Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.7% → 91.2%

Time: 19.9s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, b - y, y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{y + z \cdot \left(b - y\right)}\\ t_5 := {\left(b - y\right)}^{2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_4 \leq -4 \cdot 10^{-243}:\\ \;\;\;\;\frac{1}{\frac{t_1}{\mathsf{fma}\left(z, t - a, x \cdot y\right)}}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2 + \frac{\frac{y}{\frac{t_5}{a - t}} + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_3\right)}{t_1}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\frac{z}{\frac{z \cdot b}{t - a} - \frac{y}{\frac{t - a}{z + -1}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{t_5}{t - a}}}{z} + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- b y) y))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) (+ y (* z (- b y)))))
        (t_5 (pow (- b y) 2.0)))
   (if (<= t_4 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_4 -4e-243)
       (/ 1.0 (/ t_1 (fma z (- t a) (* x y))))
       (if (<= t_4 0.0)
         (+ t_2 (/ (+ (/ y (/ t_5 (- a t))) (/ (* x y) (- b y))) z))
         (if (<= t_4 2e+306)
           (/ (fma x y t_3) t_1)
           (if (<= t_4 INFINITY)
             (/ z (- (/ (* z b) (- t a)) (/ y (/ (- t a) (+ z -1.0)))))
             (+ (/ (- (/ x (/ (- b y) y)) (/ y (/ t_5 (- t a)))) z) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (b - y), y);
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / (y + (z * (b - y)));
	double t_5 = pow((b - y), 2.0);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_4 <= -4e-243) {
		tmp = 1.0 / (t_1 / fma(z, (t - a), (x * y)));
	} else if (t_4 <= 0.0) {
		tmp = t_2 + (((y / (t_5 / (a - t))) + ((x * y) / (b - y))) / z);
	} else if (t_4 <= 2e+306) {
		tmp = fma(x, y, t_3) / t_1;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = z / (((z * b) / (t - a)) - (y / ((t - a) / (z + -1.0))));
	} else {
		tmp = (((x / ((b - y) / y)) - (y / (t_5 / (t - a)))) / z) + t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(b - y), y)
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / Float64(y + Float64(z * Float64(b - y))))
	t_5 = Float64(b - y) ^ 2.0
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_4 <= -4e-243)
		tmp = Float64(1.0 / Float64(t_1 / fma(z, Float64(t - a), Float64(x * y))));
	elseif (t_4 <= 0.0)
		tmp = Float64(t_2 + Float64(Float64(Float64(y / Float64(t_5 / Float64(a - t))) + Float64(Float64(x * y) / Float64(b - y))) / z));
	elseif (t_4 <= 2e+306)
		tmp = Float64(fma(x, y, t_3) / t_1);
	elseif (t_4 <= Inf)
		tmp = Float64(z / Float64(Float64(Float64(z * b) / Float64(t - a)) - Float64(y / Float64(Float64(t - a) / Float64(z + -1.0)))));
	else
		tmp = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64(t_5 / Float64(t - a)))) / z) + t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -4e-243], N[(1.0 / N[(t$95$1 / N[(z * N[(t - a), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(t$95$2 + N[(N[(N[(y / N[(t$95$5 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+306], N[(N[(x * y + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(z / N[(N[(N[(z * b), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[(t - a), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$5 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

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

   1. Initial program 34.0%

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

   2. Taylor expanded in y around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

      3. associate-*r/ 53.0%

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

      4. neg-mul-1 53.0%

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

      5. sub-neg 53.0%

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

      6. metadata-eval 53.0%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in z around inf 86.5%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999998e-243

   1. Initial program 99.4%

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

      1. fma-def 99.4%

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

      2. clear-num 99.4%

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

      3. inv-pow 99.4%

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

      4. +-commutative 99.4%

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

      5. fma-udef 99.4%

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

   3. Applied egg-rr 99.4%

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

      1. unpow-1 99.4%

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

      2. fma-def 99.4%

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

      3. +-commutative 99.4%

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

      4. fma-def 99.4%

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

      5. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   if -3.99999999999999998e-243 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 33.9%

