.16e-28)
     t_1
     (if (<= z -1.65e-192)
       (/ (+ (* x y) (* z (- t a))) y)
       (if (<= z 1.25e-51) (- x (/ (* z a) y)) 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 <= -1.16e-28) {
		tmp = t_1;
	} else if (z <= -1.65e-192) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 1.25e-51) {
		tmp = x - ((z * a) / y);
	} 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 <= (-1.16d-28)) then
        tmp = t_1
    else if (z <= (-1.65d-192)) then
        tmp = ((x * y) + (z * (t - a))) / y
    else if (z <= 1.25d-51) then
        tmp = x - ((z * a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.16e-28) {
		tmp = t_1;
	} else if (z <= -1.65e-192) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 1.25e-51) {
		tmp = x - ((z * a) / y);
	} 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 <= -1.16e-28:
		tmp = t_1
	elif z <= -1.65e-192:
		tmp = ((x * y) + (z * (t - a))) / y
	elif z <= 1.25e-51:
		tmp = x - ((z * a) / y)
	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 <= -1.16e-28)
		tmp = t_1;
	elseif (z <= -1.65e-192)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	elseif (z <= 1.25e-51)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	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 <= -1.16e-28)
		tmp = t_1;
	elseif (z <= -1.65e-192)
		tmp = ((x * y) + (z * (t - a))) / y;
	elseif (z <= 1.25e-51)
		tmp = x - ((z * a) / y);
	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, -1.16e-28], t$95$1, If[LessEqual[z, -1.65e-192], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.25e-51], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1600000000000001e-28 or 1.25000000000000001e-51 < z

   1. Initial program 45.2%

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

   3. Taylor expanded in z around inf 79.7%

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

   if -1.1600000000000001e-28 < z < -1.64999999999999995e-192

   1. Initial program 92.1%

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

   3. Taylor expanded in z around 0 70.7%

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

   if -1.64999999999999995e-192 < z < 1.25000000000000001e-51

   1. Initial program 73.9%

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

   3. Taylor expanded in z around 0 39.1%

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

      1. *-commutative 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in a around inf 64.7%

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

      1. associate-*r/ 64.7%

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

      2. associate-*r* 64.7%

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

      3. neg-mul-1 64.7%

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

      4. *-commutative 64.7%

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

   8. Simplified 64.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-28}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-192}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-51}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-29} \lor \neg \left(z \leq 1.45 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e-29) (not (<= z 1.45e-38)))
   (/ (- t a) (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e-29) || !(z <= 1.45e-38)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / 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 <= (-4.5d-29)) .or. (.not. (z <= 1.45d-38))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * t) / 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 <= -4.5e-29) || !(z <= 1.45e-38)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.5e-29) or not (z <= 1.45e-38):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e-29) || !(z <= 1.45e-38))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.5e-29) || ~((z <= 1.45e-38)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e-29], N[Not[LessEqual[z, 1.45e-38]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e-29 or 1.44999999999999997e-38 < z

   1. Initial program 43.6%

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

   3. Taylor expanded in z around inf 81.3%

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

   if -4.4999999999999998e-29 < z < 1.44999999999999997e-38

   1. Initial program 80.1%

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

   3. Taylor expanded in z around 0 46.3%

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

      1. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in t around inf 59.5%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-29} \lor \neg \left(z \leq 1.45 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-157} \lor \neg \left(x \leq 2.3 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.45e-157) (not (<= x 2.3e-133)))
   (/ x (- 1.0 z))
   (* t (/ z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.45e-157) || !(x <= 2.3e-133)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t * (z / 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 ((x <= (-2.45d-157)) .or. (.not. (x <= 2.3d-133))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t * (z / 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 ((x <= -2.45e-157) || !(x <= 2.3e-133)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t * (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.45e-157) or not (x <= 2.3e-133):
		tmp = x / (1.0 - z)
	else:
		tmp = t * (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.45e-157) || !(x <= 2.3e-133))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t * Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -2.45e-157) || ~((x <= 2.3e-133)))
		tmp = x / (1.0 - z);
	else
		tmp = t * (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.45e-157], N[Not[LessEqual[x, 2.3e-133]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4499999999999999e-157 or 2.3e-133 < x

   1. Initial program 61.3%

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

   3. Taylor expanded in y around inf 38.2%

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

      1. mul-1-neg 38.2%

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

      2. unsub-neg 38.2%

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

   5. Simplified 38.2%

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

   if -2.4499999999999999e-157 < x < 2.3e-133

   1. Initial program 61.7%

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

   3. Taylor expanded in z around 0 38.0%

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

      1. *-commutative 38.0%

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

   5. Simplified 38.0%

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

   6. Taylor expanded in t around inf 22.1%

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

   7. Taylor expanded in x around 0 22.1%

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

      1. associate-*r/ 22.0%

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

   9. Simplified 22.0%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-157} \lor \neg \left(x \leq 2.3 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 33.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-160} \lor \neg \left(x \leq 2.2 \cdot 10^{-131}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -5.6e-160) (not (<= x 2.2e-131)))
   (/ x (- 1.0 z))
   (/ (* z t) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5.6e-160) || !(x <= 2.2e-131)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (z * t) / 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 ((x <= (-5.6d-160)) .or. (.not. (x <= 2.2d-131))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (z * t) / 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 ((x <= -5.6e-160) || !(x <= 2.2e-131)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (z * t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -5.6e-160) or not (x <= 2.2e-131):
		tmp = x / (1.0 - z)
	else:
		tmp = (z * t) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -5.6e-160) || !(x <= 2.2e-131))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(z * t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -5.6e-160) || ~((x <= 2.2e-131)))
		tmp = x / (1.0 - z);
	else
		tmp = (z * t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -5.6e-160], N[Not[LessEqual[x, 2.2e-131]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.60000000000000032e-160 or 2.2e-131 < x

