Development.Shake.Progress:decay from shake-0.15.5

Average Accuracy: 64.3% → 97.4%

Time: 45.1s

Precision: binary64

Cost: 5840

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := t_2 + x \cdot y\\ t_4 := \frac{t_3}{t_1}\\ t_5 := \frac{t - a}{b - y}\\ t_6 := t_5 + \frac{x}{1 - z}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\frac{t_2}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_5 + \frac{x \cdot \frac{y}{z}}{b - y}\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{t_3}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

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 (* z (- t a)))
        (t_3 (+ t_2 (* x y)))
        (t_4 (/ t_3 t_1))
        (t_5 (/ (- t a) (- b y)))
        (t_6 (+ t_5 (/ x (- 1.0 z)))))
   (if (<= t_4 (- INFINITY))
     t_6
     (if (<= t_4 -5e-306)
       (+ (/ t_2 t_1) (/ (* x y) t_1))
       (if (<= t_4 0.0)
         (+ t_5 (/ (* x (/ y z)) (- b y)))
         (if (<= t_4 5e+286) (/ t_3 (+ y (- (* z b) (* y z)))) t_6))))))

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 = z * (t - a);
	double t_3 = t_2 + (x * y);
	double t_4 = t_3 / t_1;
	double t_5 = (t - a) / (b - y);
	double t_6 = t_5 + (x / (1.0 - z));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_4 <= -5e-306) {
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = t_5 + ((x * (y / z)) / (b - y));
	} else if (t_4 <= 5e+286) {
		tmp = t_3 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_6;
	}
	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 = z * (t - a);
	double t_3 = t_2 + (x * y);
	double t_4 = t_3 / t_1;
	double t_5 = (t - a) / (b - y);
	double t_6 = t_5 + (x / (1.0 - z));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else if (t_4 <= -5e-306) {
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = t_5 + ((x * (y / z)) / (b - y));
	} else if (t_4 <= 5e+286) {
		tmp = t_3 / (y + ((z * b) - (y * z)));
	} else {
		tmp = t_6;
	}
	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 = z * (t - a)
	t_3 = t_2 + (x * y)
	t_4 = t_3 / t_1
	t_5 = (t - a) / (b - y)
	t_6 = t_5 + (x / (1.0 - z))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_6
	elif t_4 <= -5e-306:
		tmp = (t_2 / t_1) + ((x * y) / t_1)
	elif t_4 <= 0.0:
		tmp = t_5 + ((x * (y / z)) / (b - y))
	elif t_4 <= 5e+286:
		tmp = t_3 / (y + ((z * b) - (y * z)))
	else:
		tmp = t_6
	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(z * Float64(t - a))
	t_3 = Float64(t_2 + Float64(x * y))
	t_4 = Float64(t_3 / t_1)
	t_5 = Float64(Float64(t - a) / Float64(b - y))
	t_6 = Float64(t_5 + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_4 <= -5e-306)
		tmp = Float64(Float64(t_2 / t_1) + Float64(Float64(x * y) / t_1));
	elseif (t_4 <= 0.0)
		tmp = Float64(t_5 + Float64(Float64(x * Float64(y / z)) / Float64(b - y)));
	elseif (t_4 <= 5e+286)
		tmp = Float64(t_3 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	else
		tmp = t_6;
	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 = z * (t - a);
	t_3 = t_2 + (x * y);
	t_4 = t_3 / t_1;
	t_5 = (t - a) / (b - y);
	t_6 = t_5 + (x / (1.0 - z));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_6;
	elseif (t_4 <= -5e-306)
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	elseif (t_4 <= 0.0)
		tmp = t_5 + ((x * (y / z)) / (b - y));
	elseif (t_4 <= 5e+286)
		tmp = t_3 / (y + ((z * b) - (y * z)));
	else
		tmp = t_6;
	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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$6, If[LessEqual[t$95$4, -5e-306], N[(N[(t$95$2 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(t$95$5 + N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+286], N[(t$95$3 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$6]]]]]]]]]]

Target

Original	64.3%
Target	72.5%
Herbie	97.4%

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

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 5.0000000000000004e286 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 1.6%

