Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.2% → 92.4%

Time: 19.8s

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: 66.2% 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: 92.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t_2}{t_1}\\ t_4 := \frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ t_5 := \left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_2}{t_1}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_3 \leq 10^{+265}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) t_1))
        (t_4 (+ (* (/ z y) (/ (- t a) (- 1.0 z))) (/ x (- 1.0 z))))
        (t_5
         (+
          (+ (/ t (- b y)) (* (/ x z) (/ y (- b y))))
          (- (* (/ y z) (/ (- a t) (pow (- b y) 2.0))) (/ a (- b y))))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -1e-223)
       (+ (/ (* x y) t_1) (/ t_2 t_1))
       (if (<= t_3 0.0)
         t_5
         (if (<= t_3 1e+265)
           (/ (fma x y t_2) (fma z (- b y) y))
           (if (<= t_3 INFINITY) t_4 t_5)))))))

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 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double t_4 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	double t_5 = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + (((y / z) * ((a - t) / pow((b - y), 2.0))) - (a / (b - y)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -1e-223) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else if (t_3 <= 0.0) {
		tmp = t_5;
	} else if (t_3 <= 1e+265) {
		tmp = fma(x, y, t_2) / fma(z, (b - y), y);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / t_1)
	t_4 = Float64(Float64(Float64(z / y) * Float64(Float64(t - a) / Float64(1.0 - z))) + Float64(x / Float64(1.0 - z)))
	t_5 = Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / Float64(b - y)))) + Float64(Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))) - Float64(a / Float64(b - y))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -1e-223)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1));
	elseif (t_3 <= 0.0)
		tmp = t_5;
	elseif (t_3 <= 1e+265)
		tmp = Float64(fma(x, y, t_2) / fma(z, Float64(b - y), y));
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_5;
	end
	return 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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = 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]}, Block[{t$95$5 = N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -1e-223], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], t$95$5, If[LessEqual[t$95$3, 1e+265], N[(N[(x * y + t$95$2), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$4, t$95$5]]]]]]]]]]

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 1.00000000000000007e265 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 30.6%

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

   2. Taylor expanded in y around inf 25.8%

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

      1. mul-1-neg 25.8%

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

      2. unsub-neg 25.8%

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

   4. Simplified 25.8%

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

   5. Taylor expanded in x around 0 61.5%

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

      1. +-commutative 61.5%

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

      2. times-frac 72.3%

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

   7. Simplified 72.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999997e-224

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 99.4%

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

   if -9.9999999999999997e-224 < (/.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 10.9%

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

   2. Taylor expanded in z around inf 58.4%

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

      1. times-frac 72.0%

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

      2. times-frac 100.0%

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

   4. Simplified 100.0%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.00000000000000007e265

   1. Initial program 99.6%

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

      1. fma-def 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+265}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ \end{array} \]

Alternative 2: 92.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t_2}{t_1}\\ t_4 := \frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ t_5 := \left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_2}{t_1}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_3 \leq 10^{+265}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) t_1))
        (t_4 (+ (* (/ z y) (/ (- t a) (- 1.0 z))) (/ x (- 1.0 z))))
        (t_5
         (+
          (+ (/ t (- b y)) (* (/ x z) (/ y (- b y))))
          (- (* (/ y z) (/ (- a t) (pow (- b y) 2.0))) (/ a (- b y))))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -1e-223)
       (+ (/ (* x y) t_1) (/ t_2 t_1))
       (if (<= t_3 0.0)
         t_5
         (if (<= t_3 1e+265) t_3 (if (<= t_3 INFINITY) t_4 t_5)))))))

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 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double t_4 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	double t_5 = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + (((y / z) * ((a - t) / pow((b - y), 2.0))) - (a / (b - y)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -1e-223) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else if (t_3 <= 0.0) {
		tmp = t_5;
	} else if (t_3 <= 1e+265) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} 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 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double t_4 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	double t_5 = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + (((y / z) * ((a - t) / Math.pow((b - y), 2.0))) - (a / (b - y)));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -1e-223) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else if (t_3 <= 0.0) {
		tmp = t_5;
	} else if (t_3 <= 1e+265) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = ((x * y) + t_2) / t_1
	t_4 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z))
	t_5 = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + (((y / z) * ((a - t) / math.pow((b - y), 2.0))) - (a / (b - y)))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -1e-223:
		tmp = ((x * y) / t_1) + (t_2 / t_1)
	elif t_3 <= 0.0:
		tmp = t_5
	elif t_3 <= 1e+265:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_4
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / t_1)
	t_4 = Float64(Float64(Float64(z / y) * Float64(Float64(t - a) / Float64(1.0 - z))) + Float64(x / Float64(1.0 - z)))
	t_5 = Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / Float64(b - y)))) + Float64(Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))) - Float64(a / Float64(b - y))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -1e-223)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1));
	elseif (t_3 <= 0.0)
		tmp = t_5;
	elseif (t_3 <= 1e+265)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = ((x * y) + t_2) / t_1;
	t_4 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	t_5 = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + (((y / z) * ((a - t) / ((b - y) ^ 2.0))) - (a / (b - y)));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -1e-223)
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	elseif (t_3 <= 0.0)
		tmp = t_5;
	elseif (t_3 <= 1e+265)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_5;
	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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = 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]}, Block[{t$95$5 = N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -1e-223], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], t$95$5, If[LessEqual[t$95$3, 1e+265], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$4, t$95$5]]]]]]]]]]

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 1.00000000000000007e265 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 30.6%

