Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.7% → 89.1%

Time: 18.9s

Alternatives: 14

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot y + t_1}{t_2}\\ t_4 := \frac{t_1}{t_2}\\ t_5 := \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;x + t_4\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-206}:\\ \;\;\;\;t_4 + \frac{x \cdot y}{t_2}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+224}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\left(\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\right) - \frac{b}{y} \cdot \frac{x \cdot z}{{\left(1 - z\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* x y) t_1) t_2))
        (t_4 (/ t_1 t_2))
        (t_5
         (+
          (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
          (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))))
   (if (<= t_3 (- INFINITY))
     (+ x t_4)
     (if (<= t_3 -5e-206)
       (+ t_4 (/ (* x y) t_2))
       (if (<= t_3 0.0)
         t_5
         (if (<= t_3 5e+224)
           t_3
           (if (<= t_3 INFINITY)
             (-
              (+ (* (/ z y) (/ (- t a) (- 1.0 z))) (/ x (- 1.0 z)))
              (* (/ b y) (/ (* x z) (pow (- 1.0 z) 2.0))))
             t_5)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + t_1) / t_2;
	double t_4 = t_1 / t_2;
	double t_5 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x + t_4;
	} else if (t_3 <= -5e-206) {
		tmp = t_4 + ((x * y) / t_2);
	} else if (t_3 <= 0.0) {
		tmp = t_5;
	} else if (t_3 <= 5e+224) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = (((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z))) - ((b / y) * ((x * z) / pow((1.0 - z), 2.0)));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + t_1) / t_2;
	double t_4 = t_1 / t_2;
	double t_5 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / Math.pow((b - y), 2.0)));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x + t_4;
	} else if (t_3 <= -5e-206) {
		tmp = t_4 + ((x * y) / t_2);
	} else if (t_3 <= 0.0) {
		tmp = t_5;
	} else if (t_3 <= 5e+224) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = (((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z))) - ((b / y) * ((x * z) / Math.pow((1.0 - z), 2.0)));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = ((x * y) + t_1) / t_2
	t_4 = t_1 / t_2
	t_5 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / math.pow((b - y), 2.0)))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x + t_4
	elif t_3 <= -5e-206:
		tmp = t_4 + ((x * y) / t_2)
	elif t_3 <= 0.0:
		tmp = t_5
	elif t_3 <= 5e+224:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = (((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z))) - ((b / y) * ((x * z) / math.pow((1.0 - z), 2.0)))
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(x * y) + t_1) / t_2)
	t_4 = Float64(t_1 / t_2)
	t_5 = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x + t_4);
	elseif (t_3 <= -5e-206)
		tmp = Float64(t_4 + Float64(Float64(x * y) / t_2));
	elseif (t_3 <= 0.0)
		tmp = t_5;
	elseif (t_3 <= 5e+224)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(Float64(Float64(Float64(z / y) * Float64(Float64(t - a) / Float64(1.0 - z))) + Float64(x / Float64(1.0 - z))) - Float64(Float64(b / y) * Float64(Float64(x * z) / (Float64(1.0 - z) ^ 2.0))));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = y + (z * (b - y));
	t_3 = ((x * y) + t_1) / t_2;
	t_4 = t_1 / t_2;
	t_5 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / ((b - y) ^ 2.0)));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x + t_4;
	elseif (t_3 <= -5e-206)
		tmp = t_4 + ((x * y) / t_2);
	elseif (t_3 <= 0.0)
		tmp = t_5;
	elseif (t_3 <= 5e+224)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = (((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z))) - ((b / y) * ((x * z) / ((1.0 - z) ^ 2.0)));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 / t$95$2), $MachinePrecision]}, Block[{t$95$5 = 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[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x + t$95$4), $MachinePrecision], If[LessEqual[t$95$3, -5e-206], N[(t$95$4 + N[(N[(x * y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], t$95$5, If[LessEqual[t$95$3, 5e+224], t$95$3, If[LessEqual[t$95$3, Infinity], N[(N[(N[(N[(z / y), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b / y), $MachinePrecision] * N[(N[(x * z), $MachinePrecision] / N[Power[N[(1.0 - z), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]