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

      1. sub-neg 33.9%

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

      2. distribute-lft-in 33.9%

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

   3. Applied egg-rr 33.9%

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

   4. Taylor expanded in z around -inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. associate-*r/ 75.0%

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

      4. mul-1-neg 75.0%

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

      5. mul-1-neg 75.0%

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

      6. unsub-neg 75.0%

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

   6. Simplified 95.9%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.0%

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

      1. fma-def 99.0%

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

      2. +-commutative 99.0%

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

      3. fma-def 99.0%

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

   3. Simplified 99.0%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 42.9%

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

   2. Taylor expanded in x around 0 41.5%

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

      1. associate-/l* 64.9%

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

      2. +-commutative 64.9%

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

      3. fma-def 64.9%

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

   4. Simplified 64.9%

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

   5. Taylor expanded in y around -inf 64.9%

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

      1. +-commutative 64.9%

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

      2. mul-1-neg 64.9%

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

      3. unsub-neg 64.9%

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

      4. *-commutative 64.9%

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

      5. associate-/l* 64.9%

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

      6. sub-neg 64.9%

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

      7. metadata-eval 64.9%

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

   7. Simplified 64.9%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around -inf 11.1%

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

      1. associate--l+ 11.1%

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

      2. mul-1-neg 11.1%

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

      3. distribute-lft-out-- 11.1%

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

      4. associate-/l* 18.1%

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

      5. associate-/l* 99.9%

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

      6. div-sub 99.9%

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

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}\right)}{z}\right) + \frac{t - a}{b - y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-243}:\\ \;\;\;\;\frac{1}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{\mathsf{fma}\left(z, t - a, x \cdot y\right)}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{{\left(b - y\right)}^{2}}{a - t}} + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{z}{\frac{z \cdot b}{t - a} - \frac{y}{\frac{t - a}{z + -1}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 2: 91.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ t_5 := {\left(b - y\right)}^{2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_4 \leq -4 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2 + \frac{\frac{y}{\frac{t_5}{a - t}} + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_3\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\frac{z}{\frac{z \cdot b}{t - a} - \frac{y}{\frac{t - a}{z + -1}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{t_5}{t - a}}}{z} + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (pow (- b y) 2.0)))
   (if (<= t_4 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_4 -4e-243)
       (/ (+ (* x y) (- (* z t) (* z a))) t_1)
       (if (<= t_4 0.0)
         (+ t_2 (/ (+ (/ y (/ t_5 (- a t))) (/ (* x y) (- b y))) z))
         (if (<= t_4 2e+306)
           (/ (fma x y t_3) (fma z (- b y) y))
           (if (<= t_4 INFINITY)
             (/ z (- (/ (* z b) (- t a)) (/ y (/ (- t a) (+ z -1.0)))))
             (+ (/ (- (/ x (/ (- b y) y)) (/ y (/ t_5 (- t a)))) z) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = pow((b - y), 2.0);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_4 <= -4e-243) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_4 <= 0.0) {
		tmp = t_2 + (((y / (t_5 / (a - t))) + ((x * y) / (b - y))) / z);
	} else if (t_4 <= 2e+306) {
		tmp = fma(x, y, t_3) / fma(z, (b - y), y);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = z / (((z * b) / (t - a)) - (y / ((t - a) / (z + -1.0))));
	} else {
		tmp = (((x / ((b - y) / y)) - (y / (t_5 / (t - a)))) / z) + t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(b - y) ^ 2.0
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_4 <= -4e-243)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_4 <= 0.0)
		tmp = Float64(t_2 + Float64(Float64(Float64(y / Float64(t_5 / Float64(a - t))) + Float64(Float64(x * y) / Float64(b - y))) / z));
	elseif (t_4 <= 2e+306)
		tmp = Float64(fma(x, y, t_3) / fma(z, Float64(b - y), y));
	elseif (t_4 <= Inf)
		tmp = Float64(z / Float64(Float64(Float64(z * b) / Float64(t - a)) - Float64(y / Float64(Float64(t - a) / Float64(z + -1.0)))));
	else
		tmp = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64(t_5 / Float64(t - a)))) / z) + t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -4e-243], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(t$95$2 + N[(N[(N[(y / N[(t$95$5 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+306], N[(N[(x * y + t$95$3), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(z / N[(N[(N[(z * b), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[(t - a), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$5 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

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

   1. Initial program 34.0%

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

   2. Taylor expanded in y around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

      3. associate-*r/ 53.0%

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

      4. neg-mul-1 53.0%

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

      5. sub-neg 53.0%

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

      6. metadata-eval 53.0%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in z around inf 86.5%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999998e-243

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   3. Applied egg-rr 99.4%

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

   if -3.99999999999999998e-243 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 33.9%