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

   2. Taylor expanded in y around inf 25.8%

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

      1. mul-1-neg 25.8%

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

      2. unsub-neg 25.8%

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

   4. Simplified 25.8%

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

   5. Taylor expanded in x around 0 61.5%

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

      1. +-commutative 61.5%

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

      2. times-frac 72.3%

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

   7. Simplified 72.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999997e-224

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 99.4%

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

   if -9.9999999999999997e-224 < (/.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 10.9%

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

   2. Taylor expanded in z around inf 58.4%

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

      1. times-frac 72.0%

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

      2. times-frac 100.0%

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

   4. Simplified 100.0%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.00000000000000007e265

   1. Initial program 99.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+265}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ \end{array} \]

Alternative 3: 89.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ t_5 := \frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_3}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\left(t_2 + \frac{\frac{x \cdot y}{z}}{b - y}\right) - \frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;t_4 \leq 10^{+265}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (+ (* (/ z y) (/ (- t a) (- 1.0 z))) (/ x (- 1.0 z)))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -1e-223)
       (+ (/ (* x y) t_1) (/ t_3 t_1))
       (if (<= t_4 0.0)
         (-
          (+ t_2 (/ (/ (* x y) z) (- b y)))
          (* (/ y z) (/ (- t a) (pow (- b y) 2.0))))
         (if (<= t_4 1e+265) t_4 (if (<= t_4 INFINITY) t_5 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 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -1e-223) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else if (t_4 <= 0.0) {
		tmp = (t_2 + (((x * y) / z) / (b - y))) - ((y / z) * ((t - a) / pow((b - y), 2.0)));
	} else if (t_4 <= 1e+265) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -1e-223) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else if (t_4 <= 0.0) {
		tmp = (t_2 + (((x * y) / z) / (b - y))) - ((y / z) * ((t - a) / Math.pow((b - y), 2.0)));
	} else if (t_4 <= 1e+265) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} 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 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	t_5 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -1e-223:
		tmp = ((x * y) / t_1) + (t_3 / t_1)
	elif t_4 <= 0.0:
		tmp = (t_2 + (((x * y) / z) / (b - y))) - ((y / z) * ((t - a) / math.pow((b - y), 2.0)))
	elif t_4 <= 1e+265:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_5
	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(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(Float64(z / y) * Float64(Float64(t - a) / Float64(1.0 - z))) + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -1e-223)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_3 / t_1));
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(t_2 + Float64(Float64(Float64(x * y) / z) / Float64(b - y))) - Float64(Float64(y / z) * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0))));
	elseif (t_4 <= 1e+265)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	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 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	t_5 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -1e-223)
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	elseif (t_4 <= 0.0)
		tmp = (t_2 + (((x * y) / z) / (b - y))) - ((y / z) * ((t - a) / ((b - y) ^ 2.0)));
	elseif (t_4 <= 1e+265)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = 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]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -1e-223], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(N[(t$95$2 + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+265], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$5, t$95$2]]]]]]]]]]

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 or 1.00000000000000007e265 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 30.6%

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

   2. Taylor expanded in y around inf 25.8%

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

      1. mul-1-neg 25.8%

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

      2. unsub-neg 25.8%

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

   4. Simplified 25.8%

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

   5. Taylor expanded in x around 0 61.5%

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

      1. +-commutative 61.5%

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

      2. times-frac 72.3%

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

   7. Simplified 72.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999997e-224

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 99.4%

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

   if -9.9999999999999997e-224 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 27.6%

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

   2. Taylor expanded in z around inf 65.5%

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

      1. associate--r+ 65.5%

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

      2. +-commutative 65.5%

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

      3. associate--l+ 65.5%

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

      4. associate-/r* 85.1%

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

      5. *-commutative 85.1%

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

      6. div-sub 85.1%

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

      7. times-frac 99.9%

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

   4. Simplified 99.9%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.00000000000000007e265

   1. Initial program 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf 85.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{\frac{x \cdot y}{z}}{b - y}\right) - \frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+265}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_2}\\ t_5 := \frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -4 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y}{t_2} + \frac{t_3}{t_2}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{b - y} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + t_1\\ \mathbf{elif}\;t_4 \leq 10^{+265}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_2))
        (t_5 (+ (* (/ z y) (/ (- t a) (- 1.0 z))) (/ x (- 1.0 z)))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -4e-292)
       (+ (/ (* x y) t_2) (/ t_3 t_2))
       (if (<= t_4 0.0)
         (+
          (/ (- (/ (* x y) (- b y)) (/ y (/ (pow (- b y) 2.0) (- t a)))) z)
          t_1)
         (if (<= t_4 1e+265) t_4 (if (<= t_4 INFINITY) t_5 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 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_2;
	double t_5 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -4e-292) {
		tmp = ((x * y) / t_2) + (t_3 / t_2);
	} else if (t_4 <= 0.0) {
		tmp = ((((x * y) / (b - y)) - (y / (pow((b - y), 2.0) / (t - a)))) / z) + t_1;
	} else if (t_4 <= 1e+265) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_2;
	double t_5 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -4e-292) {
		tmp = ((x * y) / t_2) + (t_3 / t_2);
	} else if (t_4 <= 0.0) {
		tmp = ((((x * y) / (b - y)) - (y / (Math.pow((b - y), 2.0) / (t - a)))) / z) + t_1;
	} else if (t_4 <= 1e+265) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} 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 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_2
	t_5 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -4e-292:
		tmp = ((x * y) / t_2) + (t_3 / t_2)
	elif t_4 <= 0.0:
		tmp = ((((x * y) / (b - y)) - (y / (math.pow((b - y), 2.0) / (t - a)))) / z) + t_1
	elif t_4 <= 1e+265:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_5
	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(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_2)
	t_5 = Float64(Float64(Float64(z / y) * Float64(Float64(t - a) / Float64(1.0 - z))) + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -4e-292)
		tmp = Float64(Float64(Float64(x * y) / t_2) + Float64(t_3 / t_2));
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(x * y) / Float64(b - y)) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(t - a)))) / z) + t_1);
	elseif (t_4 <= 1e+265)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	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 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_2;
	t_5 = ((z / y) * ((t - a) / (1.0 - z))) + (x / (1.0 - z));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -4e-292)
		tmp = ((x * y) / t_2) + (t_3 / t_2);
	elseif (t_4 <= 0.0)
		tmp = ((((x * y) / (b - y)) - (y / (((b - y) ^ 2.0) / (t - a)))) / z) + t_1;
	elseif (t_4 <= 1e+265)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = 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]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -4e-292], N[(N[(N[(x * y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(t$95$3 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(N[(N[(N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$4, 1e+265], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$5, 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 or 1.00000000000000007e265 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 30.6%

