Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.3% → 90.6%

Time: 15.8s

Alternatives: 18

Speedup: 1.5×

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: 66.3% 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: 90.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_4 := \frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(x \cdot z\right)}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot a - z \cdot t\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (-
          (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
          (* (/ (- t a) z) (/ y (pow (- b y) 2.0)))))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_4
         (-
          (/
           (-
            (* (/ z (+ z -1.0)) (- a t))
            (* (/ b (pow (+ z -1.0) 2.0)) (* x z)))
           y)
          (/ x (+ z -1.0)))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -5e-233)
       t_3
       (if (<= t_3 2e-300)
         t_2
         (if (<= t_3 5e+262)
           (/ (- (* x y) (- (* z a) (* z t))) t_1)
           (if (<= t_3 INFINITY) t_4 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) - (((t - a) / z) * (y / pow((b - y), 2.0)));
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = ((((z / (z + -1.0)) * (a - t)) - ((b / pow((z + -1.0), 2.0)) * (x * z))) / y) - (x / (z + -1.0));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -5e-233) {
		tmp = t_3;
	} else if (t_3 <= 2e-300) {
		tmp = t_2;
	} else if (t_3 <= 5e+262) {
		tmp = ((x * y) - ((z * a) - (z * t))) / t_1;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	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 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) - (((t - a) / z) * (y / Math.pow((b - y), 2.0)));
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = ((((z / (z + -1.0)) * (a - t)) - ((b / Math.pow((z + -1.0), 2.0)) * (x * z))) / y) - (x / (z + -1.0));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -5e-233) {
		tmp = t_3;
	} else if (t_3 <= 2e-300) {
		tmp = t_2;
	} else if (t_3 <= 5e+262) {
		tmp = ((x * y) - ((z * a) - (z * t))) / t_1;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) - (((t - a) / z) * (y / math.pow((b - y), 2.0)))
	t_3 = ((x * y) + (z * (t - a))) / t_1
	t_4 = ((((z / (z + -1.0)) * (a - t)) - ((b / math.pow((z + -1.0), 2.0)) * (x * z))) / y) - (x / (z + -1.0))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -5e-233:
		tmp = t_3
	elif t_3 <= 2e-300:
		tmp = t_2
	elif t_3 <= 5e+262:
		tmp = ((x * y) - ((z * a) - (z * t))) / t_1
	elif t_3 <= math.inf:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) - Float64(Float64(Float64(t - a) / z) * Float64(y / (Float64(b - y) ^ 2.0))))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_4 = Float64(Float64(Float64(Float64(Float64(z / Float64(z + -1.0)) * Float64(a - t)) - Float64(Float64(b / (Float64(z + -1.0) ^ 2.0)) * Float64(x * z))) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -5e-233)
		tmp = t_3;
	elseif (t_3 <= 2e-300)
		tmp = t_2;
	elseif (t_3 <= 5e+262)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * a) - Float64(z * t))) / t_1);
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) - (((t - a) / z) * (y / ((b - y) ^ 2.0)));
	t_3 = ((x * y) + (z * (t - a))) / t_1;
	t_4 = ((((z / (z + -1.0)) * (a - t)) - ((b / ((z + -1.0) ^ 2.0)) * (x * z))) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -5e-233)
		tmp = t_3;
	elseif (t_3 <= 2e-300)
		tmp = t_2;
	elseif (t_3 <= 5e+262)
		tmp = ((x * y) - ((z * a) - (z * t))) / t_1;
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision] * N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(N[(b / N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -5e-233], t$95$3, If[LessEqual[t$95$3, 2e-300], t$95$2, If[LessEqual[t$95$3, 5e+262], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$4, t$95$2]]]]]]]]]

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 5.00000000000000008e262 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 35.5%

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

   2. Taylor expanded in y around -inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. associate-*r/ 67.2%

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

      4. neg-mul-1 67.2%

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

      5. sub-neg 67.2%

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

      6. metadata-eval 67.2%

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

   4. Simplified 78.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000012e-233

   1. Initial program 99.7%

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

   if -5.00000000000000012e-233 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000005e-300 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 16.2%

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

   2. Taylor expanded in z around inf 52.2%

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

      1. associate--r+ 52.2%

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

      2. +-commutative 52.2%

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

      3. associate--l+ 52.2%

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

      4. *-commutative 52.2%

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

      5. times-frac 60.0%

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

      6. div-sub 60.0%

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

      7. *-commutative 60.0%

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

      8. times-frac 98.3%

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

   4. Simplified 98.3%

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

   if 2.00000000000000005e-300 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000008e262

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.5%

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

   3. Applied egg-rr 99.5%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(x \cdot z\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-233}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{-300}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot a - z \cdot t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(x \cdot z\right)}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\\ \end{array} \]