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 46.0%

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

   3. Taylor expanded in x around 0 46.0%

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

   4. Taylor expanded in z around 0 78.1%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5e-206

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

   if -5e-206 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.1%

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

   3. Taylor expanded in z around inf 52.0%

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

      1. associate--r+ 52.0%

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

      2. +-commutative 52.0%

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

      3. associate--l+ 52.0%

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

      4. *-commutative 52.0%

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

      5. times-frac 64.7%

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

      6. div-sub 64.7%

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

      7. times-frac 99.8%

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

   5. Simplified 99.8%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.99999999999999964e224

   1. Initial program 99.5%

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

   if 4.99999999999999964e224 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 32.6%

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

   3. Taylor expanded in y around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. times-frac 79.8%

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

      3. mul-1-neg 79.8%

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

      4. times-frac 79.8%

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

      5. *-commutative 79.8%

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

      6. mul-1-neg 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-206}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+224}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\left(\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\right) - \frac{b}{y} \cdot \frac{x \cdot z}{{\left(1 - z\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+58} \lor \neg \left(z \leq 1.65 \cdot 10^{+16}\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_1} + \frac{x \cdot y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -6.2e+58) (not (<= z 1.65e+16)))
     (+
      (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
      (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))
     (+ (/ (* z (- t a)) t_1) (/ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -6.2e+58) || !(z <= 1.65e+16)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	} else {
		tmp = ((z * (t - a)) / t_1) + ((x * y) / 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 = y + (z * (b - y))
    if ((z <= (-6.2d+58)) .or. (.not. (z <= 1.65d+16))) then
        tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / ((b - y) ** 2.0d0)))
    else
        tmp = ((z * (t - a)) / t_1) + ((x * y) / 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 = y + (z * (b - y));
	double tmp;
	if ((z <= -6.2e+58) || !(z <= 1.65e+16)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / Math.pow((b - y), 2.0)));
	} else {
		tmp = ((z * (t - a)) / t_1) + ((x * y) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -6.2e+58) or not (z <= 1.65e+16):
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / math.pow((b - y), 2.0)))
	else:
		tmp = ((z * (t - a)) / t_1) + ((x * y) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -6.2e+58) || !(z <= 1.65e+16))
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) / t_1) + Float64(Float64(x * y) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -6.2e+58) || ~((z <= 1.65e+16)))
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / ((b - y) ^ 2.0)));
	else
		tmp = ((z * (t - a)) / t_1) + ((x * y) / t_1);
	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]}, If[Or[LessEqual[z, -6.2e+58], N[Not[LessEqual[z, 1.65e+16]], $MachinePrecision]], 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[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999998e58 or 1.65e16 < z

   1. Initial program 40.6%

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

   3. Taylor expanded in z around inf 67.4%

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

      1. associate--r+ 67.4%

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

      2. +-commutative 67.4%

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

      3. associate--l+ 67.4%

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

      4. *-commutative 67.4%

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

      5. times-frac 73.4%

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

      6. div-sub 74.4%

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

      7. times-frac 90.3%

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

   5. Simplified 90.3%

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

   if -6.1999999999999998e58 < z < 1.65e16

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 89.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+58} \lor \neg \left(z \leq 1.65 \cdot 10^{+16}\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (<= z -1.15e+36)
     (- (/ t (- b y)) (/ a (- b y)))
     (if (<= z 4.8e+30)
       (+ (/ (* z (- t a)) t_1) (/ (* x y) t_1))
       (/ (- t a) (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if (z <= -1.15e+36) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else if (z <= 4.8e+30) {
		tmp = ((z * (t - a)) / t_1) + ((x * y) / t_1);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if (z <= (-1.15d+36)) then
        tmp = (t / (b - y)) - (a / (b - y))
    else if (z <= 4.8d+30) then
        tmp = ((z * (t - a)) / t_1) + ((x * y) / t_1)
    else
        tmp = (t - a) / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if (z <= -1.15e+36) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else if (z <= 4.8e+30) {
		tmp = ((z * (t - a)) / t_1) + ((x * y) / t_1);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if z <= -1.15e+36:
		tmp = (t / (b - y)) - (a / (b - y))
	elif z <= 4.8e+30:
		tmp = ((z * (t - a)) / t_1) + ((x * y) / t_1)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -1.15e+36)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	elseif (z <= 4.8e+30)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) / t_1) + Float64(Float64(x * y) / t_1));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -1.15e+36)
		tmp = (t / (b - y)) - (a / (b - y));
	elseif (z <= 4.8e+30)
		tmp = ((z * (t - a)) / t_1) + ((x * y) / t_1);
	else
		tmp = (t - a) / (b - y);
	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]}, If[LessEqual[z, -1.15e+36], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+30], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.14999999999999998e36

