Development.Shake.Progress:decay from shake-0.15.5

Average Accuracy: 64.1% → 93.9%

Time: 40.7s

Precision: binary64

Cost: 33872

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := {\left(b - y\right)}^{2}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ t_5 := \frac{t_3 + x \cdot y}{t_1}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{t - a}{1 - z} \cdot \frac{z}{y}\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-270}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{t_2} \cdot \frac{y}{z}\right)\right)\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, \frac{x}{b - y}, \frac{\mathsf{fma}\left(-1, \frac{y}{\frac{b - y}{x}}, \frac{t - a}{\frac{t_2}{y}}\right)}{\frac{b - y}{\frac{y}{z \cdot z}}}\right) + \left(\frac{t - a}{b - y} + \frac{y}{t_2} \cdot \frac{a - t}{z}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (pow (- b y) 2.0))
        (t_3 (* z (- t a)))
        (t_4 (+ (/ t_3 t_1) (/ (* x y) t_1)))
        (t_5 (/ (+ t_3 (* x y)) t_1)))
   (if (<= t_5 (- INFINITY))
     (+ (/ y (/ (* y (- 1.0 z)) x)) (* (/ (- t a) (- 1.0 z)) (/ z y)))
     (if (<= t_5 -2e-270)
       t_4
       (if (<= t_5 0.0)
         (+
          (/ (/ (* x y) z) (- b y))
          (- (/ t (- b y)) (+ (/ a (- b y)) (* (/ (- t a) t_2) (/ y z)))))
         (if (<= t_5 2e+304)
           t_4
           (+
            (fma
             (/ y z)
             (/ x (- b y))
             (/
              (fma -1.0 (/ y (/ (- b y) x)) (/ (- t a) (/ t_2 y)))
              (/ (- b y) (/ y (* z z)))))
            (+ (/ (- t a) (- b y)) (* (/ y t_2) (/ (- a t) z))))))))))

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)));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = pow((b - y), 2.0);
	double t_3 = z * (t - a);
	double t_4 = (t_3 / t_1) + ((x * y) / t_1);
	double t_5 = (t_3 + (x * y)) / t_1;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = (y / ((y * (1.0 - z)) / x)) + (((t - a) / (1.0 - z)) * (z / y));
	} else if (t_5 <= -2e-270) {
		tmp = t_4;
	} else if (t_5 <= 0.0) {
		tmp = (((x * y) / z) / (b - y)) + ((t / (b - y)) - ((a / (b - y)) + (((t - a) / t_2) * (y / z))));
	} else if (t_5 <= 2e+304) {
		tmp = t_4;
	} else {
		tmp = fma((y / z), (x / (b - y)), (fma(-1.0, (y / ((b - y) / x)), ((t - a) / (t_2 / y))) / ((b - y) / (y / (z * z))))) + (((t - a) / (b - y)) + ((y / t_2) * ((a - t) / z)));
	}
	return tmp;
}

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

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(b - y) ^ 2.0
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(t_3 / t_1) + Float64(Float64(x * y) / t_1))
	t_5 = Float64(Float64(t_3 + Float64(x * y)) / t_1)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(Float64(y / Float64(Float64(y * Float64(1.0 - z)) / x)) + Float64(Float64(Float64(t - a) / Float64(1.0 - z)) * Float64(z / y)));
	elseif (t_5 <= -2e-270)
		tmp = t_4;
	elseif (t_5 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(x * y) / z) / Float64(b - y)) + Float64(Float64(t / Float64(b - y)) - Float64(Float64(a / Float64(b - y)) + Float64(Float64(Float64(t - a) / t_2) * Float64(y / z)))));
	elseif (t_5 <= 2e+304)
		tmp = t_4;
	else
		tmp = Float64(fma(Float64(y / z), Float64(x / Float64(b - y)), Float64(fma(-1.0, Float64(y / Float64(Float64(b - y) / x)), Float64(Float64(t - a) / Float64(t_2 / y))) / Float64(Float64(b - y) / Float64(y / Float64(z * z))))) + Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(y / t_2) * Float64(Float64(a - t) / z))));
	end
	return tmp
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]

↓

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[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(N[(y / N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, -2e-270], t$95$4, If[LessEqual[t$95$5, 0.0], N[(N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 2e+304], t$95$4, N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 * N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b - y), $MachinePrecision] / N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t$95$2), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Target