Alternative 2: 86.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_4 := \frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(x \cdot z\right)}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot a - z \cdot t\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_4
         (-
          (/
           (-
            (* (/ z (+ z -1.0)) (- a t))
            (* (/ b (pow (+ z -1.0) 2.0)) (* x z)))
           y)
          (/ x (+ z -1.0)))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -1e-254)
       t_3
       (if (<= t_3 2e-300)
         t_2
         (if (<= t_3 5e+262)
           (/ (- (* x y) (- (* z a) (* z t))) t_1)
           (if (<= t_3 INFINITY) t_4 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = ((((z / (z + -1.0)) * (a - t)) - ((b / pow((z + -1.0), 2.0)) * (x * z))) / y) - (x / (z + -1.0));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -1e-254) {
		tmp = t_3;
	} else if (t_3 <= 2e-300) {
		tmp = t_2;
	} else if (t_3 <= 5e+262) {
		tmp = ((x * y) - ((z * a) - (z * t))) / t_1;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	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 = (t - a) / (b - y);
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = ((((z / (z + -1.0)) * (a - t)) - ((b / Math.pow((z + -1.0), 2.0)) * (x * z))) / y) - (x / (z + -1.0));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -1e-254) {
		tmp = t_3;
	} else if (t_3 <= 2e-300) {
		tmp = t_2;
	} else if (t_3 <= 5e+262) {
		tmp = ((x * y) - ((z * a) - (z * t))) / t_1;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = ((x * y) + (z * (t - a))) / t_1
	t_4 = ((((z / (z + -1.0)) * (a - t)) - ((b / math.pow((z + -1.0), 2.0)) * (x * z))) / y) - (x / (z + -1.0))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -1e-254:
		tmp = t_3
	elif t_3 <= 2e-300:
		tmp = t_2
	elif t_3 <= 5e+262:
		tmp = ((x * y) - ((z * a) - (z * t))) / t_1
	elif t_3 <= math.inf:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_4 = Float64(Float64(Float64(Float64(Float64(z / Float64(z + -1.0)) * Float64(a - t)) - Float64(Float64(b / (Float64(z + -1.0) ^ 2.0)) * Float64(x * z))) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -1e-254)
		tmp = t_3;
	elseif (t_3 <= 2e-300)
		tmp = t_2;
	elseif (t_3 <= 5e+262)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * a) - Float64(z * t))) / t_1);
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = ((x * y) + (z * (t - a))) / t_1;
	t_4 = ((((z / (z + -1.0)) * (a - t)) - ((b / ((z + -1.0) ^ 2.0)) * (x * z))) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -1e-254)
		tmp = t_3;
	elseif (t_3 <= 2e-300)
		tmp = t_2;
	elseif (t_3 <= 5e+262)
		tmp = ((x * y) - ((z * a) - (z * t))) / t_1;
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(N[(b / N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -1e-254], t$95$3, If[LessEqual[t$95$3, 2e-300], t$95$2, If[LessEqual[t$95$3, 5e+262], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$4, t$95$2]]]]]]]]]

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 5.00000000000000008e262 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 35.5%

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

   2. Taylor expanded in y around -inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. associate-*r/ 67.2%

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

      4. neg-mul-1 67.2%

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

      5. sub-neg 67.2%

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

      6. metadata-eval 67.2%

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

   4. Simplified 78.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999991e-255

   1. Initial program 99.6%

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

   if -9.9999999999999991e-255 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000005e-300 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 14.6%

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

   2. Taylor expanded in z around inf 75.4%

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

   if 2.00000000000000005e-300 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000008e262

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.5%

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

   3. Applied egg-rr 99.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(x \cdot z\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-254}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{-300}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot a - z \cdot t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(x \cdot z\right)}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 82.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t_2}{x}}\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_2)))
   (if (<= t_3 (- INFINITY))
     (/ y (/ t_2 x))
     (if (<= t_3 -1e-254)
       t_3
       (if (<= t_3 2e-300)
         t_1
         (if (<= t_3 5e+290)
           t_3
           (if (<= t_3 INFINITY) (- 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 t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + (z * (t - a))) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = y / (t_2 / x);
	} else if (t_3 <= -1e-254) {
		tmp = t_3;
	} else if (t_3 <= 2e-300) {
		tmp = t_1;
	} else if (t_3 <= 5e+290) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = x - (z * (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + (z * (t - a))) / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (t_2 / x);
	} else if (t_3 <= -1e-254) {
		tmp = t_3;
	} else if (t_3 <= 2e-300) {
		tmp = t_1;
	} else if (t_3 <= 5e+290) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		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)
	t_2 = y + (z * (b - y))
	t_3 = ((x * y) + (z * (t - a))) / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = y / (t_2 / x)
	elif t_3 <= -1e-254:
		tmp = t_3
	elif t_3 <= 2e-300:
		tmp = t_1
	elif t_3 <= 5e+290:
		tmp = t_3
	elif t_3 <= math.inf:
		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))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(y / Float64(t_2 / x));
	elseif (t_3 <= -1e-254)
		tmp = t_3;
	elseif (t_3 <= 2e-300)
		tmp = t_1;
	elseif (t_3 <= 5e+290)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(x - Float64(z * Float64(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);
	t_2 = y + (z * (b - y));
	t_3 = ((x * y) + (z * (t - a))) / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = y / (t_2 / x);
	elseif (t_3 <= -1e-254)
		tmp = t_3;
	elseif (t_3 <= 2e-300)
		tmp = t_1;
	elseif (t_3 <= 5e+290)
		tmp = t_3;
	elseif (t_3 <= Inf)
		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]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(y / N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-254], t$95$3, If[LessEqual[t$95$3, 2e-300], t$95$1, If[LessEqual[t$95$3, 5e+290], t$95$3, If[LessEqual[t$95$3, Infinity], N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 35.2%

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

   2. Taylor expanded in x around inf 4.2%

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

      1. *-commutative 4.2%

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

      2. +-commutative 4.2%

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

      3. fma-udef 4.2%

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

      4. associate-/l* 53.9%

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

   4. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}}} \]
   5. Step-by-step derivation