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

   2. Taylor expanded in y around inf 25.8%

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

      1. mul-1-neg 25.8%

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

      2. unsub-neg 25.8%

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

   4. Simplified 25.8%

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

   5. Taylor expanded in x around 0 61.5%

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

      1. +-commutative 61.5%

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

      2. times-frac 72.3%

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

   7. Simplified 72.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.0000000000000002e-292

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 99.4%

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

   if -4.0000000000000002e-292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 24.8%

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

   2. Taylor expanded in z around -inf 84.6%

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

      1. associate--l+ 84.6%

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

      2. mul-1-neg 84.6%

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

      3. distribute-lft-out-- 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-/l* 100.0%

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

      6. div-sub 100.0%

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

   4. Simplified 100.0%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.00000000000000007e265

   1. Initial program 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf 85.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{b - y} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+265}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{t_2}{t_1}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + t_4\\ \mathbf{elif}\;z \leq 10^{-210}:\\ \;\;\;\;x + t_4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot y + t_2}{y + \frac{z}{\frac{1}{b - y}}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (/ t_2 t_1)))
   (if (<= z -8.5e+21)
     t_3
     (if (<= z -3.2e-213)
       (+ (/ (* x y) t_1) t_4)
       (if (<= z 1e-210)
         (+ x t_4)
         (if (<= z 2.2e+30)
           (/ (+ (* x y) t_2) (+ y (/ z (/ 1.0 (- b y)))))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_2 / t_1;
	double tmp;
	if (z <= -8.5e+21) {
		tmp = t_3;
	} else if (z <= -3.2e-213) {
		tmp = ((x * y) / t_1) + t_4;
	} else if (z <= 1e-210) {
		tmp = x + t_4;
	} else if (z <= 2.2e+30) {
		tmp = ((x * y) + t_2) / (y + (z / (1.0 / (b - y))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = z * (t - a)
    t_3 = (t - a) / (b - y)
    t_4 = t_2 / t_1
    if (z <= (-8.5d+21)) then
        tmp = t_3
    else if (z <= (-3.2d-213)) then
        tmp = ((x * y) / t_1) + t_4
    else if (z <= 1d-210) then
        tmp = x + t_4
    else if (z <= 2.2d+30) then
        tmp = ((x * y) + t_2) / (y + (z / (1.0d0 / (b - y))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_2 / t_1;
	double tmp;
	if (z <= -8.5e+21) {
		tmp = t_3;
	} else if (z <= -3.2e-213) {
		tmp = ((x * y) / t_1) + t_4;
	} else if (z <= 1e-210) {
		tmp = x + t_4;
	} else if (z <= 2.2e+30) {
		tmp = ((x * y) + t_2) / (y + (z / (1.0 / (b - y))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = (t - a) / (b - y)
	t_4 = t_2 / t_1
	tmp = 0
	if z <= -8.5e+21:
		tmp = t_3
	elif z <= -3.2e-213:
		tmp = ((x * y) / t_1) + t_4
	elif z <= 1e-210:
		tmp = x + t_4
	elif z <= 2.2e+30:
		tmp = ((x * y) + t_2) / (y + (z / (1.0 / (b - y))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(t_2 / t_1)
	tmp = 0.0
	if (z <= -8.5e+21)
		tmp = t_3;
	elseif (z <= -3.2e-213)
		tmp = Float64(Float64(Float64(x * y) / t_1) + t_4);
	elseif (z <= 1e-210)
		tmp = Float64(x + t_4);
	elseif (z <= 2.2e+30)
		tmp = Float64(Float64(Float64(x * y) + t_2) / Float64(y + Float64(z / Float64(1.0 / Float64(b - y)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = (t - a) / (b - y);
	t_4 = t_2 / t_1;
	tmp = 0.0;
	if (z <= -8.5e+21)
		tmp = t_3;
	elseif (z <= -3.2e-213)
		tmp = ((x * y) / t_1) + t_4;
	elseif (z <= 1e-210)
		tmp = x + t_4;
	elseif (z <= 2.2e+30)
		tmp = ((x * y) + t_2) / (y + (z / (1.0 / (b - y))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$1), $MachinePrecision]}, If[LessEqual[z, -8.5e+21], t$95$3, If[LessEqual[z, -3.2e-213], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[z, 1e-210], N[(x + t$95$4), $MachinePrecision], If[LessEqual[z, 2.2e+30], N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / N[(y + N[(z / N[(1.0 / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.5e21 or 2.2e30 < z