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

      1. sub-neg 33.9%

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

      2. distribute-lft-in 33.9%

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

   3. Applied egg-rr 33.9%

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

   4. Taylor expanded in z around -inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. associate-*r/ 75.0%

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

      4. mul-1-neg 75.0%

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

      5. mul-1-neg 75.0%

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

      6. unsub-neg 75.0%

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

   6. Simplified 95.9%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.0%

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

      1. fma-def 99.0%

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

      2. +-commutative 99.0%

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

      3. fma-def 99.0%

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

   3. Simplified 99.0%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 42.9%

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

   2. Taylor expanded in x around 0 41.5%

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

      1. associate-/l* 64.9%

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

      2. +-commutative 64.9%

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

      3. fma-def 64.9%

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

   4. Simplified 64.9%

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

   5. Taylor expanded in y around -inf 64.9%

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

      1. +-commutative 64.9%

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

      2. mul-1-neg 64.9%

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

      3. unsub-neg 64.9%

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

      4. *-commutative 64.9%

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

      5. associate-/l* 64.9%

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

      6. sub-neg 64.9%

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

      7. metadata-eval 64.9%

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

   7. Simplified 64.9%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around -inf 11.1%

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

      1. associate--l+ 11.1%

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

      2. mul-1-neg 11.1%

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

      3. distribute-lft-out-- 11.1%

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

      4. associate-/l* 18.1%

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

      5. associate-/l* 99.9%

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

      6. div-sub 99.9%

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

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}\right)}{z}\right) + \frac{t - a}{b - y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{{\left(b - y\right)}^{2}}{a - t}} + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{z}{\frac{z \cdot b}{t - a} - \frac{y}{\frac{t - a}{z + -1}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 91.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := {\left(b - y\right)}^{2}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3 + \frac{\frac{y}{\frac{t_4}{a - t}} + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{z}{\frac{z \cdot b}{t - a} - \frac{y}{\frac{t - a}{z + -1}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{t_4}{t - a}}}{z} + t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (pow (- b y) 2.0)))
   (if (<= t_2 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_2 -4e-243)
       (/ (+ (* x y) (- (* z t) (* z a))) t_1)
       (if (<= t_2 0.0)
         (+ t_3 (/ (+ (/ y (/ t_4 (- a t))) (/ (* x y) (- b y))) z))
         (if (<= t_2 2e+306)
           t_2
           (if (<= t_2 INFINITY)
             (/ z (- (/ (* z b) (- t a)) (/ y (/ (- t a) (+ z -1.0)))))
             (+ (/ (- (/ x (/ (- b y) y)) (/ y (/ t_4 (- t a)))) z) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = pow((b - y), 2.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -4e-243) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_3 + (((y / (t_4 / (a - t))) + ((x * y) / (b - y))) / z);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = z / (((z * b) / (t - a)) - (y / ((t - a) / (z + -1.0))));
	} else {
		tmp = (((x / ((b - y) / y)) - (y / (t_4 / (t - a)))) / z) + t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = Math.pow((b - y), 2.0);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -4e-243) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_3 + (((y / (t_4 / (a - t))) + ((x * y) / (b - y))) / z);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = z / (((z * b) / (t - a)) - (y / ((t - a) / (z + -1.0))));
	} else {
		tmp = (((x / ((b - y) / y)) - (y / (t_4 / (t - a)))) / z) + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	t_3 = (t - a) / (b - y)
	t_4 = math.pow((b - y), 2.0)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif t_2 <= -4e-243:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	elif t_2 <= 0.0:
		tmp = t_3 + (((y / (t_4 / (a - t))) + ((x * y) / (b - y))) / z)
	elif t_2 <= 2e+306:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = z / (((z * b) / (t - a)) - (y / ((t - a) / (z + -1.0))))
	else:
		tmp = (((x / ((b - y) / y)) - (y / (t_4 / (t - a)))) / z) + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(b - y) ^ 2.0
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_2 <= -4e-243)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(t_3 + Float64(Float64(Float64(y / Float64(t_4 / Float64(a - t))) + Float64(Float64(x * y) / Float64(b - y))) / z));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(z / Float64(Float64(Float64(z * b) / Float64(t - a)) - Float64(y / Float64(Float64(t - a) / Float64(z + -1.0)))));
	else
		tmp = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64(t_4 / Float64(t - a)))) / z) + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((x * y) + (z * (t - a))) / t_1;
	t_3 = (t - a) / (b - y);
	t_4 = (b - y) ^ 2.0;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif (t_2 <= -4e-243)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = t_3 + (((y / (t_4 / (a - t))) + ((x * y) / (b - y))) / z);
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = z / (((z * b) / (t - a)) - (y / ((t - a) / (z + -1.0))));
	else
		tmp = (((x / ((b - y) / y)) - (y / (t_4 / (t - a)))) / z) + t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-243], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t$95$3 + N[(N[(N[(y / N[(t$95$4 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], t$95$2, If[LessEqual[t$95$2, Infinity], N[(z / N[(N[(N[(z * b), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[(t - a), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$4 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$3), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

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

   1. Initial program 34.0%

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

   2. Taylor expanded in y around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

      3. associate-*r/ 53.0%

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

      4. neg-mul-1 53.0%

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

      5. sub-neg 53.0%

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

      6. metadata-eval 53.0%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in z around inf 86.5%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999998e-243

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   3. Applied egg-rr 99.4%

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

   if -3.99999999999999998e-243 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 33.9%

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

      1. sub-neg 33.9%

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

      2. distribute-lft-in 33.9%

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

   3. Applied egg-rr 33.9%

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

   4. Taylor expanded in z around -inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. associate-*r/ 75.0%

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

      4. mul-1-neg 75.0%

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

      5. mul-1-neg 75.0%

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

      6. unsub-neg 75.0%

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

   6. Simplified 95.9%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.0%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 42.9%

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

   2. Taylor expanded in x around 0 41.5%

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

      1. associate-/l* 64.9%

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

      2. +-commutative 64.9%

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

      3. fma-def 64.9%

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

   4. Simplified 64.9%

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

   5. Taylor expanded in y around -inf 64.9%

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

      1. +-commutative 64.9%

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

      2. mul-1-neg 64.9%

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

      3. unsub-neg 64.9%

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

      4. *-commutative 64.9%

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

      5. associate-/l* 64.9%

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

      6. sub-neg 64.9%

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

      7. metadata-eval 64.9%

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

   7. Simplified 64.9%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around -inf 11.1%

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

      1. associate--l+ 11.1%

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

      2. mul-1-neg 11.1%

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

      3. distribute-lft-out-- 11.1%

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

      4. associate-/l* 18.1%

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

      5. associate-/l* 99.9%

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

      6. div-sub 99.9%

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

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}\right)}{z}\right) + \frac{t - a}{b - y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{{\left(b - y\right)}^{2}}{a - t}} + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{z}{\frac{z \cdot b}{t - a} - \frac{y}{\frac{t - a}{z + -1}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 88.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3 + \frac{\frac{y}{\frac{{\left(b - y\right)}^{2}}{a - t}} + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3 (/ (- t a) (- b y))))
   (if (<= t_2 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_2 -4e-243)
       (/ (+ (* x y) (- (* z t) (* z a))) t_1)
       (if (<= t_2 0.0)
         (+
          t_3
          (/ (+ (/ y (/ (pow (- b y) 2.0) (- a t))) (/ (* x y) (- b y))) z))
         (if (<= t_2 2e+306) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -4e-243) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_3 + (((y / (pow((b - y), 2.0) / (a - t))) + ((x * y) / (b - y))) / z);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -4e-243) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_3 + (((y / (Math.pow((b - y), 2.0) / (a - t))) + ((x * y) / (b - y))) / z);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	t_3 = (t - a) / (b - y)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif t_2 <= -4e-243:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	elif t_2 <= 0.0:
		tmp = t_3 + (((y / (math.pow((b - y), 2.0) / (a - t))) + ((x * y) / (b - y))) / z)
	elif t_2 <= 2e+306:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_2 <= -4e-243)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(t_3 + Float64(Float64(Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(a - t))) + Float64(Float64(x * y) / Float64(b - y))) / z));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((x * y) + (z * (t - a))) / t_1;
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif (t_2 <= -4e-243)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = t_3 + (((y / (((b - y) ^ 2.0) / (a - t))) + ((x * y) / (b - y))) / z);
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-243], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t$95$3 + N[(N[(N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 34.0%