      1. fma-udef 53.9%

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

   6. Applied egg-rr 53.9%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999991e-255 or 2.00000000000000005e-300 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.9999999999999998e290

   1. Initial program 99.5%

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

   if -9.9999999999999991e-255 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000005e-300 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 14.6%

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

   2. Taylor expanded in z around inf 75.4%

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

   if 4.9999999999999998e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 30.9%

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

   2. Taylor expanded in z around 0 14.2%

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

      1. associate-/l* 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in a around inf 73.0%

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

      1. mul-1-neg 73.0%

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

   7. Simplified 73.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-254}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{-300}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 82.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t_2}{x}}\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot a - z \cdot t\right)}{t_2}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_2)))
   (if (<= t_3 (- INFINITY))
     (/ y (/ t_2 x))
     (if (<= t_3 -1e-254)
       t_3
       (if (<= t_3 2e-300)
         t_1
         (if (<= t_3 5e+290)
           (/ (- (* x y) (- (* z a) (* z t))) t_2)
           (if (<= t_3 INFINITY) (- 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 t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + (z * (t - a))) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = y / (t_2 / x);
	} else if (t_3 <= -1e-254) {
		tmp = t_3;
	} else if (t_3 <= 2e-300) {
		tmp = t_1;
	} else if (t_3 <= 5e+290) {
		tmp = ((x * y) - ((z * a) - (z * t))) / t_2;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = x - (z * (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + (z * (t - a))) / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (t_2 / x);
	} else if (t_3 <= -1e-254) {
		tmp = t_3;
	} else if (t_3 <= 2e-300) {
		tmp = t_1;
	} else if (t_3 <= 5e+290) {
		tmp = ((x * y) - ((z * a) - (z * t))) / t_2;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		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)
	t_2 = y + (z * (b - y))
	t_3 = ((x * y) + (z * (t - a))) / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = y / (t_2 / x)
	elif t_3 <= -1e-254:
		tmp = t_3
	elif t_3 <= 2e-300:
		tmp = t_1
	elif t_3 <= 5e+290:
		tmp = ((x * y) - ((z * a) - (z * t))) / t_2
	elif t_3 <= math.inf:
		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))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(y / Float64(t_2 / x));
	elseif (t_3 <= -1e-254)
		tmp = t_3;
	elseif (t_3 <= 2e-300)
		tmp = t_1;
	elseif (t_3 <= 5e+290)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * a) - Float64(z * t))) / t_2);
	elseif (t_3 <= Inf)
		tmp = Float64(x - Float64(z * Float64(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);
	t_2 = y + (z * (b - y));
	t_3 = ((x * y) + (z * (t - a))) / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = y / (t_2 / x);
	elseif (t_3 <= -1e-254)
		tmp = t_3;
	elseif (t_3 <= 2e-300)
		tmp = t_1;
	elseif (t_3 <= 5e+290)
		tmp = ((x * y) - ((z * a) - (z * t))) / t_2;
	elseif (t_3 <= Inf)
		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]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(y / N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-254], t$95$3, If[LessEqual[t$95$3, 2e-300], t$95$1, If[LessEqual[t$95$3, 5e+290], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

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 35.2%

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

   2. Taylor expanded in x around inf 4.2%

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

      1. *-commutative 4.2%

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

      2. +-commutative 4.2%

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

      3. fma-udef 4.2%

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

      4. associate-/l* 53.9%

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

   4. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}}} \]
   5. Step-by-step derivation

      1. fma-udef 53.9%

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

   6. Applied egg-rr 53.9%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999991e-255

   1. Initial program 99.6%

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

   if -9.9999999999999991e-255 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000005e-300 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 14.6%

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

   2. Taylor expanded in z around inf 75.4%

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

   if 2.00000000000000005e-300 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.9999999999999998e290

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.5%

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

   3. Applied egg-rr 99.5%

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

   if 4.9999999999999998e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 30.9%

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

   2. Taylor expanded in z around 0 14.2%

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

      1. associate-/l* 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in a around inf 73.0%

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

      1. mul-1-neg 73.0%

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

   7. Simplified 73.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-254}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{-300}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot a - z \cdot t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 80.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-271}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 6.7:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z b))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.75e+44)
     t_2
     (if (<= z -2.1e-174)
       t_1
       (if (<= z 7e-271) (- x (/ (* z a) y)) (if (<= z 6.7) 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));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.75e+44) {
		tmp = t_2;
	} else if (z <= -2.1e-174) {
		tmp = t_1;
	} else if (z <= 7e-271) {
		tmp = x - ((z * a) / y);
	} else if (z <= 6.7) {
		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))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.75d+44)) then
        tmp = t_2
    else if (z <= (-2.1d-174)) then
        tmp = t_1
    else if (z <= 7d-271) then
        tmp = x - ((z * a) / y)
    else if (z <= 6.7d0) 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));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.75e+44) {
		tmp = t_2;
	} else if (z <= -2.1e-174) {
		tmp = t_1;
	} else if (z <= 7e-271) {
		tmp = x - ((z * a) / y);
	} else if (z <= 6.7) {
		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))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.75e+44:
		tmp = t_2
	elif z <= -2.1e-174:
		tmp = t_1
	elif z <= 7e-271:
		tmp = x - ((z * a) / y)
	elif z <= 6.7:
		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 * b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.75e+44)
		tmp = t_2;
	elseif (z <= -2.1e-174)
		tmp = t_1;
	elseif (z <= 7e-271)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 6.7)
		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));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.75e+44)
		tmp = t_2;
	elseif (z <= -2.1e-174)
		tmp = t_1;
	elseif (z <= 7e-271)
		tmp = x - ((z * a) / y);
	elseif (z <= 6.7)
		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 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+44], t$95$2, If[LessEqual[z, -2.1e-174], t$95$1, If[LessEqual[z, 7e-271], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.7], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75e44 or 6.70000000000000018 < z