   1. Initial program 37.9%

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

   2. Taylor expanded in z around inf 84.6%

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

   if -8.5e21 < z < -3.19999999999999972e-213

   1. Initial program 92.3%

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

   2. Taylor expanded in x around 0 92.3%

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

   if -3.19999999999999972e-213 < z < 1e-210

   1. Initial program 71.1%

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

   2. Taylor expanded in x around 0 71.1%

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

   3. Taylor expanded in z around 0 94.6%

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

   if 1e-210 < z < 2.2e30

   1. Initial program 92.2%

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

      1. flip-- 55.3%

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

      2. associate-*r/ 54.9%

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

      3. associate-/l* 55.4%

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

      4. *-un-lft-identity 55.4%

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

      5. associate-/l* 55.3%

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

      6. flip-- 92.2%

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

   3. Applied egg-rr 92.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 10^{-210}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \frac{z}{\frac{1}{b - y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := x \cdot y + t_1\\ t_3 := y + z \cdot \left(b - y\right)\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.45 \cdot 10^{+18}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-212}:\\ \;\;\;\;\frac{t_2}{t_3}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{t_1}{t_3}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{t_2}{y + \frac{z}{\frac{1}{b - y}}}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ (* x y) t_1))
        (t_3 (+ y (* z (- b y))))
        (t_4 (/ (- t a) (- b y))))
   (if (<= z -3.45e+18)
     t_4
     (if (<= z -9.2e-212)
       (/ t_2 t_3)
       (if (<= z 7e-216)
         (+ x (/ t_1 t_3))
         (if (<= z 1.9e+30) (/ t_2 (+ y (/ z (/ 1.0 (- b y))))) t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (x * y) + t_1;
	double t_3 = y + (z * (b - y));
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.45e+18) {
		tmp = t_4;
	} else if (z <= -9.2e-212) {
		tmp = t_2 / t_3;
	} else if (z <= 7e-216) {
		tmp = x + (t_1 / t_3);
	} else if (z <= 1.9e+30) {
		tmp = t_2 / (y + (z / (1.0 / (b - y))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (x * y) + t_1
    t_3 = y + (z * (b - y))
    t_4 = (t - a) / (b - y)
    if (z <= (-3.45d+18)) then
        tmp = t_4
    else if (z <= (-9.2d-212)) then
        tmp = t_2 / t_3
    else if (z <= 7d-216) then
        tmp = x + (t_1 / t_3)
    else if (z <= 1.9d+30) then
        tmp = t_2 / (y + (z / (1.0d0 / (b - y))))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (x * y) + t_1;
	double t_3 = y + (z * (b - y));
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.45e+18) {
		tmp = t_4;
	} else if (z <= -9.2e-212) {
		tmp = t_2 / t_3;
	} else if (z <= 7e-216) {
		tmp = x + (t_1 / t_3);
	} else if (z <= 1.9e+30) {
		tmp = t_2 / (y + (z / (1.0 / (b - y))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (x * y) + t_1
	t_3 = y + (z * (b - y))
	t_4 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.45e+18:
		tmp = t_4
	elif z <= -9.2e-212:
		tmp = t_2 / t_3
	elif z <= 7e-216:
		tmp = x + (t_1 / t_3)
	elif z <= 1.9e+30:
		tmp = t_2 / (y + (z / (1.0 / (b - y))))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(x * y) + t_1)
	t_3 = Float64(y + Float64(z * Float64(b - y)))
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.45e+18)
		tmp = t_4;
	elseif (z <= -9.2e-212)
		tmp = Float64(t_2 / t_3);
	elseif (z <= 7e-216)
		tmp = Float64(x + Float64(t_1 / t_3));
	elseif (z <= 1.9e+30)
		tmp = Float64(t_2 / Float64(y + Float64(z / Float64(1.0 / Float64(b - y)))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (x * y) + t_1;
	t_3 = y + (z * (b - y));
	t_4 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.45e+18)
		tmp = t_4;
	elseif (z <= -9.2e-212)
		tmp = t_2 / t_3;
	elseif (z <= 7e-216)
		tmp = x + (t_1 / t_3);
	elseif (z <= 1.9e+30)
		tmp = t_2 / (y + (z / (1.0 / (b - y))));
	else
		tmp = t_4;
	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[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.45e+18], t$95$4, If[LessEqual[z, -9.2e-212], N[(t$95$2 / t$95$3), $MachinePrecision], If[LessEqual[z, 7e-216], N[(x + N[(t$95$1 / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+30], N[(t$95$2 / N[(y + N[(z / N[(1.0 / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.45e18 or 1.9000000000000001e30 < z

   1. Initial program 37.9%

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

   2. Taylor expanded in z around inf 84.6%

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

   if -3.45e18 < z < -9.2000000000000004e-212

   1. Initial program 92.3%

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

   if -9.2000000000000004e-212 < z < 6.99999999999999965e-216

   1. Initial program 71.1%

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

   2. Taylor expanded in x around 0 71.1%

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

   3. Taylor expanded in z around 0 94.6%

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

   if 6.99999999999999965e-216 < z < 1.9000000000000001e30

   1. Initial program 92.2%

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

      1. flip-- 55.3%

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

      2. associate-*r/ 54.9%

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

      3. associate-/l* 55.4%

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

      4. *-un-lft-identity 55.4%

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

      5. associate-/l* 55.3%

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

      6. flip-- 92.2%

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

   3. Applied egg-rr 92.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-212}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \frac{z}{\frac{1}{b - y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot y + t_1}{t_2}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+23}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-214}:\\ \;\;\;\;x + \frac{t_1}{t_2}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

