Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.9% → 91.2%

Time: 23.0s

Alternatives: 24

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.9% 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: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := x \cdot y + t_2\\ t_4 := \frac{t_3}{y + z \cdot \left(b - y\right)}\\ t_5 := \left(-\frac{x}{z + -1}\right) - \frac{\frac{z}{\frac{z + -1}{t - a}} + \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-269}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_1 - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{elif}\;t_4 \leq 10^{+267}:\\ \;\;\;\;\frac{t_3}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1 - \frac{\frac{x}{\frac{y - b}{y}} + \frac{y}{\frac{{\left(y - b\right)}^{2}}{t - a}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b)))
        (t_2 (* z (- t a)))
        (t_3 (+ (* x y) t_2))
        (t_4 (/ t_3 (+ y (* z (- b y)))))
        (t_5
         (-
          (- (/ x (+ z -1.0)))
          (/
           (+
            (/ z (/ (+ z -1.0) (- t a)))
            (/ b (/ (pow (+ z -1.0) 2.0) (* x z))))
           y))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -1e-269)
       (/ (fma x y t_2) (fma z (- b y) y))
       (if (<= t_4 0.0)
         (- t_1 (* (/ x z) (/ y (- y b))))
         (if (<= t_4 1e+267)
           (/ t_3 (+ y (- (* z b) (* y z))))
           (if (<= t_4 INFINITY)
             t_5
             (-
              t_1
              (/
               (+ (/ x (/ (- y b) y)) (/ y (/ (pow (- y b) 2.0) (- t a))))
               z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = z * (t - a);
	double t_3 = (x * y) + t_2;
	double t_4 = t_3 / (y + (z * (b - y)));
	double t_5 = -(x / (z + -1.0)) - (((z / ((z + -1.0) / (t - a))) + (b / (pow((z + -1.0), 2.0) / (x * z)))) / y);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -1e-269) {
		tmp = fma(x, y, t_2) / fma(z, (b - y), y);
	} else if (t_4 <= 0.0) {
		tmp = t_1 - ((x / z) * (y / (y - b)));
	} else if (t_4 <= 1e+267) {
		tmp = t_3 / (y + ((z * b) - (y * z)));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = t_1 - (((x / ((y - b) / y)) + (y / (pow((y - b), 2.0) / (t - a)))) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(x * y) + t_2)
	t_4 = Float64(t_3 / Float64(y + Float64(z * Float64(b - y))))
	t_5 = Float64(Float64(-Float64(x / Float64(z + -1.0))) - Float64(Float64(Float64(z / Float64(Float64(z + -1.0) / Float64(t - a))) + Float64(b / Float64((Float64(z + -1.0) ^ 2.0) / Float64(x * z)))) / y))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -1e-269)
		tmp = Float64(fma(x, y, t_2) / fma(z, Float64(b - y), y));
	elseif (t_4 <= 0.0)
		tmp = Float64(t_1 - Float64(Float64(x / z) * Float64(y / Float64(y - b))));
	elseif (t_4 <= 1e+267)
		tmp = Float64(t_3 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(t_1 - Float64(Float64(Float64(x / Float64(Float64(y - b) / y)) + Float64(y / Float64((Float64(y - b) ^ 2.0) / Float64(t - a)))) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[((-N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]) - N[(N[(N[(z / N[(N[(z + -1.0), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -1e-269], N[(N[(x * y + t$95$2), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(t$95$1 - N[(N[(x / z), $MachinePrecision] * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+267], N[(t$95$3 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, N[(t$95$1 - N[(N[(N[(x / N[(N[(y - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[Power[N[(y - b), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

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 9.9999999999999997e266 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 26.4%

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

   2. Taylor expanded in y around -inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

      3. associate-*r/ 70.7%

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

      4. neg-mul-1 70.7%

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

      5. sub-neg 70.7%

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

      6. metadata-eval 70.7%

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

   4. Simplified 82.8%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999996e-270

   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%

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

   if -9.9999999999999996e-270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 23.7%

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

      1. sub-neg 23.7%

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

      2. distribute-lft-in 23.1%

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

   3. Applied egg-rr 23.1%

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

   4. Taylor expanded in z around -inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

      3. mul-1-neg 76.2%

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

      4. mul-1-neg 76.2%

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

      5. unsub-neg 76.2%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in x around inf 63.8%

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

      1. times-frac 94.0%

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

   9. Simplified 94.0%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.9999999999999997e266

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.6%

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

   3. Applied egg-rr 99.6%

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

   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. Step-by-step derivation

      1. sub-neg 0.0%

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

      2. distribute-lft-in 0.0%

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

   3. Applied egg-rr 0.0%

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

   4. Taylor expanded in z around -inf 43.9%

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

      1. mul-1-neg 43.9%

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

      2. unsub-neg 43.9%

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

      3. mul-1-neg 43.9%

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

      4. mul-1-neg 43.9%

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

      5. unsub-neg 43.9%

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

   6. Simplified 99.9%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\left(-\frac{x}{z + -1}\right) - \frac{\frac{z}{\frac{z + -1}{t - a}} + \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-269}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+267}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\left(-\frac{x}{z + -1}\right) - \frac{\frac{z}{\frac{z + -1}{t - a}} + \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{\frac{x}{\frac{y - b}{y}} + \frac{y}{\frac{{\left(y - b\right)}^{2}}{t - a}}}{z}\\ \end{array} \]

Alternative 2: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{a - t}{y - b}\\ t_3 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ t_4 := \left(-\frac{x}{z + -1}\right) - \frac{\frac{z}{\frac{z + -1}{t - a}} + \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-269}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_2 - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{elif}\;t_3 \leq 10^{+267}:\\ \;\;\;\;\frac{t_1}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 - \frac{\frac{x}{\frac{y - b}{y}} + \frac{y}{\frac{{\left(y - b\right)}^{2}}{t - a}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a))))
        (t_2 (/ (- a t) (- y b)))
        (t_3 (/ t_1 (+ y (* z (- b y)))))
        (t_4
         (-
          (- (/ x (+ z -1.0)))
          (/
           (+
            (/ z (/ (+ z -1.0) (- t a)))
            (/ b (/ (pow (+ z -1.0) 2.0) (* x z))))
           y))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -1e-269)
       t_3
       (if (<= t_3 0.0)
         (- t_2 (* (/ x z) (/ y (- y b))))
         (if (<= t_3 1e+267)
           (/ t_1 (+ y (- (* z b) (* y z))))
           (if (<= t_3 INFINITY)
             t_4
             (-
              t_2
              (/
               (+ (/ x (/ (- y b) y)) (/ y (/ (pow (- y b) 2.0) (- t a))))
               z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = (a - t) / (y - b);
	double t_3 = t_1 / (y + (z * (b - y)));
	double t_4 = -(x / (z + -1.0)) - (((z / ((z + -1.0) / (t - a))) + (b / (pow((z + -1.0), 2.0) / (x * z)))) / y);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -1e-269) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2 - ((x / z) * (y / (y - b)));
	} else if (t_3 <= 1e+267) {
		tmp = t_1 / (y + ((z * b) - (y * z)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_2 - (((x / ((y - b) / y)) + (y / (pow((y - b), 2.0) / (t - a)))) / z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = (a - t) / (y - b);
	double t_3 = t_1 / (y + (z * (b - y)));
	double t_4 = -(x / (z + -1.0)) - (((z / ((z + -1.0) / (t - a))) + (b / (Math.pow((z + -1.0), 2.0) / (x * z)))) / y);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -1e-269) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2 - ((x / z) * (y / (y - b)));
	} else if (t_3 <= 1e+267) {
		tmp = t_1 / (y + ((z * b) - (y * z)));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = t_2 - (((x / ((y - b) / y)) + (y / (Math.pow((y - b), 2.0) / (t - a)))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * (t - a))
	t_2 = (a - t) / (y - b)
	t_3 = t_1 / (y + (z * (b - y)))
	t_4 = -(x / (z + -1.0)) - (((z / ((z + -1.0) / (t - a))) + (b / (math.pow((z + -1.0), 2.0) / (x * z)))) / y)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -1e-269:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = t_2 - ((x / z) * (y / (y - b)))
	elif t_3 <= 1e+267:
		tmp = t_1 / (y + ((z * b) - (y * z)))
	elif t_3 <= math.inf:
		tmp = t_4
	else:
		tmp = t_2 - (((x / ((y - b) / y)) + (y / (math.pow((y - b), 2.0) / (t - a)))) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	t_3 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	t_4 = Float64(Float64(-Float64(x / Float64(z + -1.0))) - Float64(Float64(Float64(z / Float64(Float64(z + -1.0) / Float64(t - a))) + Float64(b / Float64((Float64(z + -1.0) ^ 2.0) / Float64(x * z)))) / y))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -1e-269)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(t_2 - Float64(Float64(x / z) * Float64(y / Float64(y - b))));
	elseif (t_3 <= 1e+267)
		tmp = Float64(t_1 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(t_2 - Float64(Float64(Float64(x / Float64(Float64(y - b) / y)) + Float64(y / Float64((Float64(y - b) ^ 2.0) / Float64(t - a)))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * (t - a));
	t_2 = (a - t) / (y - b);
	t_3 = t_1 / (y + (z * (b - y)));
	t_4 = -(x / (z + -1.0)) - (((z / ((z + -1.0) / (t - a))) + (b / (((z + -1.0) ^ 2.0) / (x * z)))) / y);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -1e-269)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2 - ((x / z) * (y / (y - b)));
	elseif (t_3 <= 1e+267)
		tmp = t_1 / (y + ((z * b) - (y * z)));
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_2 - (((x / ((y - b) / y)) + (y / (((y - b) ^ 2.0) / (t - a)))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[((-N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]) - N[(N[(N[(z / N[(N[(z + -1.0), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -1e-269], t$95$3, If[LessEqual[t$95$3, 0.0], N[(t$95$2 - N[(N[(x / z), $MachinePrecision] * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+267], N[(t$95$1 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$4, N[(t$95$2 - N[(N[(N[(x / N[(N[(y - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[Power[N[(y - b), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

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 9.9999999999999997e266 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 26.4%

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

   2. Taylor expanded in y around -inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

      3. associate-*r/ 70.7%

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

      4. neg-mul-1 70.7%

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

      5. sub-neg 70.7%

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

      6. metadata-eval 70.7%

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

   4. Simplified 82.8%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999996e-270

   1. Initial program 99.6%

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

   if -9.9999999999999996e-270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 23.7%