   1. Initial program 43.7%

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

   3. Taylor expanded in z around inf 72.4%

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

      1. associate--r+ 72.4%

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

      2. +-commutative 72.4%

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

      3. associate--l+ 72.4%

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

      4. *-commutative 72.4%

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

      5. times-frac 79.6%

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

      6. div-sub 79.5%

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

      7. times-frac 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in z around inf 84.1%

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

   if -1.14999999999999998e36 < z < 4.7999999999999999e30

   1. Initial program 88.2%

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

   3. Taylor expanded in x around 0 88.3%

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

   if 4.7999999999999999e30 < z

   1. Initial program 42.2%

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

   3. Taylor expanded in z around inf 83.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1200000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.95e-69)
     t_1
     (if (<= z 1.12e-128)
       x
       (if (<= z 4.3e-63)
         (/ (- t a) b)
         (if (<= z 1200000000.0) (/ x (- 1.0 z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.95e-69) {
		tmp = t_1;
	} else if (z <= 1.12e-128) {
		tmp = x;
	} else if (z <= 4.3e-63) {
		tmp = (t - a) / b;
	} else if (z <= 1200000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.95d-69)) then
        tmp = t_1
    else if (z <= 1.12d-128) then
        tmp = x
    else if (z <= 4.3d-63) then
        tmp = (t - a) / b
    else if (z <= 1200000000.0d0) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.95e-69) {
		tmp = t_1;
	} else if (z <= 1.12e-128) {
		tmp = x;
	} else if (z <= 4.3e-63) {
		tmp = (t - a) / b;
	} else if (z <= 1200000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.95e-69:
		tmp = t_1
	elif z <= 1.12e-128:
		tmp = x
	elif z <= 4.3e-63:
		tmp = (t - a) / b
	elif z <= 1200000000.0:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.95e-69)
		tmp = t_1;
	elseif (z <= 1.12e-128)
		tmp = x;
	elseif (z <= 4.3e-63)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 1200000000.0)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.95e-69)
		tmp = t_1;
	elseif (z <= 1.12e-128)
		tmp = x;
	elseif (z <= 4.3e-63)
		tmp = (t - a) / b;
	elseif (z <= 1200000000.0)
		tmp = x / (1.0 - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e-69], t$95$1, If[LessEqual[z, 1.12e-128], x, If[LessEqual[z, 4.3e-63], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1200000000.0], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9499999999999999e-69 or 1.2e9 < z

   1. Initial program 54.1%

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

   3. Taylor expanded in z around inf 79.0%

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

   if -1.9499999999999999e-69 < z < 1.12e-128

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 59.8%

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

   if 1.12e-128 < z < 4.2999999999999999e-63

   1. Initial program 88.7%

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

   3. Taylor expanded in y around 0 68.3%

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

   if 4.2999999999999999e-63 < z < 1.2e9

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. unsub-neg 51.8%

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

   5. Simplified 51.8%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-69}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1200000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 4.95 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.6e+35)
   (- (/ t (- b y)) (/ a (- b y)))
   (if (<= z 4.95e+30)
     (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))
     (/ (- t a) (- b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.6e+35) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else if (z <= 4.95e+30) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-7.6d+35)) then
        tmp = (t / (b - y)) - (a / (b - y))
    else if (z <= 4.95d+30) then
        tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    else
        tmp = (t - a) / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.6e+35) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else if (z <= 4.95e+30) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.6e+35:
		tmp = (t / (b - y)) - (a / (b - y))
	elif z <= 4.95e+30:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.6e+35)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	elseif (z <= 4.95e+30)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.6e+35)
		tmp = (t / (b - y)) - (a / (b - y));
	elseif (z <= 4.95e+30)
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.6e+35], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.95e+30], 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], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5999999999999999e35