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 a) (- b y))))
   (if (<= z -2.2e+23)
     t_4
     (if (<= z -4.6e-215)
       t_3
       (if (<= z 7e-214) (+ x (/ t_1 t_2)) (if (<= z 6.2e+30) t_3 t_4))))))

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 - a) / (b - y);
	double tmp;
	if (z <= -2.2e+23) {
		tmp = t_4;
	} else if (z <= -4.6e-215) {
		tmp = t_3;
	} else if (z <= 7e-214) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 6.2e+30) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = ((x * y) + t_1) / t_2
    t_4 = (t - a) / (b - y)
    if (z <= (-2.2d+23)) then
        tmp = t_4
    else if (z <= (-4.6d-215)) then
        tmp = t_3
    else if (z <= 7d-214) then
        tmp = x + (t_1 / t_2)
    else if (z <= 6.2d+30) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + t_1) / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.2e+23) {
		tmp = t_4;
	} else if (z <= -4.6e-215) {
		tmp = t_3;
	} else if (z <= 7e-214) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 6.2e+30) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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 - a) / (b - y)
	tmp = 0
	if z <= -2.2e+23:
		tmp = t_4
	elif z <= -4.6e-215:
		tmp = t_3
	elif z <= 7e-214:
		tmp = x + (t_1 / t_2)
	elif z <= 6.2e+30:
		tmp = t_3
	else:
		tmp = t_4
	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(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.2e+23)
		tmp = t_4;
	elseif (z <= -4.6e-215)
		tmp = t_3;
	elseif (z <= 7e-214)
		tmp = Float64(x + Float64(t_1 / t_2));
	elseif (z <= 6.2e+30)
		tmp = t_3;
	else
		tmp = t_4;
	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 - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.2e+23)
		tmp = t_4;
	elseif (z <= -4.6e-215)
		tmp = t_3;
	elseif (z <= 7e-214)
		tmp = x + (t_1 / t_2);
	elseif (z <= 6.2e+30)
		tmp = t_3;
	else
		tmp = t_4;
	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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+23], t$95$4, If[LessEqual[z, -4.6e-215], t$95$3, If[LessEqual[z, 7e-214], N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+30], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000008e23 or 6.1999999999999995e30 < z

   1. Initial program 37.9%

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

   2. Taylor expanded in z around inf 84.6%

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

   if -2.20000000000000008e23 < z < -4.5999999999999998e-215 or 7e-214 < z < 6.1999999999999995e30

   1. Initial program 92.2%

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

   if -4.5999999999999998e-215 < z < 7e-214

   1. Initial program 71.1%

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

   2. Taylor expanded in x around 0 71.1%

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

   3. Taylor expanded in z around 0 94.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-215}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-214}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 46.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y}\\ t_2 := \frac{x}{1 - z}\\ t_3 := \frac{t - a}{b}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+272}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) y)) (t_2 (/ x (- 1.0 z))) (t_3 (/ (- t a) b)))
   (if (<= y -3.9e+224)
     t_2
     (if (<= y -3.8e+117)
       t_1
       (if (<= y -1.5e-24)
         t_2
         (if (<= y 1.25e-41)
           t_3
           (if (<= y 3e+25)
             t_2
             (if (<= y 1.02e+32) t_3 (if (<= y 6e+272) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double t_2 = x / (1.0 - z);
	double t_3 = (t - a) / b;
	double tmp;
	if (y <= -3.9e+224) {
		tmp = t_2;
	} else if (y <= -3.8e+117) {
		tmp = t_1;
	} else if (y <= -1.5e-24) {
		tmp = t_2;
	} else if (y <= 1.25e-41) {
		tmp = t_3;
	} else if (y <= 3e+25) {
		tmp = t_2;
	} else if (y <= 1.02e+32) {
		tmp = t_3;
	} else if (y <= 6e+272) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (a - t) / y
    t_2 = x / (1.0d0 - z)
    t_3 = (t - a) / b
    if (y <= (-3.9d+224)) then
        tmp = t_2
    else if (y <= (-3.8d+117)) then
        tmp = t_1
    else if (y <= (-1.5d-24)) then
        tmp = t_2
    else if (y <= 1.25d-41) then
        tmp = t_3
    else if (y <= 3d+25) then
        tmp = t_2
    else if (y <= 1.02d+32) then
        tmp = t_3
    else if (y <= 6d+272) 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 = (a - t) / y;
	double t_2 = x / (1.0 - z);
	double t_3 = (t - a) / b;
	double tmp;
	if (y <= -3.9e+224) {
		tmp = t_2;
	} else if (y <= -3.8e+117) {
		tmp = t_1;
	} else if (y <= -1.5e-24) {
		tmp = t_2;
	} else if (y <= 1.25e-41) {
		tmp = t_3;
	} else if (y <= 3e+25) {
		tmp = t_2;
	} else if (y <= 1.02e+32) {
		tmp = t_3;
	} else if (y <= 6e+272) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / y
	t_2 = x / (1.0 - z)
	t_3 = (t - a) / b
	tmp = 0
	if y <= -3.9e+224:
		tmp = t_2
	elif y <= -3.8e+117:
		tmp = t_1
	elif y <= -1.5e-24:
		tmp = t_2
	elif y <= 1.25e-41:
		tmp = t_3
	elif y <= 3e+25:
		tmp = t_2
	elif y <= 1.02e+32:
		tmp = t_3
	elif y <= 6e+272:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / y)
	t_2 = Float64(x / Float64(1.0 - z))
	t_3 = Float64(Float64(t - a) / b)
	tmp = 0.0
	if (y <= -3.9e+224)
		tmp = t_2;
	elseif (y <= -3.8e+117)
		tmp = t_1;
	elseif (y <= -1.5e-24)
		tmp = t_2;
	elseif (y <= 1.25e-41)
		tmp = t_3;
	elseif (y <= 3e+25)
		tmp = t_2;
	elseif (y <= 1.02e+32)
		tmp = t_3;
	elseif (y <= 6e+272)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / y;
	t_2 = x / (1.0 - z);
	t_3 = (t - a) / b;
	tmp = 0.0;
	if (y <= -3.9e+224)
		tmp = t_2;
	elseif (y <= -3.8e+117)
		tmp = t_1;
	elseif (y <= -1.5e-24)
		tmp = t_2;
	elseif (y <= 1.25e-41)
		tmp = t_3;
	elseif (y <= 3e+25)
		tmp = t_2;
	elseif (y <= 1.02e+32)
		tmp = t_3;
	elseif (y <= 6e+272)
		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[(a - t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -3.9e+224], t$95$2, If[LessEqual[y, -3.8e+117], t$95$1, If[LessEqual[y, -1.5e-24], t$95$2, If[LessEqual[y, 1.25e-41], t$95$3, If[LessEqual[y, 3e+25], t$95$2, If[LessEqual[y, 1.02e+32], t$95$3, If[LessEqual[y, 6e+272], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.90000000000000007e224 or -3.8000000000000002e117 < y < -1.49999999999999998e-24 or 1.2499999999999999e-41 < y < 3.00000000000000006e25 or 6.0000000000000004e272 < y