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

      1. sub-neg 23.7%

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

      2. distribute-lft-in 23.1%

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

   3. Applied egg-rr 23.1%

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

   4. Taylor expanded in z around -inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

      3. mul-1-neg 76.2%

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

      4. mul-1-neg 76.2%

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

      5. unsub-neg 76.2%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in x around inf 63.8%

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

      1. times-frac 94.0%

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

   9. Simplified 94.0%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.9999999999999997e266

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.6%

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

   3. Applied egg-rr 99.6%

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

   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. Step-by-step derivation

      1. sub-neg 0.0%

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

      2. distribute-lft-in 0.0%

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

   3. Applied egg-rr 0.0%

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

   4. Taylor expanded in z around -inf 43.9%

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

      1. mul-1-neg 43.9%

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

      2. unsub-neg 43.9%

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

      3. mul-1-neg 43.9%

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

      4. mul-1-neg 43.9%

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

      5. unsub-neg 43.9%

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

   6. Simplified 99.9%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\left(-\frac{x}{z + -1}\right) - \frac{\frac{z}{\frac{z + -1}{t - a}} + \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-269}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+267}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\left(-\frac{x}{z + -1}\right) - \frac{\frac{z}{\frac{z + -1}{t - a}} + \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{\frac{x}{\frac{y - b}{y}} + \frac{y}{\frac{{\left(y - b\right)}^{2}}{t - a}}}{z}\\ \end{array} \]

Alternative 3: 89.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{a - t}{y - b}\\ t_3 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -18000000000000:\\ \;\;\;\;t_2 - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot y}{t_3} + \frac{t_1}{t_3}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{y}}\\ \mathbf{elif}\;z \leq 480000000000:\\ \;\;\;\;\frac{x \cdot y + t_1}{t_3}\\ \mathbf{else}:\\ \;\;\;\;t_2 - \frac{\frac{x}{\frac{y - b}{y}} + \frac{y}{\frac{{\left(y - b\right)}^{2}}{t - a}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ (- a t) (- y b)))
        (t_3 (+ y (* z (- b y)))))
   (if (<= z -18000000000000.0)
     (- t_2 (* (/ x z) (/ y (- y b))))
     (if (<= z -4.7e-240)
       (+ (/ (* x y) t_3) (/ t_1 t_3))
       (if (<= z 1.12e-244)
         (/ x (/ (fma z (- b y) y) y))
         (if (<= z 480000000000.0)
           (/ (+ (* x y) t_1) t_3)
           (-
            t_2
            (/
             (+ (/ x (/ (- y b) y)) (/ y (/ (pow (- y b) 2.0) (- t a))))
             z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (a - t) / (y - b);
	double t_3 = y + (z * (b - y));
	double tmp;
	if (z <= -18000000000000.0) {
		tmp = t_2 - ((x / z) * (y / (y - b)));
	} else if (z <= -4.7e-240) {
		tmp = ((x * y) / t_3) + (t_1 / t_3);
	} else if (z <= 1.12e-244) {
		tmp = x / (fma(z, (b - y), y) / y);
	} else if (z <= 480000000000.0) {
		tmp = ((x * y) + t_1) / t_3;
	} else {
		tmp = t_2 - (((x / ((y - b) / y)) + (y / (pow((y - b), 2.0) / (t - a)))) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	t_3 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -18000000000000.0)
		tmp = Float64(t_2 - Float64(Float64(x / z) * Float64(y / Float64(y - b))));
	elseif (z <= -4.7e-240)
		tmp = Float64(Float64(Float64(x * y) / t_3) + Float64(t_1 / t_3));
	elseif (z <= 1.12e-244)
		tmp = Float64(x / Float64(fma(z, Float64(b - y), y) / y));
	elseif (z <= 480000000000.0)
		tmp = Float64(Float64(Float64(x * y) + t_1) / t_3);
	else
		tmp = Float64(t_2 - Float64(Float64(Float64(x / Float64(Float64(y - b) / y)) + Float64(y / Float64((Float64(y - b) ^ 2.0) / Float64(t - a)))) / z));
	end
	return 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[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -18000000000000.0], N[(t$95$2 - N[(N[(x / z), $MachinePrecision] * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.7e-240], N[(N[(N[(x * y), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(t$95$1 / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e-244], N[(x / N[(N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 480000000000.0], N[(N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$3), $MachinePrecision], N[(t$95$2 - N[(N[(N[(x / N[(N[(y - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[Power[N[(y - b), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.8e13

   1. Initial program 50.5%

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

      1. sub-neg 50.5%

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

      2. distribute-lft-in 50.4%

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

   3. Applied egg-rr 50.4%

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

   4. Taylor expanded in z around -inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. unsub-neg 64.1%

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

      3. mul-1-neg 64.1%

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

      4. mul-1-neg 64.1%

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

      5. unsub-neg 64.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in x around inf 81.0%

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

      1. times-frac 99.9%

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

   9. Simplified 99.9%

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

   if -1.8e13 < z < -4.70000000000000012e-240

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 86.0%

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

   if -4.70000000000000012e-240 < z < 1.1200000000000001e-244

   1. Initial program 64.0%

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

   2. Taylor expanded in x around inf 57.3%

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

      1. associate-/l* 90.1%

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

      2. +-commutative 90.1%

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

      3. fma-def 90.1%

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

   4. Simplified 90.1%

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

   if 1.1200000000000001e-244 < z < 4.8e11

   1. Initial program 84.1%

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

   if 4.8e11 < z

   1. Initial program 33.2%

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

      1. sub-neg 33.2%

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

      2. distribute-lft-in 33.1%

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

   3. Applied egg-rr 33.1%

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

   4. Taylor expanded in z around -inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

      3. mul-1-neg 71.1%

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

      4. mul-1-neg 71.1%

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

      5. unsub-neg 71.1%

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

   6. Simplified 98.3%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18000000000000:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{y}}\\ \mathbf{elif}\;z \leq 480000000000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{\frac{x}{\frac{y - b}{y}} + \frac{y}{\frac{{\left(y - b\right)}^{2}}{t - a}}}{z}\\ \end{array} \]

Alternative 4: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ t_3 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -2150000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-244}:\\ \;\;\;\;\frac{x \cdot y}{t_3} + \frac{t_1}{t_3}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-245}:\\ \;\;\;\;\frac{x}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{y}}\\ \mathbf{elif}\;z \leq 430000000000:\\ \;\;\;\;\frac{x \cdot y + t_1}{t_3}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (- (/ (- a t) (- y b)) (* (/ x z) (/ y (- y b)))))
        (t_3 (+ y (* z (- b y)))))
   (if (<= z -2150000000000.0)
     t_2
     (if (<= z -1.32e-244)
       (+ (/ (* x y) t_3) (/ t_1 t_3))
       (if (<= z 7e-245)
         (/ x (/ (fma z (- b y) y) y))
         (if (<= z 430000000000.0) (/ (+ (* x y) t_1) t_3) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)));
	double t_3 = y + (z * (b - y));
	double tmp;
	if (z <= -2150000000000.0) {
		tmp = t_2;
	} else if (z <= -1.32e-244) {
		tmp = ((x * y) / t_3) + (t_1 / t_3);
	} else if (z <= 7e-245) {
		tmp = x / (fma(z, (b - y), y) / y);
	} else if (z <= 430000000000.0) {
		tmp = ((x * y) + t_1) / t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(Float64(x / z) * Float64(y / Float64(y - b))))
	t_3 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -2150000000000.0)
		tmp = t_2;
	elseif (z <= -1.32e-244)
		tmp = Float64(Float64(Float64(x * y) / t_3) + Float64(t_1 / t_3));
	elseif (z <= 7e-245)
		tmp = Float64(x / Float64(fma(z, Float64(b - y), y) / y));
	elseif (z <= 430000000000.0)
		tmp = Float64(Float64(Float64(x * y) + t_1) / t_3);
	else
		tmp = t_2;
	end
	return 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[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2150000000000.0], t$95$2, If[LessEqual[z, -1.32e-244], N[(N[(N[(x * y), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(t$95$1 / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-245], N[(x / N[(N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 430000000000.0], N[(N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$3), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.15e12 or 4.3e11 < z

   1. Initial program 42.1%

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

      1. sub-neg 42.1%

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

      2. distribute-lft-in 41.9%

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

   3. Applied egg-rr 41.9%

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

   4. Taylor expanded in z around -inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

      3. mul-1-neg 67.5%

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

      4. mul-1-neg 67.5%

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

      5. unsub-neg 67.5%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in x around inf 80.5%

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

      1. times-frac 99.1%

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

   9. Simplified 99.1%

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

   if -2.15e12 < z < -1.32e-244

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 86.0%

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

   if -1.32e-244 < z < 7.00000000000000033e-245

   1. Initial program 64.0%

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

   2. Taylor expanded in x around inf 57.3%

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

      1. associate-/l* 90.1%

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

      2. +-commutative 90.1%

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

      3. fma-def 90.1%

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

   4. Simplified 90.1%

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

   if 7.00000000000000033e-245 < z < 4.3e11

   1. Initial program 84.1%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2150000000000:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-244}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-245}:\\ \;\;\;\;\frac{x}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{y}}\\ \mathbf{elif}\;z \leq 430000000000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \end{array} \]