   1. Initial program 52.0%

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

   2. Taylor expanded in z around inf 81.1%

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

   if -1.75e44 < z < -2.1000000000000001e-174 or 6.9999999999999999e-271 < z < 6.70000000000000018

   1. Initial program 82.5%

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

   2. Taylor expanded in b around inf 79.3%

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

      1. *-commutative 79.3%

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

   4. Simplified 79.3%

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

   if -2.1000000000000001e-174 < z < 6.9999999999999999e-271

   1. Initial program 72.1%

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

   2. Taylor expanded in z around 0 52.2%

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

      1. associate-/l* 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in a around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. associate-*r* 84.9%

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

      3. neg-mul-1 84.9%

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

      4. *-commutative 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+44}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-174}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-271}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 6.7:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-156}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-71}:\\ \;\;\;\;\frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.25e-44)
     t_1
     (if (<= z 2.8e-156)
       (- x (/ (* z a) y))
       (if (<= z 5.3e-71) (/ y (/ (+ y (* z (- b y))) x)) 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 <= -2.25e-44) {
		tmp = t_1;
	} else if (z <= 2.8e-156) {
		tmp = x - ((z * a) / y);
	} else if (z <= 5.3e-71) {
		tmp = y / ((y + (z * (b - y))) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.25d-44)) then
        tmp = t_1
    else if (z <= 2.8d-156) then
        tmp = x - ((z * a) / y)
    else if (z <= 5.3d-71) then
        tmp = y / ((y + (z * (b - y))) / x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.25e-44) {
		tmp = t_1;
	} else if (z <= 2.8e-156) {
		tmp = x - ((z * a) / y);
	} else if (z <= 5.3e-71) {
		tmp = y / ((y + (z * (b - y))) / x);
	} 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 <= -2.25e-44:
		tmp = t_1
	elif z <= 2.8e-156:
		tmp = x - ((z * a) / y)
	elif z <= 5.3e-71:
		tmp = y / ((y + (z * (b - y))) / x)
	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 <= -2.25e-44)
		tmp = t_1;
	elseif (z <= 2.8e-156)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 5.3e-71)
		tmp = Float64(y / Float64(Float64(y + Float64(z * Float64(b - y))) / x));
	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 <= -2.25e-44)
		tmp = t_1;
	elseif (z <= 2.8e-156)
		tmp = x - ((z * a) / y);
	elseif (z <= 5.3e-71)
		tmp = y / ((y + (z * (b - y))) / x);
	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, -2.25e-44], t$95$1, If[LessEqual[z, 2.8e-156], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e-71], N[(y / N[(N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999999e-44 or 5.29999999999999999e-71 < z

   1. Initial program 58.8%

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

   2. Taylor expanded in z around inf 73.6%

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

   if -2.2499999999999999e-44 < z < 2.8000000000000002e-156

   1. Initial program 81.3%

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

   2. Taylor expanded in z around 0 56.8%

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

      1. associate-/l* 74.9%

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

   4. Simplified 74.9%

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

   5. Taylor expanded in a around inf 81.1%

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

      1. associate-*r/ 81.1%

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

      2. associate-*r* 81.1%

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

      3. neg-mul-1 81.1%

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

      4. *-commutative 81.1%

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

   7. Simplified 81.1%

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

   if 2.8000000000000002e-156 < z < 5.29999999999999999e-71

   1. Initial program 68.3%

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

   2. Taylor expanded in x around inf 40.1%

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

      1. *-commutative 40.1%

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

      2. +-commutative 40.1%

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

      3. fma-udef 40.1%

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

      4. associate-/l* 66.9%

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

   4. Simplified 66.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}}} \]
   5. Step-by-step derivation

      1. fma-udef 67.0%

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

   6. Applied egg-rr 67.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-44}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-156}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-71}:\\ \;\;\;\;\frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 44.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -170000000:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.34 \cdot 10^{-14}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-11}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -2.7e+123)
     t_1
     (if (<= z -170000000.0)
       (- (/ x z))
       (if (<= z -1.34e-14)
         (/ (- a) b)
         (if (<= z 5.8e-11) (+ x (* x z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -2.7e+123) {
		tmp = t_1;
	} else if (z <= -170000000.0) {
		tmp = -(x / z);
	} else if (z <= -1.34e-14) {
		tmp = -a / b;
	} else if (z <= 5.8e-11) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-2.7d+123)) then
        tmp = t_1
    else if (z <= (-170000000.0d0)) then
        tmp = -(x / z)
    else if (z <= (-1.34d-14)) then
        tmp = -a / b
    else if (z <= 5.8d-11) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -2.7e+123) {
		tmp = t_1;
	} else if (z <= -170000000.0) {
		tmp = -(x / z);
	} else if (z <= -1.34e-14) {
		tmp = -a / b;
	} else if (z <= 5.8e-11) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -2.7e+123:
		tmp = t_1
	elif z <= -170000000.0:
		tmp = -(x / z)
	elif z <= -1.34e-14:
		tmp = -a / b
	elif z <= 5.8e-11:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -2.7e+123)
		tmp = t_1;
	elseif (z <= -170000000.0)
		tmp = Float64(-Float64(x / z));
	elseif (z <= -1.34e-14)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 5.8e-11)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -2.7e+123)
		tmp = t_1;
	elseif (z <= -170000000.0)
		tmp = -(x / z);
	elseif (z <= -1.34e-14)
		tmp = -a / b;
	elseif (z <= 5.8e-11)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+123], t$95$1, If[LessEqual[z, -170000000.0], (-N[(x / z), $MachinePrecision]), If[LessEqual[z, -1.34e-14], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 5.8e-11], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.70000000000000013e123 or 5.8e-11 < z