   1. Initial program 43.7%

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

   3. Taylor expanded in z around inf 72.4%

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

      1. associate--r+ 72.4%

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

      2. +-commutative 72.4%

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

      3. associate--l+ 72.4%

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

      4. *-commutative 72.4%

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

      5. times-frac 79.6%

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

      6. div-sub 79.5%

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

      7. times-frac 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in z around inf 84.1%

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

   if -7.5999999999999999e35 < z < 4.9500000000000001e30

   1. Initial program 88.2%

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

   if 4.9500000000000001e30 < z

   1. Initial program 42.2%

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

   3. Taylor expanded in z around inf 83.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 4.95 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-287}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.8e-23)
     t_2
     (if (<= y -1.05e-224)
       t_1
       (if (<= y -3.7e-287) (/ (- a) b) (if (<= y 5.8e-8) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.8e-23) {
		tmp = t_2;
	} else if (y <= -1.05e-224) {
		tmp = t_1;
	} else if (y <= -3.7e-287) {
		tmp = -a / b;
	} else if (y <= 5.8e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.8d-23)) then
        tmp = t_2
    else if (y <= (-1.05d-224)) then
        tmp = t_1
    else if (y <= (-3.7d-287)) then
        tmp = -a / b
    else if (y <= 5.8d-8) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.8e-23) {
		tmp = t_2;
	} else if (y <= -1.05e-224) {
		tmp = t_1;
	} else if (y <= -3.7e-287) {
		tmp = -a / b;
	} else if (y <= 5.8e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.8e-23:
		tmp = t_2
	elif y <= -1.05e-224:
		tmp = t_1
	elif y <= -3.7e-287:
		tmp = -a / b
	elif y <= 5.8e-8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.8e-23)
		tmp = t_2;
	elseif (y <= -1.05e-224)
		tmp = t_1;
	elseif (y <= -3.7e-287)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 5.8e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.8e-23)
		tmp = t_2;
	elseif (y <= -1.05e-224)
		tmp = t_1;
	elseif (y <= -3.7e-287)
		tmp = -a / b;
	elseif (y <= 5.8e-8)
		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[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e-23], t$95$2, If[LessEqual[y, -1.05e-224], t$95$1, If[LessEqual[y, -3.7e-287], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 5.8e-8], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999997e-23 or 5.8000000000000003e-8 < y

   1. Initial program 57.3%

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

   3. Taylor expanded in y around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. unsub-neg 57.4%

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

   5. Simplified 57.4%

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

   if -2.7999999999999997e-23 < y < -1.05000000000000003e-224 or -3.70000000000000027e-287 < y < 5.8000000000000003e-8

   1. Initial program 79.2%

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

   3. Taylor expanded in t around inf 40.7%

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

      1. *-commutative 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in z around inf 50.4%

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

   if -1.05000000000000003e-224 < y < -3.70000000000000027e-287

   1. Initial program 94.7%

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

   3. Taylor expanded in b around inf 84.2%

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

   4. Taylor expanded in a around inf 65.5%

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

      1. associate-*r/ 65.5%

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

      2. neg-mul-1 65.5%

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

   6. Simplified 65.5%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-224}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-287}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{-22}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 62:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.04e-22)
   (- (/ t (- b y)) (/ a (- b y)))
   (if (<= z 62.0)
     (+ x (/ (* z (- t a)) (+ y (* z (- b y)))))
     (/ (- t a) (- b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.04e-22) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else if (z <= 62.0) {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.04d-22)) then
        tmp = (t / (b - y)) - (a / (b - y))
    else if (z <= 62.0d0) then
        tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
    else
        tmp = (t - a) / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.04e-22) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else if (z <= 62.0) {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.04e-22:
		tmp = (t / (b - y)) - (a / (b - y))
	elif z <= 62.0:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.04e-22)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	elseif (z <= 62.0)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.04e-22)
		tmp = (t / (b - y)) - (a / (b - y));
	elseif (z <= 62.0)
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.04e-22], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 62.0], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04e-22