Alternative 5: 90.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ t_3 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -3700000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y}{t_3} + \frac{t_1}{t_3}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot y + t_1}{t_3}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (- (/ (- a t) (- y b)) (* (/ x z) (/ y (- y b)))))
        (t_3 (+ y (* z (- b y)))))
   (if (<= z -3700000000000.0)
     t_2
     (if (<= z -1.35e-243)
       (+ (/ (* x y) t_3) (/ t_1 t_3))
       (if (<= z 6e-245)
         x
         (if (<= z 1.16e+14) (/ (+ (* x y) t_1) t_3) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)));
	double t_3 = y + (z * (b - y));
	double tmp;
	if (z <= -3700000000000.0) {
		tmp = t_2;
	} else if (z <= -1.35e-243) {
		tmp = ((x * y) / t_3) + (t_1 / t_3);
	} else if (z <= 6e-245) {
		tmp = x;
	} else if (z <= 1.16e+14) {
		tmp = ((x * y) + t_1) / t_3;
	} 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 = z * (t - a)
    t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)))
    t_3 = y + (z * (b - y))
    if (z <= (-3700000000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.35d-243)) then
        tmp = ((x * y) / t_3) + (t_1 / t_3)
    else if (z <= 6d-245) then
        tmp = x
    else if (z <= 1.16d+14) then
        tmp = ((x * y) + t_1) / t_3
    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 = z * (t - a);
	double t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)));
	double t_3 = y + (z * (b - y));
	double tmp;
	if (z <= -3700000000000.0) {
		tmp = t_2;
	} else if (z <= -1.35e-243) {
		tmp = ((x * y) / t_3) + (t_1 / t_3);
	} else if (z <= 6e-245) {
		tmp = x;
	} else if (z <= 1.16e+14) {
		tmp = ((x * y) + t_1) / t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)))
	t_3 = y + (z * (b - y))
	tmp = 0
	if z <= -3700000000000.0:
		tmp = t_2
	elif z <= -1.35e-243:
		tmp = ((x * y) / t_3) + (t_1 / t_3)
	elif z <= 6e-245:
		tmp = x
	elif z <= 1.16e+14:
		tmp = ((x * y) + t_1) / t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(Float64(x / z) * Float64(y / Float64(y - b))))
	t_3 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -3700000000000.0)
		tmp = t_2;
	elseif (z <= -1.35e-243)
		tmp = Float64(Float64(Float64(x * y) / t_3) + Float64(t_1 / t_3));
	elseif (z <= 6e-245)
		tmp = x;
	elseif (z <= 1.16e+14)
		tmp = Float64(Float64(Float64(x * y) + t_1) / t_3);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)));
	t_3 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -3700000000000.0)
		tmp = t_2;
	elseif (z <= -1.35e-243)
		tmp = ((x * y) / t_3) + (t_1 / t_3);
	elseif (z <= 6e-245)
		tmp = x;
	elseif (z <= 1.16e+14)
		tmp = ((x * y) + t_1) / t_3;
	else
		tmp = t_2;
	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[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3700000000000.0], t$95$2, If[LessEqual[z, -1.35e-243], N[(N[(N[(x * y), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(t$95$1 / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-245], x, If[LessEqual[z, 1.16e+14], N[(N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$3), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7e12 or 1.16e14 < z

   1. Initial program 42.1%

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

      1. sub-neg 42.1%

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

      2. distribute-lft-in 41.9%

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

   3. Applied egg-rr 41.9%

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

   4. Taylor expanded in z around -inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

      3. mul-1-neg 67.5%

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

      4. mul-1-neg 67.5%

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

      5. unsub-neg 67.5%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in x around inf 80.5%

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

      1. times-frac 99.1%

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

   9. Simplified 99.1%

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

   if -3.7e12 < z < -1.35000000000000005e-243

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 86.0%

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

   if -1.35000000000000005e-243 < z < 6.0000000000000004e-245

   1. Initial program 64.0%

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

   2. Taylor expanded in z around 0 83.4%

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

   if 6.0000000000000004e-245 < z < 1.16e14

   1. Initial program 84.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3700000000000:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \end{array} \]

Alternative 6: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b} - \frac{x}{z}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot y + z \cdot t}{t_2}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-244}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_2}\\ \mathbf{elif}\;z \leq 440000000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) (- y b)) (/ x z)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* x y) (* z t)) t_2)))
   (if (<= z -4.4e-5)
     t_1
     (if (<= z -1.12e-244)
       t_3
       (if (<= z 5.5e-113)
         x
         (if (<= z 4.5e-59)
           (/ (* z (- t a)) t_2)
           (if (<= z 440000000000.0) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) - (x / z);
	double t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + (z * t)) / t_2;
	double tmp;
	if (z <= -4.4e-5) {
		tmp = t_1;
	} else if (z <= -1.12e-244) {
		tmp = t_3;
	} else if (z <= 5.5e-113) {
		tmp = x;
	} else if (z <= 4.5e-59) {
		tmp = (z * (t - a)) / t_2;
	} else if (z <= 440000000000.0) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((a - t) / (y - b)) - (x / z)
    t_2 = y + (z * (b - y))
    t_3 = ((x * y) + (z * t)) / t_2
    if (z <= (-4.4d-5)) then
        tmp = t_1
    else if (z <= (-1.12d-244)) then
        tmp = t_3
    else if (z <= 5.5d-113) then
        tmp = x
    else if (z <= 4.5d-59) then
        tmp = (z * (t - a)) / t_2
    else if (z <= 440000000000.0d0) then
        tmp = t_3
    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 = ((a - t) / (y - b)) - (x / z);
	double t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + (z * t)) / t_2;
	double tmp;
	if (z <= -4.4e-5) {
		tmp = t_1;
	} else if (z <= -1.12e-244) {
		tmp = t_3;
	} else if (z <= 5.5e-113) {
		tmp = x;
	} else if (z <= 4.5e-59) {
		tmp = (z * (t - a)) / t_2;
	} else if (z <= 440000000000.0) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / (y - b)) - (x / z)
	t_2 = y + (z * (b - y))
	t_3 = ((x * y) + (z * t)) / t_2
	tmp = 0
	if z <= -4.4e-5:
		tmp = t_1
	elif z <= -1.12e-244:
		tmp = t_3
	elif z <= 5.5e-113:
		tmp = x
	elif z <= 4.5e-59:
		tmp = (z * (t - a)) / t_2
	elif z <= 440000000000.0:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * t)) / t_2)
	tmp = 0.0
	if (z <= -4.4e-5)
		tmp = t_1;
	elseif (z <= -1.12e-244)
		tmp = t_3;
	elseif (z <= 5.5e-113)
		tmp = x;
	elseif (z <= 4.5e-59)
		tmp = Float64(Float64(z * Float64(t - a)) / t_2);
	elseif (z <= 440000000000.0)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / (y - b)) - (x / z);
	t_2 = y + (z * (b - y));
	t_3 = ((x * y) + (z * t)) / t_2;
	tmp = 0.0;
	if (z <= -4.4e-5)
		tmp = t_1;
	elseif (z <= -1.12e-244)
		tmp = t_3;
	elseif (z <= 5.5e-113)
		tmp = x;
	elseif (z <= 4.5e-59)
		tmp = (z * (t - a)) / t_2;
	elseif (z <= 440000000000.0)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[z, -4.4e-5], t$95$1, If[LessEqual[z, -1.12e-244], t$95$3, If[LessEqual[z, 5.5e-113], x, If[LessEqual[z, 4.5e-59], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 440000000000.0], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.3999999999999999e-5 or 4.4e11 < z

   1. Initial program 43.6%

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

      1. sub-neg 43.6%

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

      2. distribute-lft-in 43.5%

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

   3. Applied egg-rr 43.5%

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

   4. Taylor expanded in z around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. unsub-neg 66.4%

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

      3. mul-1-neg 66.4%

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

      4. mul-1-neg 66.4%

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

      5. unsub-neg 66.4%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in y around inf 86.3%

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

   if -4.3999999999999999e-5 < z < -1.1200000000000001e-244 or 4.50000000000000012e-59 < z < 4.4e11

   1. Initial program 86.3%

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

   2. Taylor expanded in t around inf 75.7%

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

      1. *-commutative 75.7%

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

   4. Simplified 75.7%

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

   if -1.1200000000000001e-244 < z < 5.50000000000000053e-113

   1. Initial program 70.0%

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

   2. Taylor expanded in z around 0 74.6%

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

   if 5.50000000000000053e-113 < z < 4.50000000000000012e-59

   1. Initial program 93.7%

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

   2. Taylor expanded in x around 0 81.4%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-244}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 440000000000:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \end{array} \]

Alternative 7: 83.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (- (/ (- a t) (- y b)) (/ x z))))
   (if (<= z -1.62e+22)
     t_2
     (if (<= z -6.7e-245)
       t_1
       (if (<= z 5e-245) x (if (<= z 3.2e+14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.62e+22) {
		tmp = t_2;
	} else if (z <= -6.7e-245) {
		tmp = t_1;
	} else if (z <= 5e-245) {
		tmp = x;
	} else if (z <= 3.2e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    t_2 = ((a - t) / (y - b)) - (x / z)
    if (z <= (-1.62d+22)) then
        tmp = t_2
    else if (z <= (-6.7d-245)) then
        tmp = t_1
    else if (z <= 5d-245) then
        tmp = x
    else if (z <= 3.2d+14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.62e+22) {
		tmp = t_2;
	} else if (z <= -6.7e-245) {
		tmp = t_1;
	} else if (z <= 5e-245) {
		tmp = x;
	} else if (z <= 3.2e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = ((a - t) / (y - b)) - (x / z)
	tmp = 0
	if z <= -1.62e+22:
		tmp = t_2
	elif z <= -6.7e-245:
		tmp = t_1
	elif z <= 5e-245:
		tmp = x
	elif z <= 3.2e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z))
	tmp = 0.0
	if (z <= -1.62e+22)
		tmp = t_2;
	elseif (z <= -6.7e-245)
		tmp = t_1;
	elseif (z <= 5e-245)
		tmp = x;
	elseif (z <= 3.2e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = ((a - t) / (y - b)) - (x / z);
	tmp = 0.0;
	if (z <= -1.62e+22)
		tmp = t_2;
	elseif (z <= -6.7e-245)
		tmp = t_1;
	elseif (z <= 5e-245)
		tmp = x;
	elseif (z <= 3.2e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.62e+22], t$95$2, If[LessEqual[z, -6.7e-245], t$95$1, If[LessEqual[z, 5e-245], x, If[LessEqual[z, 3.2e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.62e22 or 3.2e14 < z

   1. Initial program 40.1%

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

      1. sub-neg 40.1%

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

      2. distribute-lft-in 39.9%

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

   3. Applied egg-rr 39.9%

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

   4. Taylor expanded in z around -inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. mul-1-neg 67.2%

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

      4. mul-1-neg 67.2%

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

      5. unsub-neg 67.2%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in y around inf 87.7%

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

   if -1.62e22 < z < -6.7e-245 or 4.9999999999999997e-245 < z < 3.2e14

   1. Initial program 85.6%

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

   if -6.7e-245 < z < 4.9999999999999997e-245

   1. Initial program 64.0%

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

   2. Taylor expanded in z around 0 83.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+22}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-245}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \end{array} \]