   1. Initial program 64.4%

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

   2. Taylor expanded in y around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   4. Simplified 64.4%

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

   if -3.90000000000000007e224 < y < -3.8000000000000002e117 or 1.0199999999999999e32 < y < 6.0000000000000004e272

   1. Initial program 41.7%

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

   2. Taylor expanded in y around inf 37.8%

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

      1. mul-1-neg 37.8%

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

      2. unsub-neg 37.8%

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

   4. Simplified 37.8%

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

   5. Taylor expanded in z around inf 51.2%

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

      1. associate-*r/ 51.2%

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

      2. neg-mul-1 51.2%

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

   7. Simplified 51.2%

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

   if -1.49999999999999998e-24 < y < 1.2499999999999999e-41 or 3.00000000000000006e25 < y < 1.0199999999999999e32

   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 y around 0 64.9%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+224}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-41}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+32}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+272}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 9: 72.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6.1 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-46}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -6.1e-28)
     t_1
     (if (<= z 3.1e-46)
       (+ x (* z (+ x (/ (- t a) y))))
       (if (<= z 1.6e+28)
         (/ (* z (- t a)) (+ y (* z (- b y))))
         (if (<= z 3.9e+67) (+ (/ x (- 1.0 z)) (/ (- a 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 <= -6.1e-28) {
		tmp = t_1;
	} else if (z <= 3.1e-46) {
		tmp = x + (z * (x + ((t - a) / y)));
	} else if (z <= 1.6e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 3.9e+67) {
		tmp = (x / (1.0 - z)) + ((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 = (t - a) / (b - y)
    if (z <= (-6.1d-28)) then
        tmp = t_1
    else if (z <= 3.1d-46) then
        tmp = x + (z * (x + ((t - a) / y)))
    else if (z <= 1.6d+28) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else if (z <= 3.9d+67) then
        tmp = (x / (1.0d0 - z)) + ((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 = (t - a) / (b - y);
	double tmp;
	if (z <= -6.1e-28) {
		tmp = t_1;
	} else if (z <= 3.1e-46) {
		tmp = x + (z * (x + ((t - a) / y)));
	} else if (z <= 1.6e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 3.9e+67) {
		tmp = (x / (1.0 - z)) + ((a - 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 <= -6.1e-28:
		tmp = t_1
	elif z <= 3.1e-46:
		tmp = x + (z * (x + ((t - a) / y)))
	elif z <= 1.6e+28:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	elif z <= 3.9e+67:
		tmp = (x / (1.0 - z)) + ((a - 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 <= -6.1e-28)
		tmp = t_1;
	elseif (z <= 3.1e-46)
		tmp = Float64(x + Float64(z * Float64(x + Float64(Float64(t - a) / y))));
	elseif (z <= 1.6e+28)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 3.9e+67)
		tmp = Float64(Float64(x / Float64(1.0 - z)) + 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 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -6.1e-28)
		tmp = t_1;
	elseif (z <= 3.1e-46)
		tmp = x + (z * (x + ((t - a) / y)));
	elseif (z <= 1.6e+28)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	elseif (z <= 3.9e+67)
		tmp = (x / (1.0 - z)) + ((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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.1e-28], t$95$1, If[LessEqual[z, 3.1e-46], N[(x + N[(z * N[(x + N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+28], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+67], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.1e-28 or 3.90000000000000007e67 < z

   1. Initial program 38.3%

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

   2. Taylor expanded in z around inf 84.2%

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

   if -6.1e-28 < z < 3.1000000000000001e-46

   1. Initial program 84.0%

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

   2. Taylor expanded in y around inf 65.6%

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

      1. mul-1-neg 65.6%

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

      2. unsub-neg 65.6%

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

   4. Simplified 65.6%

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

   5. Taylor expanded in z around 0 74.6%

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

      1. +-commutative 74.6%

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

      2. associate--r+ 74.6%

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

      3. div-sub 75.6%

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

      4. mul-1-neg 75.6%

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

   7. Simplified 75.6%

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

   if 3.1000000000000001e-46 < z < 1.6e28

   1. Initial program 95.4%

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

   2. Taylor expanded in x around 0 74.6%

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

   if 1.6e28 < z < 3.90000000000000007e67

   1. Initial program 58.4%

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

   2. Taylor expanded in y around inf 48.5%

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

      1. mul-1-neg 48.5%

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

      2. unsub-neg 48.5%

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

   4. Simplified 48.5%

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

   5. Taylor expanded in x around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. times-frac 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in z around inf 90.0%