   1. Initial program 51.2%

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

   2. Taylor expanded in t around inf 28.8%

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

      1. *-commutative 28.8%

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

   4. Simplified 28.8%

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

   5. Taylor expanded in z around inf 51.3%

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

   if -2.70000000000000013e123 < z < -1.7e8

   1. Initial program 68.0%

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

   2. Taylor expanded in y around inf 43.7%

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

      1. mul-1-neg 43.7%

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

      2. unsub-neg 43.7%

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

   4. Simplified 43.7%

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

   5. Taylor expanded in z around inf 42.9%

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

      1. associate-*r/ 42.9%

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

      2. mul-1-neg 42.9%

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

   7. Simplified 42.9%

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

   if -1.7e8 < z < -1.34e-14

   1. Initial program 75.6%

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

      1. sub-neg 75.6%

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

      2. distribute-lft-in 75.6%

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

   3. Applied egg-rr 75.6%

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

   4. Taylor expanded in y around 0 75.0%

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

   5. Taylor expanded in a around inf 51.3%

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

      1. associate-*r/ 51.3%

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

      2. mul-1-neg 51.3%

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

   7. Simplified 51.3%

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

   if -1.34e-14 < z < 5.8e-11

   1. Initial program 79.2%

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

   2. Taylor expanded in y around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in z around 0 61.1%

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

      1. *-commutative 61.1%

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

   7. Simplified 61.1%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+123}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -170000000:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.34 \cdot 10^{-14}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-11}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 8: 52.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+147}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.2e-83)
     t_1
     (if (<= y 2.7e+14)
       (/ (- t a) b)
       (if (<= y 9.2e+79) x (if (<= y 1.7e+147) (/ (- a t) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.2e-83) {
		tmp = t_1;
	} else if (y <= 2.7e+14) {
		tmp = (t - a) / b;
	} else if (y <= 9.2e+79) {
		tmp = x;
	} else if (y <= 1.7e+147) {
		tmp = (a - t) / 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 = x / (1.0d0 - z)
    if (y <= (-1.2d-83)) then
        tmp = t_1
    else if (y <= 2.7d+14) then
        tmp = (t - a) / b
    else if (y <= 9.2d+79) then
        tmp = x
    else if (y <= 1.7d+147) then
        tmp = (a - t) / 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 = x / (1.0 - z);
	double tmp;
	if (y <= -1.2e-83) {
		tmp = t_1;
	} else if (y <= 2.7e+14) {
		tmp = (t - a) / b;
	} else if (y <= 9.2e+79) {
		tmp = x;
	} else if (y <= 1.7e+147) {
		tmp = (a - t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1.2e-83:
		tmp = t_1
	elif y <= 2.7e+14:
		tmp = (t - a) / b
	elif y <= 9.2e+79:
		tmp = x
	elif y <= 1.7e+147:
		tmp = (a - t) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.2e-83)
		tmp = t_1;
	elseif (y <= 2.7e+14)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 9.2e+79)
		tmp = x;
	elseif (y <= 1.7e+147)
		tmp = Float64(Float64(a - t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.2e-83)
		tmp = t_1;
	elseif (y <= 2.7e+14)
		tmp = (t - a) / b;
	elseif (y <= 9.2e+79)
		tmp = x;
	elseif (y <= 1.7e+147)
		tmp = (a - t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e-83], t$95$1, If[LessEqual[y, 2.7e+14], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 9.2e+79], x, If[LessEqual[y, 1.7e+147], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2e-83 or 1.7e147 < y

   1. Initial program 50.4%

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

   2. Taylor expanded in y around inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. unsub-neg 63.4%

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

   4. Simplified 63.4%

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

   if -1.2e-83 < y < 2.7e14

   1. Initial program 88.1%

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

   2. Taylor expanded in y around 0 59.8%

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

   if 2.7e14 < y < 9.2000000000000002e79

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   if 9.2000000000000002e79 < y < 1.7e147