Alternative 8: 90.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{if}\;z \leq -6500000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-244}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1400000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (- (/ (- a t) (- y b)) (* (/ x z) (/ y (- y b))))))
   (if (<= z -6500000000000.0)
     t_2
     (if (<= z -1.35e-243)
       t_1
       (if (<= z 2.25e-244) x (if (<= z 1400000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)));
	double tmp;
	if (z <= -6500000000000.0) {
		tmp = t_2;
	} else if (z <= -1.35e-243) {
		tmp = t_1;
	} else if (z <= 2.25e-244) {
		tmp = x;
	} else if (z <= 1400000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)))
    if (z <= (-6500000000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.35d-243)) then
        tmp = t_1
    else if (z <= 2.25d-244) then
        tmp = x
    else if (z <= 1400000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)));
	double tmp;
	if (z <= -6500000000000.0) {
		tmp = t_2;
	} else if (z <= -1.35e-243) {
		tmp = t_1;
	} else if (z <= 2.25e-244) {
		tmp = x;
	} else if (z <= 1400000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)))
	tmp = 0
	if z <= -6500000000000.0:
		tmp = t_2
	elif z <= -1.35e-243:
		tmp = t_1
	elif z <= 2.25e-244:
		tmp = x
	elif z <= 1400000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(Float64(x / z) * Float64(y / Float64(y - b))))
	tmp = 0.0
	if (z <= -6500000000000.0)
		tmp = t_2;
	elseif (z <= -1.35e-243)
		tmp = t_1;
	elseif (z <= 2.25e-244)
		tmp = x;
	elseif (z <= 1400000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = ((a - t) / (y - b)) - ((x / z) * (y / (y - b)));
	tmp = 0.0;
	if (z <= -6500000000000.0)
		tmp = t_2;
	elseif (z <= -1.35e-243)
		tmp = t_1;
	elseif (z <= 2.25e-244)
		tmp = x;
	elseif (z <= 1400000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6500000000000.0], t$95$2, If[LessEqual[z, -1.35e-243], t$95$1, If[LessEqual[z, 2.25e-244], x, If[LessEqual[z, 1400000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e12 or 1.4e12 < z

   1. Initial program 42.1%

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

      1. sub-neg 42.1%

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

      2. distribute-lft-in 41.9%

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

   3. Applied egg-rr 41.9%

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

   4. Taylor expanded in z around -inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

      3. mul-1-neg 67.5%

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

      4. mul-1-neg 67.5%

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

      5. unsub-neg 67.5%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in x around inf 80.5%

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

      1. times-frac 99.1%

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

   9. Simplified 99.1%

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

   if -6.5e12 < z < -1.35000000000000005e-243 or 2.2500000000000001e-244 < z < 1.4e12

   1. Initial program 85.1%

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

   if -1.35000000000000005e-243 < z < 2.2500000000000001e-244

   1. Initial program 64.0%

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

   2. Taylor expanded in z around 0 83.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500000000000:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-244}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1400000000000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z} \cdot \frac{y}{y - b}\\ \end{array} \]

Alternative 9: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 88000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z (- t a)) (+ y (* z (- b y)))))
        (t_2 (- (/ (- a t) (- y b)) (/ x z))))
   (if (<= z -2.6e+20)
     t_2
     (if (<= z -2.3e-173)
       t_1
       (if (<= z 1.3e-112)
         x
         (if (<= z 2.8e-36)
           t_1
           (if (<= z 88000000000.0) (/ x (- 1.0 z)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * (b - y)));
	double t_2 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -2.6e+20) {
		tmp = t_2;
	} else if (z <= -2.3e-173) {
		tmp = t_1;
	} else if (z <= 1.3e-112) {
		tmp = x;
	} else if (z <= 2.8e-36) {
		tmp = t_1;
	} else if (z <= 88000000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (t - a)) / (y + (z * (b - y)))
    t_2 = ((a - t) / (y - b)) - (x / z)
    if (z <= (-2.6d+20)) then
        tmp = t_2
    else if (z <= (-2.3d-173)) then
        tmp = t_1
    else if (z <= 1.3d-112) then
        tmp = x
    else if (z <= 2.8d-36) then
        tmp = t_1
    else if (z <= 88000000000.0d0) then
        tmp = x / (1.0d0 - z)
    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 = (z * (t - a)) / (y + (z * (b - y)));
	double t_2 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -2.6e+20) {
		tmp = t_2;
	} else if (z <= -2.3e-173) {
		tmp = t_1;
	} else if (z <= 1.3e-112) {
		tmp = x;
	} else if (z <= 2.8e-36) {
		tmp = t_1;
	} else if (z <= 88000000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) / (y + (z * (b - y)))
	t_2 = ((a - t) / (y - b)) - (x / z)
	tmp = 0
	if z <= -2.6e+20:
		tmp = t_2
	elif z <= -2.3e-173:
		tmp = t_1
	elif z <= 1.3e-112:
		tmp = x
	elif z <= 2.8e-36:
		tmp = t_1
	elif z <= 88000000000.0:
		tmp = x / (1.0 - z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z))
	tmp = 0.0
	if (z <= -2.6e+20)
		tmp = t_2;
	elseif (z <= -2.3e-173)
		tmp = t_1;
	elseif (z <= 1.3e-112)
		tmp = x;
	elseif (z <= 2.8e-36)
		tmp = t_1;
	elseif (z <= 88000000000.0)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (t - a)) / (y + (z * (b - y)));
	t_2 = ((a - t) / (y - b)) - (x / z);
	tmp = 0.0;
	if (z <= -2.6e+20)
		tmp = t_2;
	elseif (z <= -2.3e-173)
		tmp = t_1;
	elseif (z <= 1.3e-112)
		tmp = x;
	elseif (z <= 2.8e-36)
		tmp = t_1;
	elseif (z <= 88000000000.0)
		tmp = x / (1.0 - z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+20], t$95$2, If[LessEqual[z, -2.3e-173], t$95$1, If[LessEqual[z, 1.3e-112], x, If[LessEqual[z, 2.8e-36], t$95$1, If[LessEqual[z, 88000000000.0], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e20 or 8.8e10 < z

   1. Initial program 40.1%

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

      1. sub-neg 40.1%

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

      2. distribute-lft-in 39.9%

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

   3. Applied egg-rr 39.9%

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

   4. Taylor expanded in z around -inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. mul-1-neg 67.2%

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

      4. mul-1-neg 67.2%

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

      5. unsub-neg 67.2%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in y around inf 87.7%

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

   if -2.6e20 < z < -2.29999999999999988e-173 or 1.29999999999999996e-112 < z < 2.8000000000000001e-36

   1. Initial program 89.2%

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

   2. Taylor expanded in x around 0 64.3%

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

   if -2.29999999999999988e-173 < z < 1.29999999999999996e-112

   1. Initial program 73.7%

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

   2. Taylor expanded in z around 0 71.7%

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

   if 2.8000000000000001e-36 < z < 8.8e10

   1. Initial program 80.9%

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

   2. Taylor expanded in y around inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. unsub-neg 70.9%

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

   4. Simplified 70.9%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-173}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 88000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \end{array} \]

Alternative 10: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-166}:\\ \;\;\;\;\frac{t_1}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-36}:\\ \;\;\;\;\frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 88000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (- (/ (- a t) (- y b)) (/ x z))))
   (if (<= z -3.1e+20)
     t_2
     (if (<= z -1.65e-166)
       (/ t_1 (- (* z b) (* y (+ z -1.0))))
       (if (<= z 1.3e-112)
         x
         (if (<= z 4e-36)
           (/ t_1 (+ y (* z (- b y))))
           (if (<= z 88000000000.0) (/ x (- 1.0 z)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -3.1e+20) {
		tmp = t_2;
	} else if (z <= -1.65e-166) {
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	} else if (z <= 1.3e-112) {
		tmp = x;
	} else if (z <= 4e-36) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 88000000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = ((a - t) / (y - b)) - (x / z)
    if (z <= (-3.1d+20)) then
        tmp = t_2
    else if (z <= (-1.65d-166)) then
        tmp = t_1 / ((z * b) - (y * (z + (-1.0d0))))
    else if (z <= 1.3d-112) then
        tmp = x
    else if (z <= 4d-36) then
        tmp = t_1 / (y + (z * (b - y)))
    else if (z <= 88000000000.0d0) then
        tmp = x / (1.0d0 - z)
    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 = z * (t - a);
	double t_2 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -3.1e+20) {
		tmp = t_2;
	} else if (z <= -1.65e-166) {
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	} else if (z <= 1.3e-112) {
		tmp = x;
	} else if (z <= 4e-36) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 88000000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = ((a - t) / (y - b)) - (x / z)
	tmp = 0
	if z <= -3.1e+20:
		tmp = t_2
	elif z <= -1.65e-166:
		tmp = t_1 / ((z * b) - (y * (z + -1.0)))
	elif z <= 1.3e-112:
		tmp = x
	elif z <= 4e-36:
		tmp = t_1 / (y + (z * (b - y)))
	elif z <= 88000000000.0:
		tmp = x / (1.0 - z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z))
	tmp = 0.0
	if (z <= -3.1e+20)
		tmp = t_2;
	elseif (z <= -1.65e-166)
		tmp = Float64(t_1 / Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))));
	elseif (z <= 1.3e-112)
		tmp = x;
	elseif (z <= 4e-36)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 88000000000.0)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = ((a - t) / (y - b)) - (x / z);
	tmp = 0.0;
	if (z <= -3.1e+20)
		tmp = t_2;
	elseif (z <= -1.65e-166)
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	elseif (z <= 1.3e-112)
		tmp = x;
	elseif (z <= 4e-36)
		tmp = t_1 / (y + (z * (b - y)));
	elseif (z <= 88000000000.0)
		tmp = x / (1.0 - z);
	else
		tmp = t_2;
	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[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+20], t$95$2, If[LessEqual[z, -1.65e-166], N[(t$95$1 / N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-112], x, If[LessEqual[z, 4e-36], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 88000000000.0], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.1e20 or 8.8e10 < z

   1. Initial program 40.1%

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

      1. sub-neg 40.1%

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

      2. distribute-lft-in 39.9%

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

   3. Applied egg-rr 39.9%

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

   4. Taylor expanded in z around -inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. mul-1-neg 67.2%

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

      4. mul-1-neg 67.2%

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

      5. unsub-neg 67.2%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in y around inf 87.7%

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

   if -3.1e20 < z < -1.65000000000000009e-166

   1. Initial program 86.8%

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

   2. Taylor expanded in x around 0 55.7%

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

   3. Taylor expanded in y around -inf 55.8%

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

      1. +-commutative 55.8%

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

      2. *-commutative 55.8%

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

      3. mul-1-neg 55.8%

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

      4. unsub-neg 55.8%

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

      5. *-commutative 55.8%

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

      6. sub-neg 55.8%

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

      7. metadata-eval 55.8%

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

   5. Simplified 55.8%

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

   if -1.65000000000000009e-166 < z < 1.29999999999999996e-112

   1. Initial program 73.7%

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

   2. Taylor expanded in z around 0 71.7%

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

   if 1.29999999999999996e-112 < z < 3.9999999999999998e-36

   1. Initial program 94.6%

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

   2. Taylor expanded in x around 0 84.2%

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

   if 3.9999999999999998e-36 < z < 8.8e10

   1. Initial program 80.9%

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

   2. Taylor expanded in y around inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. unsub-neg 70.9%

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

   4. Simplified 70.9%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+20}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-166}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-36}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 88000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \end{array} \]