   1. Initial program 61.3%

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

   3. Taylor expanded in y around inf 38.2%

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

      1. mul-1-neg 38.2%

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

      2. unsub-neg 38.2%

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

   5. Simplified 38.2%

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

   if -5.60000000000000032e-160 < x < 2.2e-131

   1. Initial program 61.7%

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

   3. Taylor expanded in z around 0 40.0%

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

   4. Taylor expanded in t around inf 22.1%

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

      1. *-commutative 22.1%

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

   6. Simplified 22.1%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-160} \lor \neg \left(x \leq 2.2 \cdot 10^{-131}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-22} \lor \neg \left(y \leq 3.8 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.5e-22) (not (<= y 3.8e+68))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.5e-22) || !(y <= 3.8e+68)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - 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 ((y <= (-3.5d-22)) .or. (.not. (y <= 3.8d+68))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - 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 ((y <= -3.5e-22) || !(y <= 3.8e+68)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.5e-22) or not (y <= 3.8e+68):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.5e-22) || !(y <= 3.8e+68))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.5e-22) || ~((y <= 3.8e+68)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.5e-22], N[Not[LessEqual[y, 3.8e+68]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.50000000000000005e-22 or 3.8000000000000001e68 < y

   1. Initial program 46.1%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   if -3.50000000000000005e-22 < y < 3.8000000000000001e68

   1. Initial program 75.4%

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

   3. Taylor expanded in y around 0 57.4%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-22} \lor \neg \left(y \leq 3.8 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.5e-70) x (if (<= x 1.55e-132) (* t (/ z y)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.5e-70) {
		tmp = x;
	} else if (x <= 1.55e-132) {
		tmp = t * (z / 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 (x <= (-3.5d-70)) then
        tmp = x
    else if (x <= 1.55d-132) then
        tmp = t * (z / 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 (x <= -3.5e-70) {
		tmp = x;
	} else if (x <= 1.55e-132) {
		tmp = t * (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.5e-70:
		tmp = x
	elif x <= 1.55e-132:
		tmp = t * (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.5e-70)
		tmp = x;
	elseif (x <= 1.55e-132)
		tmp = Float64(t * Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.5e-70)
		tmp = x;
	elseif (x <= 1.55e-132)
		tmp = t * (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.5e-70], x, If[LessEqual[x, 1.55e-132], N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.49999999999999974e-70 or 1.55000000000000004e-132 < x

   1. Initial program 59.9%

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

   3. Taylor expanded in z around 0 32.9%

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

   if -3.49999999999999974e-70 < x < 1.55000000000000004e-132

   1. Initial program 64.5%

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

   3. Taylor expanded in z around 0 35.2%

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

      1. *-commutative 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in t around inf 23.3%

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

   7. Taylor expanded in x around 0 20.2%

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

      1. associate-*r/ 19.0%

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

   9. Simplified 19.0%

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

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 25.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-70}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-131}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.45e-70) (+ x (* x z)) (if (<= x 8.2e-131) (* t (/ z y)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.45e-70) {
		tmp = x + (x * z);
	} else if (x <= 8.2e-131) {
		tmp = t * (z / 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 (x <= (-1.45d-70)) then
        tmp = x + (x * z)
    else if (x <= 8.2d-131) then
        tmp = t * (z / 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 (x <= -1.45e-70) {
		tmp = x + (x * z);
	} else if (x <= 8.2e-131) {
		tmp = t * (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.45e-70:
		tmp = x + (x * z)
	elif x <= 8.2e-131:
		tmp = t * (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.45e-70)
		tmp = Float64(x + Float64(x * z));
	elseif (x <= 8.2e-131)
		tmp = Float64(t * Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.45e-70)
		tmp = x + (x * z);
	elseif (x <= 8.2e-131)
		tmp = t * (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.45e-70], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-131], N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44999999999999986e-70

   1. Initial program 58.8%

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

   3. Taylor expanded in z around 0 21.3%

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

      1. *-commutative 21.3%

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

   5. Simplified 21.3%

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

   6. Taylor expanded in y around inf 29.6%

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

      1. *-commutative 29.6%

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

   8. Simplified 29.6%

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

   if -1.44999999999999986e-70 < x < 8.2000000000000004e-131

   1. Initial program 64.5%

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

   3. Taylor expanded in z around 0 35.2%

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

      1. *-commutative 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in t around inf 23.3%

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

   7. Taylor expanded in x around 0 20.2%

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

      1. associate-*r/ 19.0%

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

   9. Simplified 19.0%

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

   if 8.2000000000000004e-131 < x

   1. Initial program 60.8%

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

   3. Taylor expanded in z around 0 36.2%

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

4. Final simplification 28.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-70}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-131}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.8% 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 61.4%

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

3. Taylor expanded in z around 0 24.5%

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

4. Final simplification 24.5%

   \[\leadsto x \]
5. Add Preprocessing

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 2024066 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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