   1. Initial program 57.0%

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

   2. Taylor expanded in z around inf 73.1%

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

   3. Taylor expanded in b around 0 58.7%

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

      1. associate-*r/ 58.7%

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

      2. mul-1-neg 58.7%

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

   5. Simplified 58.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+147}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 9: 51.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 80000000000000:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+147}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.3e-84)
     t_1
     (if (<= y 80000000000000.0)
       (- (/ t b) (/ a b))
       (if (<= y 2.9e+82) x (if (<= y 1.7e+147) (/ (- a t) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.3e-84) {
		tmp = t_1;
	} else if (y <= 80000000000000.0) {
		tmp = (t / b) - (a / b);
	} else if (y <= 2.9e+82) {
		tmp = x;
	} else if (y <= 1.7e+147) {
		tmp = (a - t) / 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 = x / (1.0d0 - z)
    if (y <= (-3.3d-84)) then
        tmp = t_1
    else if (y <= 80000000000000.0d0) then
        tmp = (t / b) - (a / b)
    else if (y <= 2.9d+82) then
        tmp = x
    else if (y <= 1.7d+147) then
        tmp = (a - t) / 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 = x / (1.0 - z);
	double tmp;
	if (y <= -3.3e-84) {
		tmp = t_1;
	} else if (y <= 80000000000000.0) {
		tmp = (t / b) - (a / b);
	} else if (y <= 2.9e+82) {
		tmp = x;
	} else if (y <= 1.7e+147) {
		tmp = (a - t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.3e-84:
		tmp = t_1
	elif y <= 80000000000000.0:
		tmp = (t / b) - (a / b)
	elif y <= 2.9e+82:
		tmp = x
	elif y <= 1.7e+147:
		tmp = (a - t) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.3e-84)
		tmp = t_1;
	elseif (y <= 80000000000000.0)
		tmp = Float64(Float64(t / b) - Float64(a / b));
	elseif (y <= 2.9e+82)
		tmp = x;
	elseif (y <= 1.7e+147)
		tmp = Float64(Float64(a - t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.3e-84)
		tmp = t_1;
	elseif (y <= 80000000000000.0)
		tmp = (t / b) - (a / b);
	elseif (y <= 2.9e+82)
		tmp = x;
	elseif (y <= 1.7e+147)
		tmp = (a - t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e-84], t$95$1, If[LessEqual[y, 80000000000000.0], N[(N[(t / b), $MachinePrecision] - N[(a / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+82], x, If[LessEqual[y, 1.7e+147], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.29999999999999984e-84 or 1.7e147 < y

   1. Initial program 50.4%

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

   2. Taylor expanded in y around inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. unsub-neg 63.4%

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

   4. Simplified 63.4%

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

   if -3.29999999999999984e-84 < y < 8e13

   1. Initial program 88.1%

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

   2. Taylor expanded in y around 0 59.8%

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

   3. Taylor expanded in t around 0 59.8%

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

      1. +-commutative 59.8%

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

      2. neg-mul-1 59.8%

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

      3. sub-neg 59.8%

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

   5. Simplified 59.8%

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

   if 8e13 < y < 2.9000000000000001e82

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   if 2.9000000000000001e82 < y < 1.7e147

   1. Initial program 57.0%

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

   2. Taylor expanded in z around inf 73.1%

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

   3. Taylor expanded in b around 0 58.7%

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

      1. associate-*r/ 58.7%

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

      2. mul-1-neg 58.7%

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

   5. Simplified 58.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 80000000000000:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+147}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 10: 68.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-137}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.6e-47)
     t_1
     (if (<= z 6.4e-137)
       (- x (* z (/ a y)))
       (if (<= z 2.8e-14) (+ x (* z (/ t 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 <= -1.6e-47) {
		tmp = t_1;
	} else if (z <= 6.4e-137) {
		tmp = x - (z * (a / y));
	} else if (z <= 2.8e-14) {
		tmp = x + (z * (t / 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 <= (-1.6d-47)) then
        tmp = t_1
    else if (z <= 6.4d-137) then
        tmp = x - (z * (a / y))
    else if (z <= 2.8d-14) then
        tmp = x + (z * (t / 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 <= -1.6e-47) {
		tmp = t_1;
	} else if (z <= 6.4e-137) {
		tmp = x - (z * (a / y));
	} else if (z <= 2.8e-14) {
		tmp = x + (z * (t / 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 <= -1.6e-47:
		tmp = t_1
	elif z <= 6.4e-137:
		tmp = x - (z * (a / y))
	elif z <= 2.8e-14:
		tmp = x + (z * (t / 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 <= -1.6e-47)
		tmp = t_1;
	elseif (z <= 6.4e-137)
		tmp = Float64(x - Float64(z * Float64(a / y)));
	elseif (z <= 2.8e-14)
		tmp = Float64(x + Float64(z * Float64(t / 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 <= -1.6e-47)
		tmp = t_1;
	elseif (z <= 6.4e-137)
		tmp = x - (z * (a / y));
	elseif (z <= 2.8e-14)
		tmp = x + (z * (t / 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, -1.6e-47], t$95$1, If[LessEqual[z, 6.4e-137], N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-14], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e-47 or 2.8000000000000001e-14 < z