Alternative 11: 54.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+131}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-29}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-19}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -9.5e+145)
     t_1
     (if (<= y -4.6e+131)
       (/ t (- b y))
       (if (<= y -1.3e+114)
         t_1
         (if (<= y -4.4e+48)
           (/ (- a t) y)
           (if (<= y -1.25e+17)
             (/ a (- y b))
             (if (<= y -5e-29)
               (+ x (* x z))
               (if (<= y 1.15e-19) (/ (- t a) b) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -9.5e+145) {
		tmp = t_1;
	} else if (y <= -4.6e+131) {
		tmp = t / (b - y);
	} else if (y <= -1.3e+114) {
		tmp = t_1;
	} else if (y <= -4.4e+48) {
		tmp = (a - t) / y;
	} else if (y <= -1.25e+17) {
		tmp = a / (y - b);
	} else if (y <= -5e-29) {
		tmp = x + (x * z);
	} else if (y <= 1.15e-19) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-9.5d+145)) then
        tmp = t_1
    else if (y <= (-4.6d+131)) then
        tmp = t / (b - y)
    else if (y <= (-1.3d+114)) then
        tmp = t_1
    else if (y <= (-4.4d+48)) then
        tmp = (a - t) / y
    else if (y <= (-1.25d+17)) then
        tmp = a / (y - b)
    else if (y <= (-5d-29)) then
        tmp = x + (x * z)
    else if (y <= 1.15d-19) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -9.5e+145) {
		tmp = t_1;
	} else if (y <= -4.6e+131) {
		tmp = t / (b - y);
	} else if (y <= -1.3e+114) {
		tmp = t_1;
	} else if (y <= -4.4e+48) {
		tmp = (a - t) / y;
	} else if (y <= -1.25e+17) {
		tmp = a / (y - b);
	} else if (y <= -5e-29) {
		tmp = x + (x * z);
	} else if (y <= 1.15e-19) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -9.5e+145:
		tmp = t_1
	elif y <= -4.6e+131:
		tmp = t / (b - y)
	elif y <= -1.3e+114:
		tmp = t_1
	elif y <= -4.4e+48:
		tmp = (a - t) / y
	elif y <= -1.25e+17:
		tmp = a / (y - b)
	elif y <= -5e-29:
		tmp = x + (x * z)
	elif y <= 1.15e-19:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -9.5e+145)
		tmp = t_1;
	elseif (y <= -4.6e+131)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -1.3e+114)
		tmp = t_1;
	elseif (y <= -4.4e+48)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= -1.25e+17)
		tmp = Float64(a / Float64(y - b));
	elseif (y <= -5e-29)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 1.15e-19)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -9.5e+145)
		tmp = t_1;
	elseif (y <= -4.6e+131)
		tmp = t / (b - y);
	elseif (y <= -1.3e+114)
		tmp = t_1;
	elseif (y <= -4.4e+48)
		tmp = (a - t) / y;
	elseif (y <= -1.25e+17)
		tmp = a / (y - b);
	elseif (y <= -5e-29)
		tmp = x + (x * z);
	elseif (y <= 1.15e-19)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+145], t$95$1, If[LessEqual[y, -4.6e+131], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e+114], t$95$1, If[LessEqual[y, -4.4e+48], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.25e+17], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-29], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-19], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -9.49999999999999948e145 or -4.59999999999999983e131 < y < -1.3e114 or 1.1499999999999999e-19 < y

   1. Initial program 44.3%

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

   2. Taylor expanded in y around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

   4. Simplified 62.7%

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

   if -9.49999999999999948e145 < y < -4.59999999999999983e131

   1. Initial program 15.9%

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

   2. Taylor expanded in t around inf 15.9%

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

      1. *-commutative 15.9%

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

   4. Simplified 15.9%

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

   5. Taylor expanded in z around inf 72.5%

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

   if -1.3e114 < y < -4.3999999999999999e48

   1. Initial program 72.5%

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

   2. Taylor expanded in x around 0 59.2%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. mul-1-neg 52.1%

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

      2. sub-neg 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in z around inf 45.5%

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

      1. mul-1-neg 45.5%

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

   8. Simplified 45.5%

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

   if -4.3999999999999999e48 < y < -1.25e17

   1. Initial program 76.5%

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

      1. sub-neg 76.5%

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

      2. distribute-lft-in 76.5%

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

   3. Applied egg-rr 76.5%

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

   4. Taylor expanded in z around -inf 27.3%

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

      1. mul-1-neg 27.3%

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

      2. unsub-neg 27.3%

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

      3. mul-1-neg 27.3%

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

      4. mul-1-neg 27.3%

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

      5. unsub-neg 27.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in x around inf 52.7%

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

      1. times-frac 52.7%

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

   9. Simplified 52.7%

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

   10. Taylor expanded in a around inf 40.9%

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

   if -1.25e17 < y < -4.99999999999999986e-29

   1. Initial program 62.9%

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

   2. Taylor expanded in y around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. unsub-neg 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in z around 0 61.8%

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

   if -4.99999999999999986e-29 < y < 1.1499999999999999e-19

   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 0 59.5%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+131}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-29}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-19}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 12: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{if}\;z \leq -750:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-40}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 88000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))) (t_2 (- (/ (- a t) (- y b)) (/ x z))))
   (if (<= z -750.0)
     t_2
     (if (<= z 1.6e-126)
       t_1
       (if (<= z 2.4e-40)
         (/ (- (+ t (/ (* x y) z)) a) b)
         (if (<= z 88000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -750.0) {
		tmp = t_2;
	} else if (z <= 1.6e-126) {
		tmp = t_1;
	} else if (z <= 2.4e-40) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (z <= 88000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    t_2 = ((a - t) / (y - b)) - (x / z)
    if (z <= (-750.0d0)) then
        tmp = t_2
    else if (z <= 1.6d-126) then
        tmp = t_1
    else if (z <= 2.4d-40) then
        tmp = ((t + ((x * y) / z)) - a) / b
    else if (z <= 88000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -750.0) {
		tmp = t_2;
	} else if (z <= 1.6e-126) {
		tmp = t_1;
	} else if (z <= 2.4e-40) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (z <= 88000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = ((a - t) / (y - b)) - (x / z)
	tmp = 0
	if z <= -750.0:
		tmp = t_2
	elif z <= 1.6e-126:
		tmp = t_1
	elif z <= 2.4e-40:
		tmp = ((t + ((x * y) / z)) - a) / b
	elif z <= 88000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z))
	tmp = 0.0
	if (z <= -750.0)
		tmp = t_2;
	elseif (z <= 1.6e-126)
		tmp = t_1;
	elseif (z <= 2.4e-40)
		tmp = Float64(Float64(Float64(t + Float64(Float64(x * y) / z)) - a) / b);
	elseif (z <= 88000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	t_2 = ((a - t) / (y - b)) - (x / z);
	tmp = 0.0;
	if (z <= -750.0)
		tmp = t_2;
	elseif (z <= 1.6e-126)
		tmp = t_1;
	elseif (z <= 2.4e-40)
		tmp = ((t + ((x * y) / z)) - a) / b;
	elseif (z <= 88000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -750.0], t$95$2, If[LessEqual[z, 1.6e-126], t$95$1, If[LessEqual[z, 2.4e-40], N[(N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 88000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -750 or 8.8e10 < z

   1. Initial program 43.5%

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

      1. sub-neg 43.5%

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

      2. distribute-lft-in 43.3%

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

   3. Applied egg-rr 43.3%

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

   4. Taylor expanded in z around -inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

      3. mul-1-neg 67.5%

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

      4. mul-1-neg 67.5%

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

      5. unsub-neg 67.5%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in y around inf 87.4%

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

   if -750 < z < 1.6e-126 or 2.39999999999999991e-40 < z < 8.8e10

   1. Initial program 78.2%

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

   2. Taylor expanded in y around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

   4. Simplified 60.7%

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

   if 1.6e-126 < z < 2.39999999999999991e-40

   1. Initial program 90.9%

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

   2. Taylor expanded in y around 0 40.7%

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

      1. associate--l+ 40.7%

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

      2. associate-/r* 40.7%

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

      3. times-frac 40.7%

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

      4. mul-1-neg 40.7%

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

      5. div-sub 40.7%

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

   4. Simplified 40.7%

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

   5. Taylor expanded in b around inf 63.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -750:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-40}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 88000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \end{array} \]

Alternative 13: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -0.56)
     t_2
     (if (<= z 1.65e-126)
       t_1
       (if (<= z 5.8e-41)
         (/ (+ t (- (/ x (/ z y)) a)) b)
         (if (<= z 1.5e+39) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.56) {
		tmp = t_2;
	} else if (z <= 1.65e-126) {
		tmp = t_1;
	} else if (z <= 5.8e-41) {
		tmp = (t + ((x / (z / y)) - a)) / b;
	} else if (z <= 1.5e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    t_2 = (t - a) / (b - y)
    if (z <= (-0.56d0)) then
        tmp = t_2
    else if (z <= 1.65d-126) then
        tmp = t_1
    else if (z <= 5.8d-41) then
        tmp = (t + ((x / (z / y)) - a)) / b
    else if (z <= 1.5d+39) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.56) {
		tmp = t_2;
	} else if (z <= 1.65e-126) {
		tmp = t_1;
	} else if (z <= 5.8e-41) {
		tmp = (t + ((x / (z / y)) - a)) / b;
	} else if (z <= 1.5e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.56:
		tmp = t_2
	elif z <= 1.65e-126:
		tmp = t_1
	elif z <= 5.8e-41:
		tmp = (t + ((x / (z / y)) - a)) / b
	elif z <= 1.5e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.56)
		tmp = t_2;
	elseif (z <= 1.65e-126)
		tmp = t_1;
	elseif (z <= 5.8e-41)
		tmp = Float64(Float64(t + Float64(Float64(x / Float64(z / y)) - a)) / b);
	elseif (z <= 1.5e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.56)
		tmp = t_2;
	elseif (z <= 1.65e-126)
		tmp = t_1;
	elseif (z <= 5.8e-41)
		tmp = (t + ((x / (z / y)) - a)) / b;
	elseif (z <= 1.5e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.56], t$95$2, If[LessEqual[z, 1.65e-126], t$95$1, If[LessEqual[z, 5.8e-41], N[(N[(t + N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.5e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.56000000000000005 or 1.5e39 < z