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

      1. associate-*r/ 90.0%

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

      2. neg-mul-1 90.0%

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

   10. Simplified 90.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-28}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-46}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10: 81.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1800 \lor \neg \left(z \leq 1.7 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1800.0) (not (<= z 1.7e-17)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1800.0) || !(z <= 1.7e-17)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1800.0d0)) .or. (.not. (z <= 1.7d-17))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1800.0) || !(z <= 1.7e-17)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1800.0) or not (z <= 1.7e-17):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1800.0) || !(z <= 1.7e-17))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1800.0) || ~((z <= 1.7e-17)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1800.0], N[Not[LessEqual[z, 1.7e-17]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1800 or 1.6999999999999999e-17 < z

   1. Initial program 45.5%

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

   2. Taylor expanded in z around inf 82.5%

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

   if -1800 < z < 1.6999999999999999e-17

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0 84.6%

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

   3. Taylor expanded in z around 0 86.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1800 \lor \neg \left(z \leq 1.7 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 11: 72.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-24} \lor \neg \left(z \leq 1.2 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.1e-24) (not (<= z 1.2e-17)))
   (/ (- t a) (- b y))
   (+ x (* z (- (/ t y) (/ a y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.1e-24) || !(z <= 1.2e-17)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t / y) - (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 <= (-5.1d-24)) .or. (.not. (z <= 1.2d-17))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * ((t / y) - (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 <= -5.1e-24) || !(z <= 1.2e-17)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t / y) - (a / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.1e-24) or not (z <= 1.2e-17):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * ((t / y) - (a / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.1e-24) || !(z <= 1.2e-17))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(t / y) - Float64(a / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.1e-24) || ~((z <= 1.2e-17)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * ((t / y) - (a / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.1e-24], N[Not[LessEqual[z, 1.2e-17]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(t / y), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.10000000000000025e-24 or 1.19999999999999993e-17 < z

   1. Initial program 46.3%

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

   2. Taylor expanded in z around inf 81.2%

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

   if -5.10000000000000025e-24 < z < 1.19999999999999993e-17

   1. Initial program 84.9%

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

   2. Taylor expanded in y around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. unsub-neg 64.8%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in z around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. associate--r+ 73.3%

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

      3. div-sub 74.3%

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

      4. mul-1-neg 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in x around 0 73.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-24} \lor \neg \left(z \leq 1.2 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \end{array} \]

Alternative 12: 72.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-24} \lor \neg \left(z \leq 3.2 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.8e-24) (not (<= z 3.2e-19)))
   (/ (- t a) (- b y))
   (+ x (* z (+ x (/ (- t a) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.8e-24) || !(z <= 3.2e-19)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (x + ((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 <= (-1.8d-24)) .or. (.not. (z <= 3.2d-19))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * (x + ((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 <= -1.8e-24) || !(z <= 3.2e-19)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (x + ((t - a) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.8e-24) or not (z <= 3.2e-19):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * (x + ((t - a) / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.8e-24) || !(z <= 3.2e-19))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(x + Float64(Float64(t - a) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.8e-24) || ~((z <= 3.2e-19)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * (x + ((t - a) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.8e-24], N[Not[LessEqual[z, 3.2e-19]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x + N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e-24 or 3.19999999999999982e-19 < z

   1. Initial program 46.3%

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

   2. Taylor expanded in z around inf 81.2%

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

   if -1.8e-24 < z < 3.19999999999999982e-19

   1. Initial program 84.9%

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

   2. Taylor expanded in y around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. unsub-neg 64.8%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in z around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. associate--r+ 73.3%

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

      3. div-sub 74.3%

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

      4. mul-1-neg 74.3%

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

   7. Simplified 74.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-24} \lor \neg \left(z \leq 3.2 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \end{array} \]

Alternative 13: 54.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-50}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+26} \lor \neg \left(y \leq 9.8 \cdot 10^{+48}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.3e-24)
     t_1
     (if (<= y 1.15e-50)
       (/ (- t a) b)
       (if (or (<= y 5.5e+26) (not (<= y 9.8e+48))) t_1 (/ t (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.3e-24) {
		tmp = t_1;
	} else if (y <= 1.15e-50) {
		tmp = (t - a) / b;
	} else if ((y <= 5.5e+26) || !(y <= 9.8e+48)) {
		tmp = t_1;
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.3d-24)) then
        tmp = t_1
    else if (y <= 1.15d-50) then
        tmp = (t - a) / b
    else if ((y <= 5.5d+26) .or. (.not. (y <= 9.8d+48))) then
        tmp = t_1
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.3e-24) {
		tmp = t_1;
	} else if (y <= 1.15e-50) {
		tmp = (t - a) / b;
	} else if ((y <= 5.5e+26) || !(y <= 9.8e+48)) {
		tmp = t_1;
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.3e-24:
		tmp = t_1
	elif y <= 1.15e-50:
		tmp = (t - a) / b
	elif (y <= 5.5e+26) or not (y <= 9.8e+48):
		tmp = t_1
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.3e-24)
		tmp = t_1;
	elseif (y <= 1.15e-50)
		tmp = Float64(Float64(t - a) / b);
	elseif ((y <= 5.5e+26) || !(y <= 9.8e+48))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.3e-24)
		tmp = t_1;
	elseif (y <= 1.15e-50)
		tmp = (t - a) / b;
	elseif ((y <= 5.5e+26) || ~((y <= 9.8e+48)))
		tmp = t_1;
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e-24], t$95$1, If[LessEqual[y, 1.15e-50], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[y, 5.5e+26], N[Not[LessEqual[y, 9.8e+48]], $MachinePrecision]], t$95$1, N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.29999999999999984e-24 or 1.1500000000000001e-50 < y < 5.4999999999999997e26 or 9.80000000000000059e48 < y