   1. Initial program 56.9%

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

   2. Taylor expanded in z around inf 75.8%

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

   if -1.6e-47 < z < 6.40000000000000043e-137

   1. Initial program 81.9%

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

   2. Taylor expanded in z around 0 53.3%

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

      1. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in a around inf 73.7%

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

      1. mul-1-neg 73.7%

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

   7. Simplified 73.7%

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

   if 6.40000000000000043e-137 < z < 2.8000000000000001e-14

   1. Initial program 68.0%

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

   2. Taylor expanded in z around 0 43.3%

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

      1. associate-/l* 68.5%

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

   4. Simplified 68.5%

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

   5. Taylor expanded in t around inf 68.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-137}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 11: 69.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-137}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-15}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.06e-45)
     t_1
     (if (<= z 1.05e-137)
       (- x (/ (* z a) y))
       (if (<= z 3.1e-15) (+ x (* z (/ t 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 <= -1.06e-45) {
		tmp = t_1;
	} else if (z <= 1.05e-137) {
		tmp = x - ((z * a) / y);
	} else if (z <= 3.1e-15) {
		tmp = x + (z * (t / 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 <= (-1.06d-45)) then
        tmp = t_1
    else if (z <= 1.05d-137) then
        tmp = x - ((z * a) / y)
    else if (z <= 3.1d-15) then
        tmp = x + (z * (t / 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 <= -1.06e-45) {
		tmp = t_1;
	} else if (z <= 1.05e-137) {
		tmp = x - ((z * a) / y);
	} else if (z <= 3.1e-15) {
		tmp = x + (z * (t / 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 <= -1.06e-45:
		tmp = t_1
	elif z <= 1.05e-137:
		tmp = x - ((z * a) / y)
	elif z <= 3.1e-15:
		tmp = x + (z * (t / 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 <= -1.06e-45)
		tmp = t_1;
	elseif (z <= 1.05e-137)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 3.1e-15)
		tmp = Float64(x + Float64(z * Float64(t / 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 <= -1.06e-45)
		tmp = t_1;
	elseif (z <= 1.05e-137)
		tmp = x - ((z * a) / y);
	elseif (z <= 3.1e-15)
		tmp = x + (z * (t / 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, -1.06e-45], t$95$1, If[LessEqual[z, 1.05e-137], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-15], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.06000000000000004e-45 or 3.0999999999999999e-15 < z

   1. Initial program 56.9%

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

   2. Taylor expanded in z around inf 75.8%

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

   if -1.06000000000000004e-45 < z < 1.04999999999999996e-137

   1. Initial program 81.9%

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

   2. Taylor expanded in z around 0 53.3%

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

      1. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in a around inf 76.8%

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

      1. associate-*r/ 76.8%

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

      2. associate-*r* 76.8%

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

      3. neg-mul-1 76.8%

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

      4. *-commutative 76.8%

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

   7. Simplified 76.8%

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

   if 1.04999999999999996e-137 < z < 3.0999999999999999e-15

   1. Initial program 68.0%

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

   2. Taylor expanded in z around 0 43.3%

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

      1. associate-/l* 68.5%

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

   4. Simplified 68.5%

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

   5. Taylor expanded in t around inf 68.9%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{-45}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-137}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-15}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 12: 67.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-36} \lor \neg \left(z \leq 4 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.8e-36) (not (<= z 4e-15)))
   (/ (- 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 <= -5.8e-36) || !(z <= 4e-15)) {
		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 <= (-5.8d-36)) .or. (.not. (z <= 4d-15))) 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 <= -5.8e-36) || !(z <= 4e-15)) {
		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 <= -5.8e-36) or not (z <= 4e-15):
		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 <= -5.8e-36) || !(z <= 4e-15))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.8e-36) || ~((z <= 4e-15)))
		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, -5.8e-36], N[Not[LessEqual[z, 4e-15]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.80000000000000026e-36 or 4.0000000000000003e-15 < z

   1. Initial program 56.6%

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

   2. Taylor expanded in z around inf 76.3%

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

   if -5.80000000000000026e-36 < z < 4.0000000000000003e-15

   1. Initial program 79.3%

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

   2. Taylor expanded in z around 0 51.8%

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

      1. associate-/l* 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in t around inf 68.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-36} \lor \neg \left(z \leq 4 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]

Alternative 13: 44.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+125} \lor \neg \left(z \leq 5.6 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.8e+125) (not (<= z 5.6e-11))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e+125) || !(z <= 5.6e-11)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.8d+125)) .or. (.not. (z <= 5.6d-11))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e+125) || !(z <= 5.6e-11)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.8e+125) or not (z <= 5.6e-11):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.8e+125) || !(z <= 5.6e-11))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.8e+125) || ~((z <= 5.6e-11)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.8e+125], N[Not[LessEqual[z, 5.6e-11]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e125 or 5.6e-11 < z

   1. Initial program 51.2%

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

   2. Taylor expanded in t around inf 28.8%

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

      1. *-commutative 28.8%

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

   4. Simplified 28.8%

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

   5. Taylor expanded in z around inf 51.3%

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

   if -2.8000000000000001e125 < z < 5.6e-11

   1. Initial program 77.3%

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

   2. Taylor expanded in y around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

   4. Simplified 56.8%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+125} \lor \neg \left(z \leq 5.6 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 14: 53.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-84} \lor \neg \left(y \leq 70000000000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e-84) (not (<= y 70000000000000.0)))
   (/ 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 <= -5.5e-84) || !(y <= 70000000000000.0)) {
		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 <= (-5.5d-84)) .or. (.not. (y <= 70000000000000.0d0))) 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 <= -5.5e-84) || !(y <= 70000000000000.0)) {
		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 <= -5.5e-84) or not (y <= 70000000000000.0):
		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 <= -5.5e-84) || !(y <= 70000000000000.0))
		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 <= -5.5e-84) || ~((y <= 70000000000000.0)))
		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, -5.5e-84], N[Not[LessEqual[y, 70000000000000.0]], $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 < -5.50000000000000019e-84 or 7e13 < y