   1. Initial program 44.4%

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

   2. Taylor expanded in z around inf 78.4%

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

   if -0.56000000000000005 < z < 1.65e-126 or 5.79999999999999955e-41 < z < 1.5e39

   1. Initial program 76.3%

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

   2. Taylor expanded in y around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. unsub-neg 60.0%

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

   4. Simplified 60.0%

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

   if 1.65e-126 < z < 5.79999999999999955e-41

   1. Initial program 90.9%

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

   2. Taylor expanded in y around 0 40.7%

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

      1. associate--l+ 40.7%

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

      2. associate-/r* 40.7%

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

      3. times-frac 40.7%

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

      4. mul-1-neg 40.7%

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

      5. div-sub 40.7%

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

   4. Simplified 40.7%

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

   5. Taylor expanded in b around inf 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-/l* 63.6%

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

   7. Simplified 63.6%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 14: 63.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.8:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.8)
     t_2
     (if (<= z 3.2e-127)
       t_1
       (if (<= z 7.2e-40)
         (/ (- (+ t (/ (* x y) z)) a) b)
         (if (<= z 2e+39) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8) {
		tmp = t_2;
	} else if (z <= 3.2e-127) {
		tmp = t_1;
	} else if (z <= 7.2e-40) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (z <= 2e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    t_2 = (t - a) / (b - y)
    if (z <= (-3.8d0)) then
        tmp = t_2
    else if (z <= 3.2d-127) then
        tmp = t_1
    else if (z <= 7.2d-40) then
        tmp = ((t + ((x * y) / z)) - a) / b
    else if (z <= 2d+39) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8) {
		tmp = t_2;
	} else if (z <= 3.2e-127) {
		tmp = t_1;
	} else if (z <= 7.2e-40) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (z <= 2e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.8:
		tmp = t_2
	elif z <= 3.2e-127:
		tmp = t_1
	elif z <= 7.2e-40:
		tmp = ((t + ((x * y) / z)) - a) / b
	elif z <= 2e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.8)
		tmp = t_2;
	elseif (z <= 3.2e-127)
		tmp = t_1;
	elseif (z <= 7.2e-40)
		tmp = Float64(Float64(Float64(t + Float64(Float64(x * y) / z)) - a) / b);
	elseif (z <= 2e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.8)
		tmp = t_2;
	elseif (z <= 3.2e-127)
		tmp = t_1;
	elseif (z <= 7.2e-40)
		tmp = ((t + ((x * y) / z)) - a) / b;
	elseif (z <= 2e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8], t$95$2, If[LessEqual[z, 3.2e-127], t$95$1, If[LessEqual[z, 7.2e-40], N[(N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7999999999999998 or 1.99999999999999988e39 < z

   1. Initial program 44.4%

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

   2. Taylor expanded in z around inf 78.4%

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

   if -3.7999999999999998 < z < 3.20000000000000017e-127 or 7.2e-40 < z < 1.99999999999999988e39

   1. Initial program 76.3%

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

   2. Taylor expanded in y around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. unsub-neg 60.0%

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

   4. Simplified 60.0%

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

   if 3.20000000000000017e-127 < z < 7.2e-40

   1. Initial program 90.9%

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

   2. Taylor expanded in y around 0 40.7%

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

      1. associate--l+ 40.7%

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

      2. associate-/r* 40.7%

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

      3. times-frac 40.7%

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

      4. mul-1-neg 40.7%

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

      5. div-sub 40.7%

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

   4. Simplified 40.7%

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

   5. Taylor expanded in b around inf 63.6%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 15: 42.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ t_2 := \frac{a}{y - b}\\ \mathbf{if}\;z \leq -0.37:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+161}:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* x z))) (t_2 (/ a (- y b))))
   (if (<= z -0.37)
     t_2
     (if (<= z 8.5e-113)
       t_1
       (if (<= z 3.8e-37)
         (/ t b)
         (if (<= z 1.0) t_1 (if (<= z 7.5e+161) (/ (- t) y) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (x * z);
	double t_2 = a / (y - b);
	double tmp;
	if (z <= -0.37) {
		tmp = t_2;
	} else if (z <= 8.5e-113) {
		tmp = t_1;
	} else if (z <= 3.8e-37) {
		tmp = t / b;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else if (z <= 7.5e+161) {
		tmp = -t / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (x * z)
    t_2 = a / (y - b)
    if (z <= (-0.37d0)) then
        tmp = t_2
    else if (z <= 8.5d-113) then
        tmp = t_1
    else if (z <= 3.8d-37) then
        tmp = t / b
    else if (z <= 1.0d0) then
        tmp = t_1
    else if (z <= 7.5d+161) then
        tmp = -t / y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (x * z);
	double t_2 = a / (y - b);
	double tmp;
	if (z <= -0.37) {
		tmp = t_2;
	} else if (z <= 8.5e-113) {
		tmp = t_1;
	} else if (z <= 3.8e-37) {
		tmp = t / b;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else if (z <= 7.5e+161) {
		tmp = -t / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (x * z)
	t_2 = a / (y - b)
	tmp = 0
	if z <= -0.37:
		tmp = t_2
	elif z <= 8.5e-113:
		tmp = t_1
	elif z <= 3.8e-37:
		tmp = t / b
	elif z <= 1.0:
		tmp = t_1
	elif z <= 7.5e+161:
		tmp = -t / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(x * z))
	t_2 = Float64(a / Float64(y - b))
	tmp = 0.0
	if (z <= -0.37)
		tmp = t_2;
	elseif (z <= 8.5e-113)
		tmp = t_1;
	elseif (z <= 3.8e-37)
		tmp = Float64(t / b);
	elseif (z <= 1.0)
		tmp = t_1;
	elseif (z <= 7.5e+161)
		tmp = Float64(Float64(-t) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (x * z);
	t_2 = a / (y - b);
	tmp = 0.0;
	if (z <= -0.37)
		tmp = t_2;
	elseif (z <= 8.5e-113)
		tmp = t_1;
	elseif (z <= 3.8e-37)
		tmp = t / b;
	elseif (z <= 1.0)
		tmp = t_1;
	elseif (z <= 7.5e+161)
		tmp = -t / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.37], t$95$2, If[LessEqual[z, 8.5e-113], t$95$1, If[LessEqual[z, 3.8e-37], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.0], t$95$1, If[LessEqual[z, 7.5e+161], N[((-t) / y), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.37 or 7.4999999999999995e161 < z

   1. Initial program 41.8%

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

      1. sub-neg 41.8%

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

      2. distribute-lft-in 41.6%

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

   3. Applied egg-rr 41.6%

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

   4. Taylor expanded in z around -inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. unsub-neg 69.3%

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

      3. mul-1-neg 69.3%

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

      4. mul-1-neg 69.3%

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

      5. unsub-neg 69.3%

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

   6. Simplified 93.5%

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

   7. Taylor expanded in x around inf 78.9%

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

      1. times-frac 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in a around inf 40.2%

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

   if -0.37 < z < 8.4999999999999995e-113 or 3.8000000000000004e-37 < z < 1

   1. Initial program 77.6%

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

   2. Taylor expanded in y around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in z around 0 59.1%

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

   if 8.4999999999999995e-113 < z < 3.8000000000000004e-37

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 50.8%

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

      1. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y around 0 30.5%

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

   if 1 < z < 7.4999999999999995e161

   1. Initial program 51.8%

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

   2. Taylor expanded in x around 0 40.8%

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

   3. Taylor expanded in y around inf 22.4%

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

      1. mul-1-neg 22.4%

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

      2. sub-neg 22.4%

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

   5. Simplified 22.4%

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

   6. Taylor expanded in t around inf 22.8%

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

      1. times-frac 37.9%

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

   8. Simplified 37.9%

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

   9. Taylor expanded in z around inf 37.9%

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

       1. associate-*r/ 37.9%

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

       2. neg-mul-1 37.9%

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

   11. Simplified 37.9%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.37:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-113}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+161}:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y - b}\\ \end{array} \]

Alternative 16: 63.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -31.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-40}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -31.5)
     t_2
     (if (<= z 1.35e-112)
       t_1
       (if (<= z 1.95e-40) (/ (- t a) b) (if (<= z 1.7e+39) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -31.5) {
		tmp = t_2;
	} else if (z <= 1.35e-112) {
		tmp = t_1;
	} else if (z <= 1.95e-40) {
		tmp = (t - a) / b;
	} else if (z <= 1.7e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    t_2 = (t - a) / (b - y)
    if (z <= (-31.5d0)) then
        tmp = t_2
    else if (z <= 1.35d-112) then
        tmp = t_1
    else if (z <= 1.95d-40) then
        tmp = (t - a) / b
    else if (z <= 1.7d+39) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -31.5) {
		tmp = t_2;
	} else if (z <= 1.35e-112) {
		tmp = t_1;
	} else if (z <= 1.95e-40) {
		tmp = (t - a) / b;
	} else if (z <= 1.7e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -31.5:
		tmp = t_2
	elif z <= 1.35e-112:
		tmp = t_1
	elif z <= 1.95e-40:
		tmp = (t - a) / b
	elif z <= 1.7e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -31.5)
		tmp = t_2;
	elseif (z <= 1.35e-112)
		tmp = t_1;
	elseif (z <= 1.95e-40)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 1.7e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -31.5)
		tmp = t_2;
	elseif (z <= 1.35e-112)
		tmp = t_1;
	elseif (z <= 1.95e-40)
		tmp = (t - a) / b;
	elseif (z <= 1.7e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -31.5], t$95$2, If[LessEqual[z, 1.35e-112], t$95$1, If[LessEqual[z, 1.95e-40], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.7e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -31.5 or 1.6999999999999999e39 < z

   1. Initial program 44.4%

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

   2. Taylor expanded in z around inf 78.4%

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

   if -31.5 < z < 1.35e-112 or 1.9499999999999999e-40 < z < 1.6999999999999999e39

   1. Initial program 76.0%

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

   2. Taylor expanded in y around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   4. Simplified 59.9%

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

   if 1.35e-112 < z < 1.9499999999999999e-40

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 59.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -31.5:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-40}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 17: 55.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+131}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-28} \lor \neg \left(y \leq 4.9 \cdot 10^{-21}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -9.5e+145)
     t_1
     (if (<= y -4.6e+131)
       (/ t (- b y))
       (if (or (<= y -3.6e-28) (not (<= y 4.9e-21))) t_1 (/ (- t a) b))))))