   1. Initial program 56.2%

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

   3. Taylor expanded in z around inf 75.1%

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

      1. associate--r+ 75.1%

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

      2. +-commutative 75.1%

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

      3. associate--l+ 75.1%

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

      4. *-commutative 75.1%

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

      5. times-frac 80.5%

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

      6. div-sub 80.5%

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

      7. times-frac 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in z around inf 81.5%

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

   if -1.04e-22 < z < 62

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 88.3%

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

   4. Taylor expanded in z around 0 83.7%

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

   if 62 < z

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf 80.3%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{-22}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 62:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-36} \lor \neg \left(z \leq 9.2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e-36) (not (<= z 9.2e-5)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-36) || !(z <= 9.2e-5)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / 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 <= (-2d-36)) .or. (.not. (z <= 9.2d-5))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / 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 <= -2e-36) || !(z <= 9.2e-5)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e-36) or not (z <= 9.2e-5):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e-36) || !(z <= 9.2e-5))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2e-36) || ~((z <= 9.2e-5)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e-36], N[Not[LessEqual[z, 9.2e-5]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e-36 or 9.20000000000000001e-5 < z

   1. Initial program 52.1%

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

   3. Taylor expanded in z around inf 81.2%

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

   if -1.9999999999999999e-36 < z < 9.20000000000000001e-5

   1. Initial program 88.1%

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

   3. Taylor expanded in x around 0 88.1%

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

   4. Taylor expanded in z around 0 83.4%

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

   5. Taylor expanded in z around 0 72.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-36} \lor \neg \left(z \leq 9.2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-50} \lor \neg \left(z \leq 0.000115\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-50) (not (<= z 0.000115))) (/ t b) (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-50) || !(z <= 0.000115)) {
		tmp = t / b;
	} else {
		tmp = x + (x * 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 <= (-1.05d-50)) .or. (.not. (z <= 0.000115d0))) then
        tmp = t / b
    else
        tmp = x + (x * 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 <= -1.05e-50) || !(z <= 0.000115)) {
		tmp = t / b;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-50) or not (z <= 0.000115):
		tmp = t / b
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-50) || !(z <= 0.000115))
		tmp = Float64(t / b);
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-50) || ~((z <= 0.000115)))
		tmp = t / b;
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-50], N[Not[LessEqual[z, 0.000115]], $MachinePrecision]], N[(t / b), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-50 or 1.15e-4 < z

   1. Initial program 53.8%

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

   3. Taylor expanded in t around inf 25.8%

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

      1. *-commutative 25.8%

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

   5. Simplified 25.8%

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

   6. Taylor expanded in y around 0 32.6%

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

   if -1.05e-50 < z < 1.15e-4

   1. Initial program 87.6%

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

   3. Taylor expanded in y around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in z around 0 53.9%

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

      1. *-commutative 53.9%

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

   8. Simplified 53.9%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-50} \lor \neg \left(z \leq 0.000115\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-52} \lor \neg \left(z \leq 1.3 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.6e-52) (not (<= z 1.3e-19))) (/ t (- b y)) (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.6e-52) || !(z <= 1.3e-19)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * 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 <= (-5.6d-52)) .or. (.not. (z <= 1.3d-19))) then
        tmp = t / (b - y)
    else
        tmp = x + (x * 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 <= -5.6e-52) || !(z <= 1.3e-19)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.6e-52) or not (z <= 1.3e-19):
		tmp = t / (b - y)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.6e-52) || !(z <= 1.3e-19))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.6e-52) || ~((z <= 1.3e-19)))
		tmp = t / (b - y);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.6e-52], N[Not[LessEqual[z, 1.3e-19]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999989e-52 or 1.30000000000000006e-19 < z