   1. Initial program 53.5%

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

   2. Taylor expanded in y around inf 49.6%

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

      1. mul-1-neg 49.6%

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

      2. unsub-neg 49.6%

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

   4. Simplified 49.6%

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

   if -3.29999999999999984e-24 < y < 1.1500000000000001e-50

   1. Initial program 72.3%

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

   2. Taylor expanded in y around 0 64.0%

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

   if 5.4999999999999997e26 < y < 9.80000000000000059e48

   1. Initial program 50.6%

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

   2. Taylor expanded in t around inf 26.8%

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

   3. Taylor expanded in z around inf 75.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-50}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+26} \lor \neg \left(y \leq 9.8 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 14: 69.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-47} \lor \neg \left(z \leq 1.25 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.4e-47) (not (<= z 1.25e-21)))
   (/ (- t a) (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e-47) || !(z <= 1.25e-21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.4d-47)) .or. (.not. (z <= 1.25d-21))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e-47) || !(z <= 1.25e-21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.4e-47) or not (z <= 1.25e-21):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.4e-47) || !(z <= 1.25e-21))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.4e-47) || ~((z <= 1.25e-21)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.4e-47], N[Not[LessEqual[z, 1.25e-21]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000037e-47 or 1.24999999999999993e-21 < z

   1. Initial program 48.0%

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

   2. Taylor expanded in z around inf 80.0%

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

   if -4.40000000000000037e-47 < z < 1.24999999999999993e-21

   1. Initial program 84.2%

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

   2. Taylor expanded in y around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in z around 0 74.0%

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

      1. +-commutative 74.0%

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

      2. associate--r+ 74.0%

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

      3. div-sub 75.0%

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

      4. mul-1-neg 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in t around inf 69.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-47} \lor \neg \left(z \leq 1.25 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 15: 45.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-47} \lor \neg \left(z \leq 2.8 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e-47) (not (<= z 2.8e-53))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e-47) || !(z <= 2.8e-53)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.8d-47)) .or. (.not. (z <= 2.8d-53))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e-47) || !(z <= 2.8e-53)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.8e-47) or not (z <= 2.8e-53):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.8e-47) || !(z <= 2.8e-53))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.8e-47) || ~((z <= 2.8e-53)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.8e-47], N[Not[LessEqual[z, 2.8e-53]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.7999999999999999e-47 or 2.79999999999999985e-53 < z

   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 t around inf 29.8%

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

   3. Taylor expanded in z around inf 45.6%

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

   if -4.7999999999999999e-47 < z < 2.79999999999999985e-53

   1. Initial program 82.8%

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

   2. Taylor expanded in z around 0 59.3%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-47} \lor \neg \left(z \leq 2.8 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 45.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-48} \lor \neg \left(z \leq 9.5 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.4e-48) (not (<= z 9.5e-54))) (/ 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 <= -5.4e-48) || !(z <= 9.5e-54)) {
		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 <= (-5.4d-48)) .or. (.not. (z <= 9.5d-54))) 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 <= -5.4e-48) || !(z <= 9.5e-54)) {
		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 <= -5.4e-48) or not (z <= 9.5e-54):
		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 <= -5.4e-48) || !(z <= 9.5e-54))
		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 <= -5.4e-48) || ~((z <= 9.5e-54)))
		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, -5.4e-48], N[Not[LessEqual[z, 9.5e-54]], $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 < -5.40000000000000023e-48 or 9.4999999999999994e-54 < z

   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 t around inf 29.8%

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

   3. Taylor expanded in z around inf 45.6%

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

   if -5.40000000000000023e-48 < z < 9.4999999999999994e-54

   1. Initial program 82.8%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. unsub-neg 59.3%

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

   4. Simplified 59.3%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-48} \lor \neg \left(z \leq 9.5 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 17: 37.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-47} \lor \neg \left(z \leq 2.5 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.4e-47) (not (<= z 2.5e-47))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e-47) || !(z <= 2.5e-47)) {
		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 <= (-4.4d-47)) .or. (.not. (z <= 2.5d-47))) 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 <= -4.4e-47) || !(z <= 2.5e-47)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.4e-47) or not (z <= 2.5e-47):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.4e-47) || !(z <= 2.5e-47))
		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 <= -4.4e-47) || ~((z <= 2.5e-47)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.4e-47], N[Not[LessEqual[z, 2.5e-47]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000037e-47 or 2.50000000000000006e-47 < z

   1. Initial program 50.2%

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

   2. Taylor expanded in t around inf 30.0%

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

   3. Taylor expanded in y around 0 30.3%

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

   if -4.40000000000000037e-47 < z < 2.50000000000000006e-47

   1. Initial program 83.0%

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

   2. Taylor expanded in z around 0 58.7%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-47} \lor \neg \left(z \leq 2.5 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 61.7%

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

2. Taylor expanded in z around 0 23.6%

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

3. Final simplification 23.6%

   \[\leadsto x \]

Developer target: 73.3% 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 2023301 
(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)))))