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 <= -9.5e+145) {
		tmp = t_1;
	} else if (y <= -4.6e+131) {
		tmp = t / (b - y);
	} else if ((y <= -3.6e-28) || !(y <= 4.9e-21)) {
		tmp = t_1;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-9.5d+145)) then
        tmp = t_1
    else if (y <= (-4.6d+131)) then
        tmp = t / (b - y)
    else if ((y <= (-3.6d-28)) .or. (.not. (y <= 4.9d-21))) then
        tmp = t_1
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -9.5e+145) {
		tmp = t_1;
	} else if (y <= -4.6e+131) {
		tmp = t / (b - y);
	} else if ((y <= -3.6e-28) || !(y <= 4.9e-21)) {
		tmp = t_1;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -9.5e+145:
		tmp = t_1
	elif y <= -4.6e+131:
		tmp = t / (b - y)
	elif (y <= -3.6e-28) or not (y <= 4.9e-21):
		tmp = t_1
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -9.5e+145)
		tmp = t_1;
	elseif (y <= -4.6e+131)
		tmp = Float64(t / Float64(b - y));
	elseif ((y <= -3.6e-28) || !(y <= 4.9e-21))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / b);
	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 <= -9.5e+145)
		tmp = t_1;
	elseif (y <= -4.6e+131)
		tmp = t / (b - y);
	elseif ((y <= -3.6e-28) || ~((y <= 4.9e-21)))
		tmp = t_1;
	else
		tmp = (t - a) / b;
	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, -9.5e+145], t$95$1, If[LessEqual[y, -4.6e+131], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.6e-28], N[Not[LessEqual[y, 4.9e-21]], $MachinePrecision]], t$95$1, N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.49999999999999948e145 or -4.59999999999999983e131 < y < -3.5999999999999999e-28 or 4.9000000000000002e-21 < y

   1. Initial program 49.6%

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

   2. Taylor expanded in y around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

   4. Simplified 56.8%

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

   if -9.49999999999999948e145 < y < -4.59999999999999983e131

   1. Initial program 15.9%

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

   2. Taylor expanded in t around inf 15.9%

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

      1. *-commutative 15.9%

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

   4. Simplified 15.9%

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

   5. Taylor expanded in z around inf 72.5%

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

   if -3.5999999999999999e-28 < y < 4.9000000000000002e-21

   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 0 59.5%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+131}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-28} \lor \neg \left(y \leq 4.9 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 18: 33.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4400:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4400.0)
   (/ a y)
   (if (<= z 1.55e-112)
     x
     (if (<= z 3.2e-41) (/ t b) (if (<= z 1.0) (+ x (* x z)) (/ (- t) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4400.0) {
		tmp = a / y;
	} else if (z <= 1.55e-112) {
		tmp = x;
	} else if (z <= 3.2e-41) {
		tmp = t / b;
	} else if (z <= 1.0) {
		tmp = x + (x * z);
	} else {
		tmp = -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 <= (-4400.0d0)) then
        tmp = a / y
    else if (z <= 1.55d-112) then
        tmp = x
    else if (z <= 3.2d-41) then
        tmp = t / b
    else if (z <= 1.0d0) then
        tmp = x + (x * z)
    else
        tmp = -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 <= -4400.0) {
		tmp = a / y;
	} else if (z <= 1.55e-112) {
		tmp = x;
	} else if (z <= 3.2e-41) {
		tmp = t / b;
	} else if (z <= 1.0) {
		tmp = x + (x * z);
	} else {
		tmp = -t / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4400.0:
		tmp = a / y
	elif z <= 1.55e-112:
		tmp = x
	elif z <= 3.2e-41:
		tmp = t / b
	elif z <= 1.0:
		tmp = x + (x * z)
	else:
		tmp = -t / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4400.0)
		tmp = Float64(a / y);
	elseif (z <= 1.55e-112)
		tmp = x;
	elseif (z <= 3.2e-41)
		tmp = Float64(t / b);
	elseif (z <= 1.0)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(Float64(-t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4400.0)
		tmp = a / y;
	elseif (z <= 1.55e-112)
		tmp = x;
	elseif (z <= 3.2e-41)
		tmp = t / b;
	elseif (z <= 1.0)
		tmp = x + (x * z);
	else
		tmp = -t / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4400.0], N[(a / y), $MachinePrecision], If[LessEqual[z, 1.55e-112], x, If[LessEqual[z, 3.2e-41], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.0], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[((-t) / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4400

   1. Initial program 52.0%

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

   2. Taylor expanded in x around 0 46.2%

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

   3. Taylor expanded in y around inf 26.2%

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

      1. mul-1-neg 26.2%

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

      2. sub-neg 26.2%

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

   5. Simplified 26.2%

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

   6. Taylor expanded in z around inf 41.7%

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

      1. mul-1-neg 41.7%

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

   8. Simplified 41.7%

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

   9. Taylor expanded in t around 0 26.7%

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

       1. neg-mul-1 26.7%

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

       2. distribute-neg-frac 26.7%

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

   11. Simplified 26.7%

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

   if -4400 < z < 1.5499999999999999e-112

   1. Initial program 77.7%

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

   2. Taylor expanded in z around 0 58.3%

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

   if 1.5499999999999999e-112 < z < 3.20000000000000012e-41

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 50.8%

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

      1. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y around 0 30.5%

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

   if 3.20000000000000012e-41 < z < 1

   1. Initial program 78.8%

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

   2. Taylor expanded in y around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

   4. Simplified 67.6%

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

   5. Taylor expanded in z around 0 63.3%

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

   if 1 < z

   1. Initial program 34.3%

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

   2. Taylor expanded in x around 0 29.6%

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

   3. Taylor expanded in y around inf 21.4%

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

      1. mul-1-neg 21.4%

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

      2. sub-neg 21.4%

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

   5. Simplified 21.4%

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

   6. Taylor expanded in t around inf 14.9%

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

      1. times-frac 30.3%

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

   8. Simplified 30.3%

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

   9. Taylor expanded in z around inf 30.3%

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

       1. associate-*r/ 30.3%

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

       2. neg-mul-1 30.3%

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

   11. Simplified 30.3%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \]

Alternative 19: 45.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ \mathbf{if}\;z \leq -0.38:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.43:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* x z))))
   (if (<= z -0.38)
     (/ a (- y b))
     (if (<= z 1.55e-112)
       t_1
       (if (<= z 3.4e-41) (/ t b) (if (<= z 0.43) t_1 (/ t (- b y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (x * z);
	double tmp;
	if (z <= -0.38) {
		tmp = a / (y - b);
	} else if (z <= 1.55e-112) {
		tmp = t_1;
	} else if (z <= 3.4e-41) {
		tmp = t / b;
	} else if (z <= 0.43) {
		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 + (x * z)
    if (z <= (-0.38d0)) then
        tmp = a / (y - b)
    else if (z <= 1.55d-112) then
        tmp = t_1
    else if (z <= 3.4d-41) then
        tmp = t / b
    else if (z <= 0.43d0) 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 + (x * z);
	double tmp;
	if (z <= -0.38) {
		tmp = a / (y - b);
	} else if (z <= 1.55e-112) {
		tmp = t_1;
	} else if (z <= 3.4e-41) {
		tmp = t / b;
	} else if (z <= 0.43) {
		tmp = t_1;
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (x * z)
	tmp = 0
	if z <= -0.38:
		tmp = a / (y - b)
	elif z <= 1.55e-112:
		tmp = t_1
	elif z <= 3.4e-41:
		tmp = t / b
	elif z <= 0.43:
		tmp = t_1
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(x * z))
	tmp = 0.0
	if (z <= -0.38)
		tmp = Float64(a / Float64(y - b));
	elseif (z <= 1.55e-112)
		tmp = t_1;
	elseif (z <= 3.4e-41)
		tmp = Float64(t / b);
	elseif (z <= 0.43)
		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 + (x * z);
	tmp = 0.0;
	if (z <= -0.38)
		tmp = a / (y - b);
	elseif (z <= 1.55e-112)
		tmp = t_1;
	elseif (z <= 3.4e-41)
		tmp = t / b;
	elseif (z <= 0.43)
		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[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.38], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-112], t$95$1, If[LessEqual[z, 3.4e-41], N[(t / b), $MachinePrecision], If[LessEqual[z, 0.43], t$95$1, N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.38

   1. Initial program 52.8%

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

      1. sub-neg 52.8%

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

      2. distribute-lft-in 52.6%

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

   3. Applied egg-rr 52.6%

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

   4. Taylor expanded in z around -inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

      3. mul-1-neg 64.2%

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

      4. mul-1-neg 64.2%

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

      5. unsub-neg 64.2%

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

   6. Simplified 90.3%

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

   7. Taylor expanded in x around inf 81.6%

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

      1. times-frac 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in a around inf 41.8%

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

   if -0.38 < z < 1.5499999999999999e-112 or 3.3999999999999998e-41 < z < 0.429999999999999993

   1. Initial program 77.6%

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

   2. Taylor expanded in y around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in z around 0 59.1%

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

   if 1.5499999999999999e-112 < z < 3.3999999999999998e-41

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 50.8%

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

      1. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y around 0 30.5%

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

   if 0.429999999999999993 < z

   1. Initial program 34.3%

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

   2. Taylor expanded in t around inf 23.6%

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

      1. *-commutative 23.6%

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

   4. Simplified 23.6%

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

   5. Taylor expanded in z around inf 49.8%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.38:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.43:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 20: 45.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -19000000:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.32 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= z -19000000.0)
     (/ a (- y b))
     (if (<= z 1.55e-112)
       t_1
       (if (<= z 2.32e-38) (/ t b) (if (<= z 8.8e+14) 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 (z <= -19000000.0) {
		tmp = a / (y - b);
	} else if (z <= 1.55e-112) {
		tmp = t_1;
	} else if (z <= 2.32e-38) {
		tmp = t / b;
	} else if (z <= 8.8e+14) {
		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 (z <= (-19000000.0d0)) then
        tmp = a / (y - b)
    else if (z <= 1.55d-112) then
        tmp = t_1
    else if (z <= 2.32d-38) then
        tmp = t / b
    else if (z <= 8.8d+14) 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 (z <= -19000000.0) {
		tmp = a / (y - b);
	} else if (z <= 1.55e-112) {
		tmp = t_1;
	} else if (z <= 2.32e-38) {
		tmp = t / b;
	} else if (z <= 8.8e+14) {
		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 z <= -19000000.0:
		tmp = a / (y - b)
	elif z <= 1.55e-112:
		tmp = t_1
	elif z <= 2.32e-38:
		tmp = t / b
	elif z <= 8.8e+14:
		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 (z <= -19000000.0)
		tmp = Float64(a / Float64(y - b));
	elseif (z <= 1.55e-112)
		tmp = t_1;
	elseif (z <= 2.32e-38)
		tmp = Float64(t / b);
	elseif (z <= 8.8e+14)
		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 (z <= -19000000.0)
		tmp = a / (y - b);
	elseif (z <= 1.55e-112)
		tmp = t_1;
	elseif (z <= 2.32e-38)
		tmp = t / b;
	elseif (z <= 8.8e+14)
		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[z, -19000000.0], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-112], t$95$1, If[LessEqual[z, 2.32e-38], N[(t / b), $MachinePrecision], If[LessEqual[z, 8.8e+14], t$95$1, N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9e7