Original	64.1%
Target	73.0%
Herbie	93.9%

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

Derivation

1. Split input into 4 regimes

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around inf 0.0%

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

   3. Taylor expanded in b around 0 0.0%

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

   4. Simplified 72.2%

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

      [Start] 0.0	\[ \frac{\left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y} + \frac{y \cdot x}{-1 \cdot \left(y \cdot z\right) + y} \]
      +-commutative [=>] 0.0	\[ \color{blue}{\frac{y \cdot x}{-1 \cdot \left(y \cdot z\right) + y} + \frac{\left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y}} \]
      associate-/l* [=>] 51.2	\[ \color{blue}{\frac{y}{\frac{-1 \cdot \left(y \cdot z\right) + y}{x}}} + \frac{\left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y} \]
      mul-1-neg [=>] 51.2	\[ \frac{y}{\frac{\color{blue}{\left(-y \cdot z\right)} + y}{x}} + \frac{\left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y} \]
      distribute-rgt-neg-in [=>] 51.2	\[ \frac{y}{\frac{\color{blue}{y \cdot \left(-z\right)} + y}{x}} + \frac{\left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y} \]
      *-rgt-identity [<=] 51.2	\[ \frac{y}{\frac{y \cdot \left(-z\right) + \color{blue}{y \cdot 1}}{x}} + \frac{\left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y} \]
      distribute-lft-in [<=] 51.2	\[ \frac{y}{\frac{\color{blue}{y \cdot \left(\left(-z\right) + 1\right)}}{x}} + \frac{\left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y} \]
      +-commutative [=>] 51.2	\[ \frac{y}{\frac{y \cdot \color{blue}{\left(1 + \left(-z\right)\right)}}{x}} + \frac{\left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y} \]
      unsub-neg [=>] 51.2	\[ \frac{y}{\frac{y \cdot \color{blue}{\left(1 - z\right)}}{x}} + \frac{\left(t - a\right) \cdot z}{-1 \cdot \left(y \cdot z\right) + y} \]
      +-commutative [<=] 51.2	\[ \frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{\left(t - a\right) \cdot z}{\color{blue}{y + -1 \cdot \left(y \cdot z\right)}} \]
      *-rgt-identity [<=] 51.2	\[ \frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{\left(t - a\right) \cdot z}{\color{blue}{y \cdot 1} + -1 \cdot \left(y \cdot z\right)} \]
      mul-1-neg [=>] 51.2	\[ \frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{\left(t - a\right) \cdot z}{y \cdot 1 + \color{blue}{\left(-y \cdot z\right)}} \]
      distribute-rgt-neg-in [=>] 51.2	\[ \frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{\left(t - a\right) \cdot z}{y \cdot 1 + \color{blue}{y \cdot \left(-z\right)}} \]
      distribute-lft-in [<=] 51.2	\[ \frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{\left(t - a\right) \cdot z}{\color{blue}{y \cdot \left(1 + \left(-z\right)\right)}} \]
      +-commutative [<=] 51.2	\[ \frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{\left(t - a\right) \cdot z}{y \cdot \color{blue}{\left(\left(-z\right) + 1\right)}} \]
      neg-mul-1 [=>] 51.2	\[ \frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{\left(t - a\right) \cdot z}{y \cdot \left(\color{blue}{-1 \cdot z} + 1\right)} \]
      *-commutative [<=] 51.2	\[ \frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{\left(t - a\right) \cdot z}{\color{blue}{\left(-1 \cdot z + 1\right) \cdot y}} \]
      times-frac [=>] 72.2	\[ \frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \color{blue}{\frac{t - a}{-1 \cdot z + 1} \cdot \frac{z}{y}} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-270 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.9999999999999999e304

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 99.5%

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

   if -2.0000000000000001e-270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 29.2%

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

   2. Taylor expanded in z around inf 68.3%

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

   3. Simplified 93.4%

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

      [Start] 68.3	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 68.3	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      associate-/r* [=>] 83.2	\[ \color{blue}{\frac{\frac{y \cdot x}{z}}{b - y}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 83.2	\[ \frac{\frac{y \cdot x}{z}}{b - y} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 83.2	\[ \frac{\frac{y \cdot x}{z}}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      times-frac [=>] 93.4	\[ \frac{\frac{y \cdot x}{z}}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right)\right) \]

   if 1.9999999999999999e304 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 0.5%

