Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.4 → 5.1

Time: 1.0min

Precision: binary64

Cost: 6224

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3 + x \cdot y}{t_1}\\ t_5 := x + \frac{a - t}{b - y}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-265}:\\ \;\;\;\;\frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2 + \frac{\frac{1}{\frac{b - y}{y \cdot t_5}}}{z}\\ \mathbf{elif}\;t_4 \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{t_5 \cdot \frac{y}{b - y}}{z}\\ \end{array} \]

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 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ t_3 (* x y)) t_1))
        (t_5 (+ x (/ (- a t) (- b y)))))
   (if (<= t_4 (- INFINITY))
     (/ x (- 1.0 z))
     (if (<= t_4 -1e-265)
       (+ (/ t_3 t_1) (/ (* x y) t_1))
       (if (<= t_4 0.0)
         (+ t_2 (/ (/ 1.0 (/ (- b y) (* y t_5))) z))
         (if (<= t_4 1e+300)
           (/ (+ (* x y) (- (* z t) (* z a))) t_1)
           (+ t_2 (/ (* t_5 (/ y (- b y))) 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 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = (t_3 + (x * y)) / t_1;
	double t_5 = x + ((a - t) / (b - y));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = x / (1.0 - z);
	} else if (t_4 <= -1e-265) {
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = t_2 + ((1.0 / ((b - y) / (y * t_5))) / z);
	} else if (t_4 <= 1e+300) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = t_2 + ((t_5 * (y / (b - y))) / z);
	}
	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 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = (t_3 + (x * y)) / t_1;
	double t_5 = x + ((a - t) / (b - y));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = x / (1.0 - z);
	} else if (t_4 <= -1e-265) {
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = t_2 + ((1.0 / ((b - y) / (y * t_5))) / z);
	} else if (t_4 <= 1e+300) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = t_2 + ((t_5 * (y / (b - y))) / z);
	}
	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 = (t - a) / (b - y)
	t_3 = z * (t - a)
	t_4 = (t_3 + (x * y)) / t_1
	t_5 = x + ((a - t) / (b - y))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = x / (1.0 - z)
	elif t_4 <= -1e-265:
		tmp = (t_3 / t_1) + ((x * y) / t_1)
	elif t_4 <= 0.0:
		tmp = t_2 + ((1.0 / ((b - y) / (y * t_5))) / z)
	elif t_4 <= 1e+300:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	else:
		tmp = t_2 + ((t_5 * (y / (b - y))) / 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(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(t_3 + Float64(x * y)) / t_1)
	t_5 = Float64(x + Float64(Float64(a - t) / Float64(b - y)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(x / Float64(1.0 - z));
	elseif (t_4 <= -1e-265)
		tmp = Float64(Float64(t_3 / t_1) + Float64(Float64(x * y) / t_1));
	elseif (t_4 <= 0.0)
		tmp = Float64(t_2 + Float64(Float64(1.0 / Float64(Float64(b - y) / Float64(y * t_5))) / z));
	elseif (t_4 <= 1e+300)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	else
		tmp = Float64(t_2 + Float64(Float64(t_5 * Float64(y / Float64(b - y))) / z));
	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 = (t - a) / (b - y);
	t_3 = z * (t - a);
	t_4 = (t_3 + (x * y)) / t_1;
	t_5 = x + ((a - t) / (b - y));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = x / (1.0 - z);
	elseif (t_4 <= -1e-265)
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	elseif (t_4 <= 0.0)
		tmp = t_2 + ((1.0 / ((b - y) / (y * t_5))) / z);
	elseif (t_4 <= 1e+300)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	else
		tmp = t_2 + ((t_5 * (y / (b - y))) / z);
	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[(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[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(x + N[(N[(a - t), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -1e-265], N[(N[(t$95$3 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(t$95$2 + N[(N[(1.0 / N[(N[(b - y), $MachinePrecision] / N[(y * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+300], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(t$95$2 + N[(N[(t$95$5 * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Target

Original	23.4
Target	18.0
Herbie	5.1

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

Derivation

1. Split input into 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 64.0

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

   2. Taylor expanded in y around inf 30.0

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

   3. Simplified 30.0

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
      Proof
      (/.f64 x (-.f64 1 z)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= unsub-neg_binary64 (+.f64 1 (neg.f64 z)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (+.f64 1 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 z)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 z) 1))): 0 points increase in error, 0 points decrease in error

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.99999999999999985e-266

   1. Initial program 0.3

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

   2. Taylor expanded in x around inf 0.3

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

   if -9.99999999999999985e-266 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 43.6

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

   2. Simplified 43.6

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}} \]
      Proof
      (/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 t a)) (*.f64 x y))) (fma.f64 z (-.f64 b y) y)): 1 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 b y)) y))): 1 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (Rewrite<= +-commutative_binary64 (+.f64 y (*.f64 z (-.f64 b y))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 18.8