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

   2. Taylor expanded in y around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

      3. associate-*r/ 53.0%

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

      4. neg-mul-1 53.0%

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

      5. sub-neg 53.0%

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

      6. metadata-eval 53.0%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in z around inf 86.5%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999998e-243

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   3. Applied egg-rr 99.4%

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

   if -3.99999999999999998e-243 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 33.9%

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

      1. sub-neg 33.9%

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

      2. distribute-lft-in 33.9%

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

   3. Applied egg-rr 33.9%

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

   4. Taylor expanded in z around -inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. associate-*r/ 75.0%

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

      4. mul-1-neg 75.0%

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

      5. mul-1-neg 75.0%

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

      6. unsub-neg 75.0%

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

   6. Simplified 95.9%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.0%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 21.5%

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

   2. Taylor expanded in z around inf 65.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{{\left(b - y\right)}^{2}}{a - t}} + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{a}{y} \cdot \frac{z}{z + -1} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z t)) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.55e+20)
     t_2
     (if (<= z -8.6e-288)
       t_1
       (if (<= z 3.6e-144)
         (- (* (/ a y) (/ z (+ z -1.0))) (/ x (+ z -1.0)))
         (if (<= z 4e+15) 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)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.55e+20) {
		tmp = t_2;
	} else if (z <= -8.6e-288) {
		tmp = t_1;
	} else if (z <= 3.6e-144) {
		tmp = ((a / y) * (z / (z + -1.0))) - (x / (z + -1.0));
	} else if (z <= 4e+15) {
		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)) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.55d+20)) then
        tmp = t_2
    else if (z <= (-8.6d-288)) then
        tmp = t_1
    else if (z <= 3.6d-144) then
        tmp = ((a / y) * (z / (z + (-1.0d0)))) - (x / (z + (-1.0d0)))
    else if (z <= 4d+15) 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)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.55e+20) {
		tmp = t_2;
	} else if (z <= -8.6e-288) {
		tmp = t_1;
	} else if (z <= 3.6e-144) {
		tmp = ((a / y) * (z / (z + -1.0))) - (x / (z + -1.0));
	} else if (z <= 4e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * t)) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.55e+20:
		tmp = t_2
	elif z <= -8.6e-288:
		tmp = t_1
	elif z <= 3.6e-144:
		tmp = ((a / y) * (z / (z + -1.0))) - (x / (z + -1.0))
	elif z <= 4e+15:
		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 * t)) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.55e+20)
		tmp = t_2;
	elseif (z <= -8.6e-288)
		tmp = t_1;
	elseif (z <= 3.6e-144)
		tmp = Float64(Float64(Float64(a / y) * Float64(z / Float64(z + -1.0))) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 4e+15)
		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)) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.55e+20)
		tmp = t_2;
	elseif (z <= -8.6e-288)
		tmp = t_1;
	elseif (z <= 3.6e-144)
		tmp = ((a / y) * (z / (z + -1.0))) - (x / (z + -1.0));
	elseif (z <= 4e+15)
		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 * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+20], t$95$2, If[LessEqual[z, -8.6e-288], t$95$1, If[LessEqual[z, 3.6e-144], N[(N[(N[(a / y), $MachinePrecision] * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+15], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e20 or 4e15 < z

   1. Initial program 49.4%

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

   2. Taylor expanded in z around inf 82.2%

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

   if -1.55e20 < z < -8.59999999999999951e-288 or 3.6e-144 < z < 4e15

   1. Initial program 88.4%

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

   2. Taylor expanded in a around 0 72.4%

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

   if -8.59999999999999951e-288 < z < 3.6e-144

   1. Initial program 75.6%

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

   2. Taylor expanded in y around -inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. unsub-neg 77.9%

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

      3. associate-*r/ 77.9%

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

      4. neg-mul-1 77.9%

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

      5. sub-neg 77.9%

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

      6. metadata-eval 77.9%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in a around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. times-frac 76.7%

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

      3. sub-neg 76.7%

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

      4. metadata-eval 76.7%

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

      5. distribute-rgt-neg-in 76.7%

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

   7. Simplified 76.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+20}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{a}{y} \cdot \frac{z}{z + -1} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+61} \lor \neg \left(z \leq 3.1 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.95e+61) (not (<= z 3.1e+56)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (- (* z t) (* z a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e+61) || !(z <= 3.1e+56)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.95d+61)) .or. (.not. (z <= 3.1d+56))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e+61) || !(z <= 3.1e+56)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.95e+61) or not (z <= 3.1e+56):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.95e+61) || !(z <= 3.1e+56))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.95e+61) || ~((z <= 3.1e+56)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.95e+61], N[Not[LessEqual[z, 3.1e+56]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999994e61 or 3.10000000000000005e56 < z

   1. Initial program 44.5%

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

   2. Taylor expanded in z around inf 84.4%

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

   if -1.94999999999999994e61 < z < 3.10000000000000005e56

   1. Initial program 85.7%

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

      1. sub-neg 85.7%

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

      2. distribute-lft-in 85.8%

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

   3. Applied egg-rr 85.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+61} \lor \neg \left(z \leq 3.1 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 7: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+60} \lor \neg \left(z \leq 5.4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.7e+60) (not (<= z 5.4e+57)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e+60) || !(z <= 5.4e+57)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.7d+60)) .or. (.not. (z <= 5.4d+57))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e+60) || !(z <= 5.4e+57)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.7e+60) or not (z <= 5.4e+57):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.7e+60) || !(z <= 5.4e+57))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.7e+60) || ~((z <= 5.4e+57)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.7e+60], N[Not[LessEqual[z, 5.4e+57]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e60 or 5.3999999999999997e57 < z