   1. Initial program 53.3%

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

   2. Taylor expanded in y around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. unsub-neg 61.4%

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

   4. Simplified 61.4%

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

   if -5.50000000000000019e-84 < y < 7e13

   1. Initial program 88.1%

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

   2. Taylor expanded in y around 0 59.8%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-84} \lor \neg \left(y \leq 70000000000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 15: 35.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.72:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-27}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.72) (- (/ x z)) (if (<= z 3.3e-27) (+ x (* x z)) (/ (- a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.72) {
		tmp = -(x / z);
	} else if (z <= 3.3e-27) {
		tmp = x + (x * z);
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.72d0)) then
        tmp = -(x / z)
    else if (z <= 3.3d-27) then
        tmp = x + (x * z)
    else
        tmp = -a / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.72) {
		tmp = -(x / z);
	} else if (z <= 3.3e-27) {
		tmp = x + (x * z);
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.72:
		tmp = -(x / z)
	elif z <= 3.3e-27:
		tmp = x + (x * z)
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.72)
		tmp = Float64(-Float64(x / z));
	elseif (z <= 3.3e-27)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.72)
		tmp = -(x / z);
	elseif (z <= 3.3e-27)
		tmp = x + (x * z);
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.72], (-N[(x / z), $MachinePrecision]), If[LessEqual[z, 3.3e-27], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[((-a) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.71999999999999997

   1. Initial program 50.7%

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

   2. Taylor expanded in y around inf 27.1%

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

      1. mul-1-neg 27.1%

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

      2. unsub-neg 27.1%

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

   4. Simplified 27.1%

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

   5. Taylor expanded in z around inf 25.5%

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

      1. associate-*r/ 25.5%

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

      2. mul-1-neg 25.5%

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

   7. Simplified 25.5%

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

   if -0.71999999999999997 < z < 3.29999999999999998e-27

   1. Initial program 78.8%

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

   2. Taylor expanded in y around inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. unsub-neg 60.9%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in z around 0 60.9%

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

      1. *-commutative 60.9%

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

   7. Simplified 60.9%

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

   if 3.29999999999999998e-27 < z

   1. Initial program 61.6%

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

      1. sub-neg 61.6%

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

      2. distribute-lft-in 59.9%

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

   3. Applied egg-rr 59.9%

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

   4. Taylor expanded in y around 0 36.2%

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

   5. Taylor expanded in a around inf 28.2%

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

      1. associate-*r/ 28.2%

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

      2. mul-1-neg 28.2%

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

   7. Simplified 28.2%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.72:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-27}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 16: 35.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.0) (- (/ x z)) (if (<= z 1.5e-14) x (/ (- a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.0) {
		tmp = -(x / z);
	} else if (z <= 1.5e-14) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = -(x / z)
    else if (z <= 1.5d-14) then
        tmp = x
    else
        tmp = -a / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.0) {
		tmp = -(x / z);
	} else if (z <= 1.5e-14) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.0:
		tmp = -(x / z)
	elif z <= 1.5e-14:
		tmp = x
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-Float64(x / z));
	elseif (z <= 1.5e-14)
		tmp = x;
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -(x / z);
	elseif (z <= 1.5e-14)
		tmp = x;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.0], (-N[(x / z), $MachinePrecision]), If[LessEqual[z, 1.5e-14], x, N[((-a) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 50.7%

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

   2. Taylor expanded in y around inf 27.1%

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

      1. mul-1-neg 27.1%

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

      2. unsub-neg 27.1%

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

   4. Simplified 27.1%

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

   5. Taylor expanded in z around inf 25.5%

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

      1. associate-*r/ 25.5%

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

      2. mul-1-neg 25.5%

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

   7. Simplified 25.5%

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

   if -1 < z < 1.4999999999999999e-14

   1. Initial program 78.8%

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

   2. Taylor expanded in z around 0 60.7%

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

   if 1.4999999999999999e-14 < z

   1. Initial program 61.6%

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

      1. sub-neg 61.6%

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

      2. distribute-lft-in 59.9%

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

   3. Applied egg-rr 59.9%

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

   4. Taylor expanded in y around 0 36.2%

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

   5. Taylor expanded in a around inf 28.2%

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

      1. associate-*r/ 28.2%

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

      2. mul-1-neg 28.2%

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

   7. Simplified 28.2%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 17: 34.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.2e-92) x (if (<= y 9.5e-64) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e-92) {
		tmp = x;
	} else if (y <= 9.5e-64) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.2d-92)) then
        tmp = x
    else if (y <= 9.5d-64) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e-92) {
		tmp = x;
	} else if (y <= 9.5e-64) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.2e-92:
		tmp = x
	elif y <= 9.5e-64:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.2e-92)
		tmp = x;
	elseif (y <= 9.5e-64)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.2e-92)
		tmp = x;
	elseif (y <= 9.5e-64)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.2e-92], x, If[LessEqual[y, 9.5e-64], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000002e-92 or 9.50000000000000043e-64 < y

   1. Initial program 57.1%

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

   2. Taylor expanded in z around 0 43.6%

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

   if -6.2000000000000002e-92 < y < 9.50000000000000043e-64

   1. Initial program 88.0%

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

   2. Taylor expanded in t around inf 43.3%

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

      1. *-commutative 43.3%

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

   4. Simplified 43.3%

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

   5. Taylor expanded in y around 0 42.7%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 25.9% 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 67.6%

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

2. Taylor expanded in z around 0 32.6%

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

3. Final simplification 32.6%

   \[\leadsto x \]

Developer target: 73.1% 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 2023293 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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