Development.Shake.Progress:decay from shake-0.15.5

Average Error: 22.7 → 5.7

Time: 30.1s

Precision: binary64

Cost: 18256

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t - a}{{\left(b - y\right)}^{2}}\\ t_4 := \frac{x \cdot y + t_2}{y + z \cdot \left(b - y\right)}\\ t_5 := \frac{x \cdot \frac{y}{b - y} - y \cdot t_3}{z} + t_1\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-291}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \left(t_1 - t_3 \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, t_2\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

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 (/ (- t a) (- b y)))
        (t_2 (* z (- t a)))
        (t_3 (/ (- t a) (pow (- b y) 2.0)))
        (t_4 (/ (+ (* x y) t_2) (+ y (* z (- b y)))))
        (t_5 (+ (/ (- (* x (/ y (- b y))) (* y t_3)) z) t_1)))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -5e-291)
       t_4
       (if (<= t_4 0.0)
         (+ (* (/ y z) (/ x (- b y))) (- t_1 (* t_3 (/ y z))))
         (if (<= t_4 5e+297) (/ (fma y x t_2) (fma z (- b y) y)) t_5))))))

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 = (t - a) / (b - y);
	double t_2 = z * (t - a);
	double t_3 = (t - a) / pow((b - y), 2.0);
	double t_4 = ((x * y) + t_2) / (y + (z * (b - y)));
	double t_5 = (((x * (y / (b - y))) - (y * t_3)) / z) + t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -5e-291) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = ((y / z) * (x / (b - y))) + (t_1 - (t_3 * (y / z)));
	} else if (t_4 <= 5e+297) {
		tmp = fma(y, x, t_2) / fma(z, (b - y), y);
	} else {
		tmp = t_5;
	}
	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(Float64(t - a) / Float64(b - y))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(t - a) / (Float64(b - y) ^ 2.0))
	t_4 = Float64(Float64(Float64(x * y) + t_2) / Float64(y + Float64(z * Float64(b - y))))
	t_5 = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * t_3)) / z) + t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -5e-291)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(t_1 - Float64(t_3 * Float64(y / z))));
	elseif (t_4 <= 5e+297)
		tmp = Float64(fma(y, x, t_2) / fma(z, Float64(b - y), y));
	else
		tmp = t_5;
	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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$3), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -5e-291], t$95$4, If[LessEqual[t$95$4, 0.0], N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 - N[(t$95$3 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+297], N[(N[(y * x + t$95$2), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]

Target

Original	22.7
Target	17.2
Herbie	5.7

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

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 or 4.9999999999999998e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 63.3

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

   2. Taylor expanded in z around -inf 39.3

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

   3. Simplified 17.3

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

      [Start] 39.3	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      +-commutative [=>] 39.3	\[ \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]
      associate--l+ [=>] 39.3	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000003e-291

   1. Initial program 0.3

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

   if -5.0000000000000003e-291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 45.0

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

   2. Taylor expanded in z around inf 19.2

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

   3. Simplified 5.1

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

      [Start] 19.2	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 19.2	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      times-frac [=>] 11.2	\[ \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 11.2	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 11.2	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      associate--r+ [=>] 11.2	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\left(\left(\frac{t}{b - y} - \frac{a}{b - y}\right) - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right)} \]
      div-sub [<=] 11.2	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\color{blue}{\frac{t - a}{b - y}} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right) \]
      times-frac [=>] 5.1	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t - a}{b - y} - \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right) \]

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.9999999999999998e297

   1. Initial program 0.3

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

   2. Simplified 0.3

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

      [Start] 0.3	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      *-commutative [=>] 0.3	\[ \frac{\color{blue}{y \cdot x} + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 0.3	\[ \frac{\color{blue}{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]
      +-commutative [=>] 0.3	\[ \frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\color{blue}{z \cdot \left(b - y\right) + y}} \]
      fma-def [=>] 0.3	\[ \frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 5.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t - a}{b - y} - \frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	5.7
Cost	12946

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq -5 \cdot 10^{-291} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 5 \cdot 10^{+297}\right):\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t - a}{b - y} - \frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	5.7
Cost	12816

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{t - a}{{\left(b - y\right)}^{2}}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_4 := \frac{x \cdot \frac{y}{b - y} - y \cdot t_2}{z} + t_1\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-291}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \left(t_1 - t_2 \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	10.0
Cost	10828

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-291}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{b - y} \cdot \frac{1}{z}\\ \mathbf{elif}\;t_3 \leq 10^{+194}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	10.9
Cost	5714

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+247} \lor \neg \left(t_1 \leq -5 \cdot 10^{-291}\right) \land \left(t_1 \leq 0 \lor \neg \left(t_1 \leq 10^{+194}\right)\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	37.5
Cost	1836

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y}\\ t_2 := \frac{x}{1 - z}\\ t_3 := \frac{-a}{b - y}\\ t_4 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -0.00055:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-92}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-185}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00032:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+280}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y}\\ \end{array} \]

Alternative 6
Error	21.3
Cost	1760

\[\begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := z \cdot \left(b - y\right)\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{t_1}{y}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-92}:\\ \;\;\;\;\frac{t_1}{t_2}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-170}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{-288}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-186}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{x \cdot y}{y + t_2}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	21.5
Cost	1628

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	21.4
Cost	1364

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	24.1
Cost	1232

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-212}:\\ \;\;\;\;\frac{z \cdot t}{t_1}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	36.0
Cost	849

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+83} \lor \neg \left(z \leq 5.2 \cdot 10^{+273}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 11
Error	39.8
Cost	784

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.0026:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	36.9
Cost	716

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	30.3
Cost	716

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-94}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 350000000:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	24.3
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-196} \lor \neg \left(z \leq 4 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	39.7
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-31} \lor \neg \left(z \leq 5.8 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	39.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 17
Error	46.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023018 
(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)))))