   1. Initial program 44.5%

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

   2. Taylor expanded in z around inf 84.4%

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

   if -2.6999999999999999e60 < z < 5.3999999999999997e57

   1. Initial program 85.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+60} \lor \neg \left(z \leq 5.4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 8: 72.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+18} \lor \neg \left(z \leq 3 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.2e+18) (not (<= z 3e+15)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z t)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e+18) || !(z <= 3e+15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.2d+18)) .or. (.not. (z <= 3d+15))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e+18) || !(z <= 3e+15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.2e+18) or not (z <= 3e+15):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.2e+18) || !(z <= 3e+15))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.2e+18) || ~((z <= 3e+15)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.2e+18], N[Not[LessEqual[z, 3e+15]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e18 or 3e15 < z

   1. Initial program 49.4%

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

   2. Taylor expanded in z around inf 82.2%

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

   if -6.2e18 < z < 3e15

   1. Initial program 85.8%

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

   2. Taylor expanded in a around 0 69.5%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+18} \lor \neg \left(z \leq 3 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 9: 64.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;y \leq -35:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-115}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= y -35.0)
     t_1
     (if (<= y -4.8e-115)
       (* (/ z y) (/ (- t a) (- 1.0 z)))
       (if (<= y 1.2e+21) (/ (- t a) (- b y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (y <= -35.0) {
		tmp = t_1;
	} else if (y <= -4.8e-115) {
		tmp = (z / y) * ((t - a) / (1.0 - z));
	} else if (y <= 1.2e+21) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a - t) / y) - (x / (z + (-1.0d0)))
    if (y <= (-35.0d0)) then
        tmp = t_1
    else if (y <= (-4.8d-115)) then
        tmp = (z / y) * ((t - a) / (1.0d0 - z))
    else if (y <= 1.2d+21) then
        tmp = (t - a) / (b - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (y <= -35.0) {
		tmp = t_1;
	} else if (y <= -4.8e-115) {
		tmp = (z / y) * ((t - a) / (1.0 - z));
	} else if (y <= 1.2e+21) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if y <= -35.0:
		tmp = t_1
	elif y <= -4.8e-115:
		tmp = (z / y) * ((t - a) / (1.0 - z))
	elif y <= 1.2e+21:
		tmp = (t - a) / (b - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (y <= -35.0)
		tmp = t_1;
	elseif (y <= -4.8e-115)
		tmp = Float64(Float64(z / y) * Float64(Float64(t - a) / Float64(1.0 - z)));
	elseif (y <= 1.2e+21)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (y <= -35.0)
		tmp = t_1;
	elseif (y <= -4.8e-115)
		tmp = (z / y) * ((t - a) / (1.0 - z));
	elseif (y <= 1.2e+21)
		tmp = (t - a) / (b - y);
	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] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -35.0], t$95$1, If[LessEqual[y, -4.8e-115], N[(N[(z / y), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+21], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -35 or 1.2e21 < y

   1. Initial program 51.7%

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

   2. Taylor expanded in y around -inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

      3. associate-*r/ 63.8%

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

      4. neg-mul-1 63.8%

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

      5. sub-neg 63.8%

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

      6. metadata-eval 63.8%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in z around inf 65.6%

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

   if -35 < y < -4.80000000000000042e-115

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0 75.5%

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

      1. associate-/l* 63.9%

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

      2. +-commutative 63.9%

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

      3. fma-def 63.9%

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

   4. Simplified 63.9%

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

   5. Taylor expanded in b around 0 63.7%

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

      1. *-lft-identity 63.7%

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

      2. mul-1-neg 63.7%

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

      3. *-commutative 63.7%

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

      4. distribute-lft-neg-in 63.7%

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

      5. mul-1-neg 63.7%

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

      6. distribute-rgt-in 63.8%

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

      7. times-frac 64.0%

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

      8. mul-1-neg 64.0%

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

      9. sub-neg 64.0%

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

   7. Simplified 64.0%

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

   if -4.80000000000000042e-115 < y < 1.2e21

   1. Initial program 86.9%

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

   2. Taylor expanded in z around inf 73.2%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -35:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-115}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \end{array} \]

Alternative 10: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-10} \lor \neg \left(z \leq 1.95 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.5e-10) (not (<= z 1.95e-35)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (- (* z t) (* z a))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.5e-10) || !(z <= 1.95e-35)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.5d-10)) .or. (.not. (z <= 1.95d-35))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + ((z * t) - (z * a))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.5e-10) || !(z <= 1.95e-35)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.5e-10) or not (z <= 1.95e-35):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + ((z * t) - (z * a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.5e-10) || !(z <= 1.95e-35))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.5e-10) || ~((z <= 1.95e-35)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + ((z * t) - (z * a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.5e-10], N[Not[LessEqual[z, 1.95e-35]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000016e-10 or 1.9499999999999999e-35 < z

   1. Initial program 52.6%

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

   2. Taylor expanded in z around inf 77.4%

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

   if -2.50000000000000016e-10 < z < 1.9499999999999999e-35

   1. Initial program 87.1%

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

      1. sub-neg 87.1%

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

      2. distribute-lft-in 87.1%

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

   3. Applied egg-rr 87.1%

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

   4. Taylor expanded in z around 0 61.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-10} \lor \neg \left(z \leq 1.95 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y}\\ \end{array} \]