   1. Initial program 54.5%

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

   3. Taylor expanded in t around inf 25.4%

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

      1. *-commutative 25.4%

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

   5. Simplified 25.4%

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

   6. Taylor expanded in z around inf 47.9%

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

   if -5.59999999999999989e-52 < z < 1.30000000000000006e-19

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 54.8%

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

      1. mul-1-neg 54.8%

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

      2. unsub-neg 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in z around 0 54.8%

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

      1. *-commutative 54.8%

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

   8. Simplified 54.8%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-52} \lor \neg \left(z \leq 1.3 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-12} \lor \neg \left(y \leq 9.8 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.65e-12) (not (<= y 9.8e-14))) (/ 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 <= -2.65e-12) || !(y <= 9.8e-14)) {
		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 <= (-2.65d-12)) .or. (.not. (y <= 9.8d-14))) 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 <= -2.65e-12) || !(y <= 9.8e-14)) {
		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 <= -2.65e-12) or not (y <= 9.8e-14):
		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 <= -2.65e-12) || !(y <= 9.8e-14))
		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 <= -2.65e-12) || ~((y <= 9.8e-14)))
		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, -2.65e-12], N[Not[LessEqual[y, 9.8e-14]], $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 < -2.64999999999999982e-12 or 9.79999999999999989e-14 < y

   1. Initial program 57.5%

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

   3. Taylor expanded in y around inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

   5. Simplified 58.3%

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

   if -2.64999999999999982e-12 < y < 9.79999999999999989e-14

   1. Initial program 80.8%

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

   3. Taylor expanded in y around 0 65.9%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-12} \lor \neg \left(y \leq 9.8 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 33.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-42} \lor \neg \left(z \leq 4200000000000\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.6e-42) (not (<= z 4200000000000.0))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.6e-42) || !(z <= 4200000000000.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.6d-42)) .or. (.not. (z <= 4200000000000.0d0))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.6e-42) || !(z <= 4200000000000.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.6e-42) or not (z <= 4200000000000.0):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.6e-42) || !(z <= 4200000000000.0))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.6e-42) || ~((z <= 4200000000000.0)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.6e-42], N[Not[LessEqual[z, 4200000000000.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.6000000000000002e-42 or 4.2e12 < z

   1. Initial program 52.1%

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

   3. Taylor expanded in z around inf 79.9%

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

   4. Taylor expanded in t around 0 35.3%

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

      1. associate-*r/ 35.3%

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

      2. neg-mul-1 35.3%

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

   6. Simplified 35.3%

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

   7. Taylor expanded in b around 0 14.2%

      \[\leadsto \color{blue}{\frac{a}{y}} \]

   if -8.6000000000000002e-42 < z < 4.2e12

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 51.7%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-42} \lor \neg \left(z \leq 4200000000000\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-50} \lor \neg \left(z \leq 3.9 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.7e-50) (not (<= z 3.9e-5))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e-50) || !(z <= 3.9e-5)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.7d-50)) .or. (.not. (z <= 3.9d-5))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e-50) || !(z <= 3.9e-5)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.7e-50) or not (z <= 3.9e-5):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.7e-50) || !(z <= 3.9e-5))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.7e-50) || ~((z <= 3.9e-5)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.7e-50], N[Not[LessEqual[z, 3.9e-5]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000007e-50 or 3.8999999999999999e-5 < z

   1. Initial program 53.8%

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

   3. Taylor expanded in t around inf 25.8%

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

      1. *-commutative 25.8%

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

   5. Simplified 25.8%

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

   6. Taylor expanded in y around 0 32.6%

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

   if -1.70000000000000007e-50 < z < 3.8999999999999999e-5

   1. Initial program 87.6%

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

   3. Taylor expanded in z around 0 53.9%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-50} \lor \neg \left(z \leq 3.9 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.6% 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 69.1%

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

3. Taylor expanded in z around 0 26.3%

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

4. Final simplification 26.3%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 74.0% 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 2024021 
(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)))))