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

   2. Taylor expanded in x around inf 1.6%

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

   3. Taylor expanded in z around inf 56.2%

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

   4. Taylor expanded in y around inf 93.2%

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

   5. Simplified 93.2%

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

      [Start] 93.2	\[ \frac{t - a}{b - y} + \frac{x}{-1 \cdot z + 1} \]
      +-commutative [=>] 93.2	\[ \frac{t - a}{b - y} + \frac{x}{\color{blue}{1 + -1 \cdot z}} \]
      mul-1-neg [=>] 93.2	\[ \frac{t - a}{b - y} + \frac{x}{1 + \color{blue}{\left(-z\right)}} \]
      unsub-neg [=>] 93.2	\[ \frac{t - a}{b - y} + \frac{x}{\color{blue}{1 - z}} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999998e-306

   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 -4.99999999999999998e-306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 31.2%

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

   2. Taylor expanded in x around inf 31.2%

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

   3. Taylor expanded in z around inf 81.7%

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

   4. Taylor expanded in z around inf 81.7%

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

   5. Simplified 97.5%

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

      [Start] 81.7	\[ \frac{t - a}{b - y} + \frac{y \cdot x}{z \cdot \left(b - y\right)} \]
      times-frac [=>] 93.4	\[ \frac{t - a}{b - y} + \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} \]
      associate-*r/ [=>] 97.5	\[ \frac{t - a}{b - y} + \color{blue}{\frac{\frac{y}{z} \cdot x}{b - y}} \]

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000004e286

   1. Initial program 99.5%

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

   2. Applied egg-rr 99.5%

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

      [Start] 99.5	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      sub-neg [=>] 99.5	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \color{blue}{\left(b + \left(-y\right)\right)}} \]
      distribute-lft-in [=>] 99.5	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(z \cdot b + z \cdot \left(-y\right)\right)}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x \cdot \frac{y}{z}}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	97.4%
Cost	5840

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right) + x \cdot y\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := t_3 + \frac{x}{1 - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3 + \frac{x \cdot \frac{y}{z}}{b - y}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{t_1}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Accuracy	97.4%
Cost	5712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_3 := t_1 + \frac{x}{1 - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1 + \frac{x \cdot \frac{y}{z}}{b - y}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Accuracy	65.9%
Cost	2021

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{t - a}{b - y}\\ t_4 := t_3 + \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -84:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{-27}:\\ \;\;\;\;\frac{t_1}{t_2}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-51}:\\ \;\;\;\;\frac{x \cdot y}{t_2}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-150}:\\ \;\;\;\;\frac{t_1}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-207}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+55} \lor \neg \left(z \leq 1.8 \cdot 10^{+210}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Accuracy	63.5%
Cost	1760

\[\begin{array}{l} t_1 := \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -0.028:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	82.5%
Cost	1757

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t - a}{b - y}\\ t_4 := t_3 + t_1\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -30000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq -0.031:\\ \;\;\;\;t_1 + \frac{a - t}{y}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-151}:\\ \;\;\;\;\frac{t_2 + x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+55} \lor \neg \left(z \leq 1.75 \cdot 10^{+210}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Accuracy	81.0%
Cost	1493

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := t_1 + \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -64:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+55} \lor \neg \left(z \leq 3 \cdot 10^{+210}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	81.9%
Cost	1493

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := t_1 + \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -92:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+52} \lor \neg \left(z \leq 2 \cdot 10^{+210}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	88.9%
Cost	1484

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} + \frac{x \cdot \frac{y}{z}}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -12:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-151}:\\ \;\;\;\;\frac{t_2 + x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	63.7%
Cost	1364

\[\begin{array}{l} t_1 := \frac{x}{1 - z} + \frac{a - t}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1400000:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	69.8%
Cost	1361

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\frac{t - a}{\frac{1 - z}{\frac{z}{y}}}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-78} \lor \neg \left(y \leq 1.45 \cdot 10^{-77}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \end{array} \]

Alternative 11
Accuracy	63.9%
Cost	1100

\[\begin{array}{l} t_1 := \frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	61.3%
Cost	976

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{x \cdot y}{z} - a}{b}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Accuracy	57.8%
Cost	968

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+170}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	33.9%
Cost	852

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-271}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+59}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Accuracy	41.2%
Cost	716

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+170}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	51.0%
Cost	716

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.26 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 14.5:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+174}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Accuracy	58.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-38} \lor \neg \left(y \leq 6.8 \cdot 10^{+170}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 18
Accuracy	45.6%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-19} \lor \neg \left(z \leq 0.00105\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 19
Accuracy	37.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.032:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 20
Accuracy	26.4%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023151 
(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)))))