Alternative 11: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.24 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167} \lor \neg \left(z \leq 4.8 \cdot 10^{-29}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.24e-39)
     t_1
     (if (<= z -5.5e-95)
       (/ x (- 1.0 z))
       (if (or (<= z -1.2e-167) (not (<= z 4.8e-29))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.24e-39) {
		tmp = t_1;
	} else if (z <= -5.5e-95) {
		tmp = x / (1.0 - z);
	} else if ((z <= -1.2e-167) || !(z <= 4.8e-29)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.24d-39)) then
        tmp = t_1
    else if (z <= (-5.5d-95)) then
        tmp = x / (1.0d0 - z)
    else if ((z <= (-1.2d-167)) .or. (.not. (z <= 4.8d-29))) then
        tmp = t_1
    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 t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.24e-39) {
		tmp = t_1;
	} else if (z <= -5.5e-95) {
		tmp = x / (1.0 - z);
	} else if ((z <= -1.2e-167) || !(z <= 4.8e-29)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.24e-39:
		tmp = t_1
	elif z <= -5.5e-95:
		tmp = x / (1.0 - z)
	elif (z <= -1.2e-167) or not (z <= 4.8e-29):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.24e-39)
		tmp = t_1;
	elseif (z <= -5.5e-95)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= -1.2e-167) || !(z <= 4.8e-29))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.24e-39)
		tmp = t_1;
	elseif (z <= -5.5e-95)
		tmp = x / (1.0 - z);
	elseif ((z <= -1.2e-167) || ~((z <= 4.8e-29)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.24e-39], t$95$1, If[LessEqual[z, -5.5e-95], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.2e-167], N[Not[LessEqual[z, 4.8e-29]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24000000000000004e-39 or -5.50000000000000003e-95 < z < -1.19999999999999997e-167 or 4.79999999999999984e-29 < z

   1. Initial program 58.0%

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

   2. Taylor expanded in z around inf 73.9%

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

   if -1.24000000000000004e-39 < z < -5.50000000000000003e-95

   1. Initial program 90.1%

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

   2. Taylor expanded in y around inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. unsub-neg 51.0%

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

   4. Simplified 51.0%

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

   if -1.19999999999999997e-167 < z < 4.79999999999999984e-29

   1. Initial program 85.8%

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

   2. Taylor expanded in z around 0 52.5%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.24 \cdot 10^{-39}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167} \lor \neg \left(z \leq 4.8 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 62.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-96}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167} \lor \neg \left(z \leq 1.75 \cdot 10^{-39}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.75e-42)
     t_1
     (if (<= z -1.05e-96)
       (/ (* x y) (+ y (* z b)))
       (if (or (<= z -1.2e-167) (not (<= z 1.75e-39))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.75e-42) {
		tmp = t_1;
	} else if (z <= -1.05e-96) {
		tmp = (x * y) / (y + (z * b));
	} else if ((z <= -1.2e-167) || !(z <= 1.75e-39)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.75d-42)) then
        tmp = t_1
    else if (z <= (-1.05d-96)) then
        tmp = (x * y) / (y + (z * b))
    else if ((z <= (-1.2d-167)) .or. (.not. (z <= 1.75d-39))) then
        tmp = t_1
    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 t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.75e-42) {
		tmp = t_1;
	} else if (z <= -1.05e-96) {
		tmp = (x * y) / (y + (z * b));
	} else if ((z <= -1.2e-167) || !(z <= 1.75e-39)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.75e-42:
		tmp = t_1
	elif z <= -1.05e-96:
		tmp = (x * y) / (y + (z * b))
	elif (z <= -1.2e-167) or not (z <= 1.75e-39):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.75e-42)
		tmp = t_1;
	elseif (z <= -1.05e-96)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * b)));
	elseif ((z <= -1.2e-167) || !(z <= 1.75e-39))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.75e-42)
		tmp = t_1;
	elseif (z <= -1.05e-96)
		tmp = (x * y) / (y + (z * b));
	elseif ((z <= -1.2e-167) || ~((z <= 1.75e-39)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e-42], t$95$1, If[LessEqual[z, -1.05e-96], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.2e-167], N[Not[LessEqual[z, 1.75e-39]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7500000000000001e-42 or -1.05000000000000001e-96 < z < -1.19999999999999997e-167 or 1.75e-39 < z

   1. Initial program 58.0%

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

   2. Taylor expanded in z around inf 73.9%

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

   if -1.7500000000000001e-42 < z < -1.05000000000000001e-96

   1. Initial program 90.1%

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

   2. Taylor expanded in x around inf 52.0%

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

      1. *-commutative 52.0%

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

   4. Simplified 52.0%

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

   5. Taylor expanded in b around inf 52.0%

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

      1. *-commutative 52.0%

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

   7. Simplified 52.0%

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

   if -1.19999999999999997e-167 < z < 1.75e-39

   1. Initial program 85.8%

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

   2. Taylor expanded in z around 0 52.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-42}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-96}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167} \lor \neg \left(z \leq 1.75 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 62.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6.9 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167} \lor \neg \left(z \leq 4.8 \cdot 10^{-40}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -6.9e-40)
     t_1
     (if (<= z -7.4e-97)
       (/ (* x y) (+ y (* z (- b y))))
       (if (or (<= z -1.2e-167) (not (<= z 4.8e-40))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -6.9e-40) {
		tmp = t_1;
	} else if (z <= -7.4e-97) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if ((z <= -1.2e-167) || !(z <= 4.8e-40)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-6.9d-40)) then
        tmp = t_1
    else if (z <= (-7.4d-97)) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if ((z <= (-1.2d-167)) .or. (.not. (z <= 4.8d-40))) then
        tmp = t_1
    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 t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -6.9e-40) {
		tmp = t_1;
	} else if (z <= -7.4e-97) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if ((z <= -1.2e-167) || !(z <= 4.8e-40)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -6.9e-40:
		tmp = t_1
	elif z <= -7.4e-97:
		tmp = (x * y) / (y + (z * (b - y)))
	elif (z <= -1.2e-167) or not (z <= 4.8e-40):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -6.9e-40)
		tmp = t_1;
	elseif (z <= -7.4e-97)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif ((z <= -1.2e-167) || !(z <= 4.8e-40))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -6.9e-40)
		tmp = t_1;
	elseif (z <= -7.4e-97)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif ((z <= -1.2e-167) || ~((z <= 4.8e-40)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.9e-40], t$95$1, If[LessEqual[z, -7.4e-97], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.2e-167], N[Not[LessEqual[z, 4.8e-40]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8999999999999996e-40 or -7.39999999999999951e-97 < z < -1.19999999999999997e-167 or 4.79999999999999982e-40 < z

