Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.0 → 0.9

Time: 1.7min

Precision: binary64

Cost: 14292

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \left(-\frac{-1 \cdot \left(y \cdot \left(\frac{x}{b - y} - \frac{t - a}{{\left(b - y\right)}^{2}}\right)\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_4 := \frac{t - a}{b - y} + y \cdot \frac{x}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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
         (+
          (-
           (/
            (* -1.0 (* y (- (/ x (- b y)) (/ (- t a) (pow (- b y) 2.0)))))
            z))
          (- (/ t (- b y)) (/ a (- b y)))))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_4 (+ (/ (- t a) (- b y)) (* y (/ x t_1)))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -5e-308)
       t_3
       (if (<= t_3 0.0)
         t_2
         (if (<= t_3 2e+282) t_3 (if (<= t_3 INFINITY) t_4 t_2)))))))

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 = -((-1.0 * (y * ((x / (b - y)) - ((t - a) / pow((b - y), 2.0))))) / z) + ((t / (b - y)) - (a / (b - y)));
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = ((t - a) / (b - y)) + (y * (x / t_1));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -5e-308) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+282) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

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)));
}

↓

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 = -((-1.0 * (y * ((x / (b - y)) - ((t - a) / Math.pow((b - y), 2.0))))) / z) + ((t / (b - y)) - (a / (b - y)));
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = ((t - a) / (b - y)) + (y * (x / t_1));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -5e-308) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+282) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = -((-1.0 * (y * ((x / (b - y)) - ((t - a) / math.pow((b - y), 2.0))))) / z) + ((t / (b - y)) - (a / (b - y)))
	t_3 = ((x * y) + (z * (t - a))) / t_1
	t_4 = ((t - a) / (b - y)) + (y * (x / t_1))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -5e-308:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = t_2
	elif t_3 <= 2e+282:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_4
	else:
		tmp = t_2
	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(Float64(-Float64(Float64(-1.0 * Float64(y * Float64(Float64(x / Float64(b - y)) - Float64(Float64(t - a) / (Float64(b - y) ^ 2.0))))) / z)) + Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y))))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_4 = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(y * Float64(x / t_1)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -5e-308)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 2e+282)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = -((-1.0 * (y * ((x / (b - y)) - ((t - a) / ((b - y) ^ 2.0))))) / z) + ((t / (b - y)) - (a / (b - y)));
	t_3 = ((x * y) + (z * (t - a))) / t_1;
	t_4 = ((t - a) / (b - y)) + (y * (x / t_1));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -5e-308)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 2e+282)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = 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[((-N[(N[(-1.0 * N[(y * N[(N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -5e-308], t$95$3, If[LessEqual[t$95$3, 0.0], t$95$2, If[LessEqual[t$95$3, 2e+282], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$4, t$95$2]]]]]]]]]

Target

Original	23.0
Target	17.8
Herbie	0.9

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 2.00000000000000007e282 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 61.0

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

   2. Taylor expanded in x around 0 61.0

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

   3. Simplified 29.4

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

      [Start] 61.0	\[ \frac{y \cdot x}{y + \left(b - y\right) \cdot z} + \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} \]
      rational.json-simplify-1 [=>] 61.0	\[ \color{blue}{\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z}} \]
      rational.json-simplify-2 [=>] 61.0	\[ \frac{\left(t - a\right) \cdot z}{y + \color{blue}{z \cdot \left(b - y\right)}} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z} \]
      rational.json-simplify-2 [=>] 61.0	\[ \frac{\left(t - a\right) \cdot z}{y + z \cdot \left(b - y\right)} + \frac{\color{blue}{x \cdot y}}{y + \left(b - y\right) \cdot z} \]
      rational.json-simplify-2 [=>] 61.0	\[ \frac{\left(t - a\right) \cdot z}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + \color{blue}{z \cdot \left(b - y\right)}} \]
      rational.json-simplify-49 [=>] 29.4	\[ \frac{\left(t - a\right) \cdot z}{y + z \cdot \left(b - y\right)} + \color{blue}{y \cdot \frac{x}{y + z \cdot \left(b - y\right)}} \]

   4. Taylor expanded in z around inf 2.0

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999955e-308 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000007e282

   1. Initial program 0.3

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

   if -4.99999999999999955e-308 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 57.0

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

   2. Taylor expanded in z around -inf 28.0

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

   3. Simplified 1.6

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

      [Start] 28.0	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      rational.json-simplify-48 [=>] 28.0	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y} + y \cdot \frac{x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-308}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(-\frac{-1 \cdot \left(y \cdot \left(\frac{x}{b - y} - \frac{t - a}{{\left(b - y\right)}^{2}}\right)\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{t - a}{b - y} + y \cdot \frac{x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{-1 \cdot \left(y \cdot \left(\frac{x}{b - y} - \frac{t - a}{{\left(b - y\right)}^{2}}\right)\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	3.9
Cost	5712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{y + \left(b - y\right) \cdot z} - \frac{a}{b - y}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{x}{\left(-z\right) + 1}\\ \end{array} \]

Alternative 2
Error	2.8
Cost	5712

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3 + y \cdot \frac{x}{t_1}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + \frac{x}{\left(-z\right) + 1}\\ \end{array} \]

Alternative 3
Error	21.8
Cost	1624

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-118}:\\ \;\;\;\;\frac{y \cdot x + t \cdot z}{y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{y}{y + b \cdot z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(\frac{2}{b - y} \cdot \left(y \cdot \frac{0.5}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	39.6
Cost	1508

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := -\frac{a}{b}\\ t_3 := -\left(-\frac{a}{y}\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+276}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+151}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+220}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	21.4
Cost	1492

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-13}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(\frac{2}{b - y} \cdot \left(y \cdot \frac{0.5}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	9.9
Cost	1488

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} + \frac{x}{\left(-z\right) + 1}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{-178}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z}{y + z \cdot \left(b - y\right)} + x\\ \mathbf{elif}\;z \leq 0.0015:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	18.3
Cost	1360

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{y \cdot x + t \cdot z}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(\frac{2}{b - y} \cdot \left(y \cdot \frac{0.5}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	38.1
Cost	1244

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -6 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-170}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+110}:\\ \;\;\;\;-\left(-\frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	11.2
Cost	1224

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} + \frac{x}{\left(-z\right) + 1}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-13}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z}{y + z \cdot \left(b - y\right)} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	16.5
Cost	1160

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} + \frac{x}{\left(-z\right) + 1}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot x + t \cdot z}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	41.9
Cost	1112

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ t_2 := -\left(-\frac{a}{y}\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+137}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+151}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+222}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	21.4
Cost	1104

\[\begin{array}{l} t_1 := x \cdot \frac{y}{y + b \cdot z}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{y \cdot x + t \cdot z}{y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	21.4
Cost	1104

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{y \cdot x + t \cdot z}{y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{y}{y + b \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	41.8
Cost	916

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+135}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+217}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+229}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	31.0
Cost	848

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+21}:\\ \;\;\;\;z \cdot x + x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	32.0
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-168}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+96}:\\ \;\;\;\;-\frac{a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z + -1} \cdot x\\ \end{array} \]

Alternative 17
Error	20.3
Cost	840

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \frac{y}{y + b \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	32.0
Cost	780

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-170}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;-\frac{a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	23.8
Cost	712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	41.4
Cost	652

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+224}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	41.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-60}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 22
Error	46.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023074 
(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)))))