   1. Initial program 52.0%

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

      1. sub-neg 52.0%

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

      2. distribute-lft-in 51.9%

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

   3. Applied egg-rr 51.9%

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

   4. Taylor expanded in z around -inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. unsub-neg 63.6%

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

      3. mul-1-neg 63.6%

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

      4. mul-1-neg 63.6%

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

      5. unsub-neg 63.6%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in x around inf 81.3%

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

      1. times-frac 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in a around inf 42.4%

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

   if -1.9e7 < z < 1.5499999999999999e-112 or 2.3199999999999999e-38 < z < 8.8e14

   1. Initial program 78.0%

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

   2. Taylor expanded in y around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. unsub-neg 60.0%

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

   4. Simplified 60.0%

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

   if 1.5499999999999999e-112 < z < 2.3199999999999999e-38

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 50.8%

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

      1. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y around 0 30.5%

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

   if 8.8e14 < z

   1. Initial program 33.2%

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

   2. Taylor expanded in t around inf 22.2%

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

      1. *-commutative 22.2%

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

   4. Simplified 22.2%

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

   5. Taylor expanded in z around inf 50.5%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19000000:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 2.32 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 21: 35.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.37:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-39}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.74:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.37)
   (/ t b)
   (if (<= z 1.55e-112)
     x
     (if (<= z 2.7e-39) (/ t b) (if (<= z 0.74) x (/ (- t) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.37) {
		tmp = t / b;
	} else if (z <= 1.55e-112) {
		tmp = x;
	} else if (z <= 2.7e-39) {
		tmp = t / b;
	} else if (z <= 0.74) {
		tmp = x;
	} else {
		tmp = -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 <= (-0.37d0)) then
        tmp = t / b
    else if (z <= 1.55d-112) then
        tmp = x
    else if (z <= 2.7d-39) then
        tmp = t / b
    else if (z <= 0.74d0) then
        tmp = x
    else
        tmp = -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 <= -0.37) {
		tmp = t / b;
	} else if (z <= 1.55e-112) {
		tmp = x;
	} else if (z <= 2.7e-39) {
		tmp = t / b;
	} else if (z <= 0.74) {
		tmp = x;
	} else {
		tmp = -t / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.37:
		tmp = t / b
	elif z <= 1.55e-112:
		tmp = x
	elif z <= 2.7e-39:
		tmp = t / b
	elif z <= 0.74:
		tmp = x
	else:
		tmp = -t / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.37)
		tmp = Float64(t / b);
	elseif (z <= 1.55e-112)
		tmp = x;
	elseif (z <= 2.7e-39)
		tmp = Float64(t / b);
	elseif (z <= 0.74)
		tmp = x;
	else
		tmp = Float64(Float64(-t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.37)
		tmp = t / b;
	elseif (z <= 1.55e-112)
		tmp = x;
	elseif (z <= 2.7e-39)
		tmp = t / b;
	elseif (z <= 0.74)
		tmp = x;
	else
		tmp = -t / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.37], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.55e-112], x, If[LessEqual[z, 2.7e-39], N[(t / b), $MachinePrecision], If[LessEqual[z, 0.74], x, N[((-t) / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.37 or 1.5499999999999999e-112 < z < 2.7000000000000001e-39

   1. Initial program 62.3%

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

   2. Taylor expanded in t around inf 36.6%

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

      1. *-commutative 36.6%

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

   4. Simplified 36.6%

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

   5. Taylor expanded in y around 0 27.2%

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

   if -0.37 < z < 1.5499999999999999e-112 or 2.7000000000000001e-39 < z < 0.73999999999999999

   1. Initial program 77.6%

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

   2. Taylor expanded in z around 0 58.9%

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

   if 0.73999999999999999 < z

   1. Initial program 34.3%

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

   2. Taylor expanded in x around 0 29.6%

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

   3. Taylor expanded in y around inf 21.4%

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

      1. mul-1-neg 21.4%

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

      2. sub-neg 21.4%

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

   5. Simplified 21.4%

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

   6. Taylor expanded in t around inf 14.9%

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

      1. times-frac 30.3%

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

   8. Simplified 30.3%

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

   9. Taylor expanded in z around inf 30.3%

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

       1. associate-*r/ 30.3%

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

       2. neg-mul-1 30.3%

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

   11. Simplified 30.3%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.37:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-39}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.74:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \]

Alternative 22: 33.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2800000:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2800000.0)
   (/ a y)
   (if (<= z 1.55e-112)
     x
     (if (<= z 6e-40) (/ t b) (if (<= z 1.0) x (/ (- t) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2800000.0) {
		tmp = a / y;
	} else if (z <= 1.55e-112) {
		tmp = x;
	} else if (z <= 6e-40) {
		tmp = t / b;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = -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 <= (-2800000.0d0)) then
        tmp = a / y
    else if (z <= 1.55d-112) then
        tmp = x
    else if (z <= 6d-40) then
        tmp = t / b
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = -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 <= -2800000.0) {
		tmp = a / y;
	} else if (z <= 1.55e-112) {
		tmp = x;
	} else if (z <= 6e-40) {
		tmp = t / b;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = -t / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2800000.0:
		tmp = a / y
	elif z <= 1.55e-112:
		tmp = x
	elif z <= 6e-40:
		tmp = t / b
	elif z <= 1.0:
		tmp = x
	else:
		tmp = -t / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2800000.0)
		tmp = Float64(a / y);
	elseif (z <= 1.55e-112)
		tmp = x;
	elseif (z <= 6e-40)
		tmp = Float64(t / b);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(Float64(-t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2800000.0)
		tmp = a / y;
	elseif (z <= 1.55e-112)
		tmp = x;
	elseif (z <= 6e-40)
		tmp = t / b;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = -t / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2800000.0], N[(a / y), $MachinePrecision], If[LessEqual[z, 1.55e-112], x, If[LessEqual[z, 6e-40], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.0], x, N[((-t) / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e6

   1. Initial program 52.0%

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

   2. Taylor expanded in x around 0 46.2%

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

   3. Taylor expanded in y around inf 26.2%

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

      1. mul-1-neg 26.2%

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

      2. sub-neg 26.2%

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

   5. Simplified 26.2%

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

   6. Taylor expanded in z around inf 41.7%

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

      1. mul-1-neg 41.7%

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

   8. Simplified 41.7%

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

   9. Taylor expanded in t around 0 26.7%

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

       1. neg-mul-1 26.7%

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

       2. distribute-neg-frac 26.7%

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

   11. Simplified 26.7%

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

   if -2.8e6 < z < 1.5499999999999999e-112 or 6.00000000000000039e-40 < z < 1

   1. Initial program 77.8%

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

   2. Taylor expanded in z around 0 58.5%

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

   if 1.5499999999999999e-112 < z < 6.00000000000000039e-40

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 50.8%

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

      1. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y around 0 30.5%

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

   if 1 < z

   1. Initial program 34.3%

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

   2. Taylor expanded in x around 0 29.6%

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

   3. Taylor expanded in y around inf 21.4%

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

      1. mul-1-neg 21.4%

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

      2. sub-neg 21.4%

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

   5. Simplified 21.4%

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

   6. Taylor expanded in t around inf 14.9%

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

      1. times-frac 30.3%

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

   8. Simplified 30.3%

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

   9. Taylor expanded in z around inf 30.3%

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

       1. associate-*r/ 30.3%

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

       2. neg-mul-1 30.3%

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

   11. Simplified 30.3%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \]

Alternative 23: 36.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.37 \lor \neg \left(z \leq 1.45 \cdot 10^{-112}\right) \land \left(z \leq 1.75 \cdot 10^{-40} \lor \neg \left(z \leq 88000000000\right)\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.37)
         (and (not (<= z 1.45e-112))
              (or (<= z 1.75e-40) (not (<= z 88000000000.0)))))
   (/ t b)
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.37) || (!(z <= 1.45e-112) && ((z <= 1.75e-40) || !(z <= 88000000000.0)))) {
		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 <= (-0.37d0)) .or. (.not. (z <= 1.45d-112)) .and. (z <= 1.75d-40) .or. (.not. (z <= 88000000000.0d0))) 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 <= -0.37) || (!(z <= 1.45e-112) && ((z <= 1.75e-40) || !(z <= 88000000000.0)))) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.37) or (not (z <= 1.45e-112) and ((z <= 1.75e-40) or not (z <= 88000000000.0))):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.37) || (!(z <= 1.45e-112) && ((z <= 1.75e-40) || !(z <= 88000000000.0))))
		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 <= -0.37) || (~((z <= 1.45e-112)) && ((z <= 1.75e-40) || ~((z <= 88000000000.0)))))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.37], And[N[Not[LessEqual[z, 1.45e-112]], $MachinePrecision], Or[LessEqual[z, 1.75e-40], N[Not[LessEqual[z, 88000000000.0]], $MachinePrecision]]]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.37 or 1.44999999999999996e-112 < z < 1.7500000000000001e-40 or 8.8e10 < 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 30.7%

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

      1. *-commutative 30.7%

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

   4. Simplified 30.7%

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

   5. Taylor expanded in y around 0 25.4%

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

   if -0.37 < z < 1.44999999999999996e-112 or 1.7500000000000001e-40 < z < 8.8e10

   1. Initial program 77.8%

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

   2. Taylor expanded in z around 0 58.5%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.37 \lor \neg \left(z \leq 1.45 \cdot 10^{-112}\right) \land \left(z \leq 1.75 \cdot 10^{-40} \lor \neg \left(z \leq 88000000000\right)\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 26.3% 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 62.7%

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

2. Taylor expanded in z around 0 28.5%

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

3. Final simplification 28.5%

   \[\leadsto x \]

Developer target: 73.4% 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 2023322 
(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)))))