   1. Initial program 58.0%

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

   2. Taylor expanded in z around inf 73.9%

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

   if -6.8999999999999996e-40 < z < -7.39999999999999951e-97

   1. Initial program 90.1%

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

   2. Taylor expanded in x around inf 52.0%

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

      1. *-commutative 52.0%

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

   4. Simplified 52.0%

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

   if -1.19999999999999997e-167 < z < 4.79999999999999982e-40

   1. Initial program 85.8%

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

   2. Taylor expanded in z around 0 52.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{-40}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167} \lor \neg \left(z \leq 4.8 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 43.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-190}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -5.5e-50)
     t_2
     (if (<= y 1.1e-244)
       t_1
       (if (<= y 4.8e-190) (/ (- a) b) (if (<= y 2.95e-36) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -5.5e-50) {
		tmp = t_2;
	} else if (y <= 1.1e-244) {
		tmp = t_1;
	} else if (y <= 4.8e-190) {
		tmp = -a / b;
	} else if (y <= 2.95e-36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = x / (1.0d0 - z)
    if (y <= (-5.5d-50)) then
        tmp = t_2
    else if (y <= 1.1d-244) then
        tmp = t_1
    else if (y <= 4.8d-190) then
        tmp = -a / b
    else if (y <= 2.95d-36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -5.5e-50) {
		tmp = t_2;
	} else if (y <= 1.1e-244) {
		tmp = t_1;
	} else if (y <= 4.8e-190) {
		tmp = -a / b;
	} else if (y <= 2.95e-36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -5.5e-50:
		tmp = t_2
	elif y <= 1.1e-244:
		tmp = t_1
	elif y <= 4.8e-190:
		tmp = -a / b
	elif y <= 2.95e-36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -5.5e-50)
		tmp = t_2;
	elseif (y <= 1.1e-244)
		tmp = t_1;
	elseif (y <= 4.8e-190)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 2.95e-36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -5.5e-50)
		tmp = t_2;
	elseif (y <= 1.1e-244)
		tmp = t_1;
	elseif (y <= 4.8e-190)
		tmp = -a / b;
	elseif (y <= 2.95e-36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e-50], t$95$2, If[LessEqual[y, 1.1e-244], t$95$1, If[LessEqual[y, 4.8e-190], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 2.95e-36], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.49999999999999975e-50 or 2.94999999999999998e-36 < y

   1. Initial program 54.7%

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

   2. Taylor expanded in y around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. unsub-neg 47.3%

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

   4. Simplified 47.3%

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

   if -5.49999999999999975e-50 < y < 1.09999999999999992e-244 or 4.8000000000000001e-190 < y < 2.94999999999999998e-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 a around 0 63.7%

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

   3. Taylor expanded in z around inf 50.1%

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

   if 1.09999999999999992e-244 < y < 4.8000000000000001e-190

   1. Initial program 90.2%

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

   2. Taylor expanded in a around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. distribute-lft-neg-out 55.4%

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

      3. *-commutative 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in y around 0 64.5%

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

      1. associate-*r/ 64.5%

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

      2. mul-1-neg 64.5%

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

   7. Simplified 64.5%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-244}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-190}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 15: 33.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-244}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-188}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.95e-150)
   x
   (if (<= y 1.26e-244)
     (/ t b)
     (if (<= y 3.3e-188) (/ (- a) b) (if (<= y 2.05e-47) (/ t b) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-150) {
		tmp = x;
	} else if (y <= 1.26e-244) {
		tmp = t / b;
	} else if (y <= 3.3e-188) {
		tmp = -a / b;
	} else if (y <= 2.05e-47) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.95d-150)) then
        tmp = x
    else if (y <= 1.26d-244) then
        tmp = t / b
    else if (y <= 3.3d-188) then
        tmp = -a / b
    else if (y <= 2.05d-47) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-150) {
		tmp = x;
	} else if (y <= 1.26e-244) {
		tmp = t / b;
	} else if (y <= 3.3e-188) {
		tmp = -a / b;
	} else if (y <= 2.05e-47) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.95e-150:
		tmp = x
	elif y <= 1.26e-244:
		tmp = t / b
	elif y <= 3.3e-188:
		tmp = -a / b
	elif y <= 2.05e-47:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.95e-150)
		tmp = x;
	elseif (y <= 1.26e-244)
		tmp = Float64(t / b);
	elseif (y <= 3.3e-188)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 2.05e-47)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.95e-150)
		tmp = x;
	elseif (y <= 1.26e-244)
		tmp = t / b;
	elseif (y <= 3.3e-188)
		tmp = -a / b;
	elseif (y <= 2.05e-47)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.95e-150], x, If[LessEqual[y, 1.26e-244], N[(t / b), $MachinePrecision], If[LessEqual[y, 3.3e-188], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 2.05e-47], N[(t / b), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9500000000000001e-150 or 2.05000000000000001e-47 < y

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0 34.6%

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

   if -1.9500000000000001e-150 < y < 1.25999999999999998e-244 or 3.3000000000000002e-188 < y < 2.05000000000000001e-47

   1. Initial program 88.4%

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

   2. Taylor expanded in a around 0 68.9%

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

   3. Taylor expanded in y around 0 54.8%

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

   if 1.25999999999999998e-244 < y < 3.3000000000000002e-188

   1. Initial program 90.2%

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

   2. Taylor expanded in a around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. distribute-lft-neg-out 55.4%

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

      3. *-commutative 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in y around 0 64.5%