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

   2. Taylor expanded in z around inf 38.2%

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

   3. Simplified 85.6%

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

      [Start] 38.2	\[ \left(\frac{y \cdot x}{\left(b - y\right) \cdot z} + \left(-1 \cdot \frac{y \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{\left(b - y\right) \cdot {z}^{2}} + \frac{t}{b - y}\right)\right) - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right) \]
      associate-+r+ [=>] 38.2	\[ \color{blue}{\left(\left(\frac{y \cdot x}{\left(b - y\right) \cdot z} + -1 \cdot \frac{y \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{\left(b - y\right) \cdot {z}^{2}}\right) + \frac{t}{b - y}\right)} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right) \]
      associate--l+ [=>] 38.2	\[ \color{blue}{\left(\frac{y \cdot x}{\left(b - y\right) \cdot z} + -1 \cdot \frac{y \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{\left(b - y\right) \cdot {z}^{2}}\right) + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right)\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{t - a}{1 - z} \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-270}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}\right)\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, \frac{x}{b - y}, \frac{\mathsf{fma}\left(-1, \frac{y}{\frac{b - y}{x}}, \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{\frac{b - y}{\frac{y}{z \cdot z}}}\right) + \left(\frac{t - a}{b - y} + \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	94.0%
Cost	12816

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{t_1} + \frac{x \cdot y}{t_1}\\ t_4 := \frac{t_2 + x \cdot y}{t_1}\\ t_5 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{t - a}{1 - z} \cdot \frac{z}{y}\\ \mathbf{elif}\;t_4 \leq -2 \cdot 10^{-270}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_5 + \frac{y}{b - y} \cdot \frac{x}{z}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5 - \frac{\frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}} - \frac{y}{\frac{b - y}{x}}}{z}\\ \end{array} \]

Alternative 2
Accuracy	94.0%
Cost	12816

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := {\left(b - y\right)}^{2}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ t_5 := \frac{t_3 + x \cdot y}{t_1}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{t - a}{1 - z} \cdot \frac{z}{y}\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-270}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{t_2} \cdot \frac{y}{z}\right)\right)\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{\frac{t - a}{\frac{t_2}{y}} - \frac{y}{\frac{b - y}{x}}}{z}\\ \end{array} \]

Alternative 3
Accuracy	94.1%
Cost	6224

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{t_1} + \frac{x \cdot y}{t_1}\\ t_4 := \frac{t_2 + x \cdot y}{t_1}\\ t_5 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{t - a}{1 - z} \cdot \frac{z}{y}\\ \mathbf{elif}\;t_4 \leq -2 \cdot 10^{-270}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_5 + \frac{y}{b - y} \cdot \frac{x}{z}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5 + \frac{x}{z \cdot \frac{b - y}{y}}\\ \end{array} \]

Alternative 4
Accuracy	93.0%
Cost	5712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_3 := t_1 + \frac{x}{z \cdot \frac{b - y}{y}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1 + \frac{y}{b - y} \cdot \frac{x}{z}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Accuracy	94.1%
Cost	5712

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{y \cdot \left(1 - z\right)}{x}} + \frac{t - a}{1 - z} \cdot \frac{z}{y}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t_2 + \frac{y}{b - y} \cdot \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{x}{z \cdot \frac{b - y}{y}}\\ \end{array} \]

Alternative 6
Accuracy	73.2%
Cost	1356

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{y}{b - y}}{\frac{z}{x}} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+281}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b - y}\\ \end{array} \]

Alternative 7
Accuracy	75.7%
Cost	1356

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -0.0032:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1400:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	83.1%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-7} \lor \neg \left(z \leq 1.28 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{b - y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \end{array} \]

Alternative 9
Accuracy	82.3%
Cost	1352

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-79}:\\ \;\;\;\;t_1 + \frac{x}{z \cdot \frac{b - y}{y}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{y}{b - y} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10
Accuracy	42.6%
Cost	1113

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+41}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+104} \lor \neg \left(z \leq 7.4 \cdot 10^{+267}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	45.0%
Cost	848

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 3250000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	72.9%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-9} \lor \neg \left(z \leq 8.2 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \end{array} \]

Alternative 13
Accuracy	74.1%
Cost	840

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2 \cdot 10^{-7}:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-35}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	37.2%
Cost	785

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-9} \lor \neg \left(z \leq 8.2 \cdot 10^{-33}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Accuracy	44.7%
Cost	780

\[\begin{array}{l} t_1 := \frac{-a}{b - y}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+89}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	63.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -11500000000000 \lor \neg \left(z \leq 3.7 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 17
Accuracy	52.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-58} \lor \neg \left(y \leq 2.25 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 18
Accuracy	37.4%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-21} \lor \neg \left(z \leq 7.5 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Accuracy	36.6%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 20
Accuracy	26.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023136 
(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)))))