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

      1. associate-*r/ 64.5%

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

      2. mul-1-neg 64.5%

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

   7. Simplified 64.5%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-244}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-188}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 33.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-244}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-187}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.95e-150)
   (+ x (* x z))
   (if (<= y 1.15e-244)
     (/ t b)
     (if (<= y 1.05e-187) (/ (- a) b) (if (<= y 2.5e-34) (/ t b) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-150) {
		tmp = x + (x * z);
	} else if (y <= 1.15e-244) {
		tmp = t / b;
	} else if (y <= 1.05e-187) {
		tmp = -a / b;
	} else if (y <= 2.5e-34) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.95d-150)) then
        tmp = x + (x * z)
    else if (y <= 1.15d-244) then
        tmp = t / b
    else if (y <= 1.05d-187) then
        tmp = -a / b
    else if (y <= 2.5d-34) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-150) {
		tmp = x + (x * z);
	} else if (y <= 1.15e-244) {
		tmp = t / b;
	} else if (y <= 1.05e-187) {
		tmp = -a / b;
	} else if (y <= 2.5e-34) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.95e-150:
		tmp = x + (x * z)
	elif y <= 1.15e-244:
		tmp = t / b
	elif y <= 1.05e-187:
		tmp = -a / b
	elif y <= 2.5e-34:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.95e-150)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 1.15e-244)
		tmp = Float64(t / b);
	elseif (y <= 1.05e-187)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 2.5e-34)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.95e-150)
		tmp = x + (x * z);
	elseif (y <= 1.15e-244)
		tmp = t / b;
	elseif (y <= 1.05e-187)
		tmp = -a / b;
	elseif (y <= 2.5e-34)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.95e-150], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-244], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.05e-187], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 2.5e-34], N[(t / b), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9500000000000001e-150

   1. Initial program 60.5%

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

   2. Taylor expanded in y around inf 39.4%

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

      1. mul-1-neg 39.4%

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

      2. unsub-neg 39.4%

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

   4. Simplified 39.4%

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

   5. Taylor expanded in z around 0 34.2%

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

   if -1.9500000000000001e-150 < y < 1.15e-244 or 1.04999999999999996e-187 < y < 2.5000000000000001e-34

   1. Initial program 88.4%

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

   2. Taylor expanded in a around 0 68.9%

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

   3. Taylor expanded in y around 0 54.8%

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

   if 1.15e-244 < y < 1.04999999999999996e-187

   1. Initial program 90.2%

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

   2. Taylor expanded in a around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. distribute-lft-neg-out 55.4%

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

      3. *-commutative 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in y around 0 64.5%

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

      1. associate-*r/ 64.5%

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

      2. mul-1-neg 64.5%

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

   7. Simplified 64.5%

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

   if 2.5000000000000001e-34 < y

   1. Initial program 55.4%

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

   2. Taylor expanded in z around 0 35.2%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-244}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-187}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 45.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-28} \lor \neg \left(z \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.2e-28) (not (<= z 2.35e-23))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.2e-28) || !(z <= 2.35e-23)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.2d-28)) .or. (.not. (z <= 2.35d-23))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.2e-28) || !(z <= 2.35e-23)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.2e-28) or not (z <= 2.35e-23):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.2e-28) || !(z <= 2.35e-23))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.2e-28) || ~((z <= 2.35e-23)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.2e-28], N[Not[LessEqual[z, 2.35e-23]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e-28 or 2.35e-23 < z

   1. Initial program 52.6%

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

   2. Taylor expanded in a around 0 34.5%

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

   3. Taylor expanded in z around inf 44.6%

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

   if -5.2e-28 < z < 2.35e-23

   1. Initial program 87.1%

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

   2. Taylor expanded in z around 0 48.4%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-28} \lor \neg \left(z \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 53.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-70} \lor \neg \left(y \leq 4 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.6e-70) (not (<= y 4e-36))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.6e-70) || !(y <= 4e-36)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.6d-70)) .or. (.not. (y <= 4d-36))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.6e-70) || !(y <= 4e-36)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.6e-70) or not (y <= 4e-36):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.6e-70) || !(y <= 4e-36))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.6e-70) || ~((y <= 4e-36)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.6e-70], N[Not[LessEqual[y, 4e-36]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.60000000000000001e-70 or 3.9999999999999998e-36 < y

   1. Initial program 55.6%

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

   2. Taylor expanded in y around inf 46.5%

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

      1. mul-1-neg 46.5%

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

      2. unsub-neg 46.5%

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

   4. Simplified 46.5%

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

   if -4.60000000000000001e-70 < y < 3.9999999999999998e-36

   1. Initial program 89.0%

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

   2. Taylor expanded in y around 0 65.6%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-70} \lor \neg \left(y \leq 4 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 19: 33.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.95e-150) x (if (<= y 9e-40) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-150) {
		tmp = x;
	} else if (y <= 9e-40) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.95d-150)) then
        tmp = x
    else if (y <= 9d-40) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-150) {
		tmp = x;
	} else if (y <= 9e-40) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.95e-150:
		tmp = x
	elif y <= 9e-40:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.95e-150)
		tmp = x;
	elseif (y <= 9e-40)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.95e-150)
		tmp = x;
	elseif (y <= 9e-40)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.95e-150], x, If[LessEqual[y, 9e-40], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9500000000000001e-150 or 9.0000000000000002e-40 < y

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0 34.6%

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

   if -1.9500000000000001e-150 < y < 9.0000000000000002e-40

   1. Initial program 88.6%

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

   2. Taylor expanded in a around 0 65.2%

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

   3. Taylor expanded in y around 0 49.7%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 25.0% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 69.2%

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

2. Taylor expanded in z around 0 25.4%

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

3. Final simplification 25.4%

   \[\leadsto x \]

Developer target: 72.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(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)))))