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

   4. Simplified 4.0

      \[\leadsto \color{blue}{\frac{\frac{y}{b - y} \cdot \left(x - \frac{t - a}{b - y}\right)}{z} + \frac{t - a}{b - y}} \]
      Proof
      (+.f64 (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 y (-.f64 b y)) x) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 1 points decrease in error
      (+.f64 (/.f64 (-.f64 (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (-.f64 b y) x))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 13 points increase in error, 10 points decrease in error
      (+.f64 (/.f64 (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 38 points increase in error, 14 points decrease in error
      (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y (-.f64 t a)) (*.f64 (-.f64 b y) (-.f64 b y))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 39 points increase in error, 3 points decrease in error
      (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 t a) y)) (*.f64 (-.f64 b y) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 b y) 2)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 -1 -1)) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 -1 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 -1 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z))) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 t (-.f64 b y)) (/.f64 a (-.f64 b y))))): 1 points increase in error, 1 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (/.f64 t (-.f64 b y))) (/.f64 a (-.f64 b y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 t (-.f64 b y)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 -1 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))))) z))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 -1 (Rewrite=> distribute-lft-out--_binary64 (*.f64 -1 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))))) z)) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 -1 -1) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))))) z)) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 (Rewrite=> metadata-eval 1) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (Rewrite=> *-lft-identity_binary64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (/.f64 (*.f64 y x) (-.f64 b y)) z) (/.f64 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)) z)))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (-.f64 (Rewrite<= associate-/r*_binary64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z))) (/.f64 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)) z))) (/.f64 a (-.f64 b y))): 7 points increase in error, 9 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (-.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (Rewrite<= associate-/r*_binary64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))))) (/.f64 a (-.f64 b y))): 2 points increase in error, 3 points decrease in error
      (-.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z))) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z)))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 y x) (Rewrite<= *-commutative_binary64 (*.f64 z (-.f64 b y))))) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (/.f64 t (-.f64 b y)))) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (/.f64 t (-.f64 b y))) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite<= *-commutative_binary64 (*.f64 z (pow.f64 (-.f64 b y) 2))))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--r+_binary64 (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (/.f64 t (-.f64 b y))) (+.f64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 z (pow.f64 (-.f64 b y) 2))) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error

   5. Applied egg-rr 3.5

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e300

   1. Initial program 0.3

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

   2. Applied egg-rr 0.3

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

   if 1.0000000000000001e300 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 63.7

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

   2. Simplified 63.7

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}} \]
      Proof
      (/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 t a)) (*.f64 x y))) (fma.f64 z (-.f64 b y) y)): 1 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 b y)) y))): 1 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (Rewrite<= +-commutative_binary64 (+.f64 y (*.f64 z (-.f64 b y))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 40.2

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

   4. Simplified 9.8

      \[\leadsto \color{blue}{\frac{\frac{y}{b - y} \cdot \left(x - \frac{t - a}{b - y}\right)}{z} + \frac{t - a}{b - y}} \]
      Proof
      (+.f64 (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 y (-.f64 b y)) x) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 1 points decrease in error
      (+.f64 (/.f64 (-.f64 (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (-.f64 b y) x))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 13 points increase in error, 10 points decrease in error
      (+.f64 (/.f64 (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 38 points increase in error, 14 points decrease in error
      (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y (-.f64 t a)) (*.f64 (-.f64 b y) (-.f64 b y))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 39 points increase in error, 3 points decrease in error
      (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 t a) y)) (*.f64 (-.f64 b y) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 b y) 2)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 -1 -1)) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 -1 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 -1 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z))) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 t (-.f64 b y)) (/.f64 a (-.f64 b y))))): 1 points increase in error, 1 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (/.f64 t (-.f64 b y))) (/.f64 a (-.f64 b y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 t (-.f64 b y)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 -1 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))))) z))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 -1 (Rewrite=> distribute-lft-out--_binary64 (*.f64 -1 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))))) z)) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 -1 -1) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))))) z)) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 (Rewrite=> metadata-eval 1) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (Rewrite=> *-lft-identity_binary64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (/.f64 (*.f64 y x) (-.f64 b y)) z) (/.f64 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)) z)))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (-.f64 (Rewrite<= associate-/r*_binary64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z))) (/.f64 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)) z))) (/.f64 a (-.f64 b y))): 7 points increase in error, 9 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (-.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (Rewrite<= associate-/r*_binary64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))))) (/.f64 a (-.f64 b y))): 2 points increase in error, 3 points decrease in error
      (-.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z))) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z)))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 y x) (Rewrite<= *-commutative_binary64 (*.f64 z (-.f64 b y))))) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (/.f64 t (-.f64 b y)))) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (/.f64 t (-.f64 b y))) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite<= *-commutative_binary64 (*.f64 z (pow.f64 (-.f64 b y) 2))))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--r+_binary64 (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (/.f64 t (-.f64 b y))) (+.f64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 z (pow.f64 (-.f64 b y) 2))) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
3. Recombined 5 regimes into one program.

4. Final simplification 5.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-265}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{1}{\frac{b - y}{y \cdot \left(x + \frac{a - t}{b - y}\right)}}}{z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\left(x + \frac{a - t}{b - y}\right) \cdot \frac{y}{b - y}}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	5.2
Cost	6224

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} + \frac{\left(x + \frac{a - t}{b - y}\right) \cdot \frac{y}{b - y}}{z}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{z \cdot \left(t - a\right) + x \cdot y}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-265}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	5.2
Cost	6224

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} + \frac{\left(x + \frac{a - t}{b - y}\right) \cdot \frac{y}{b - y}}{z}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3 + x \cdot y}{t_1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-265}:\\ \;\;\;\;\frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	7.2
Cost	5840

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;t_2 \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 4
Error	7.2
Cost	5712

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;t_1 \leq 10^{+300}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 5
Error	17.2
Cost	2148

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := t_1 - \frac{x}{z}\\ t_3 := t_1 + \frac{\frac{x}{\frac{b}{y}}}{z}\\ \mathbf{if}\;z \leq -1.2235532495334988 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.78901551646289 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq -1.1901853585280145 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.138142619996208 \cdot 10^{-28}:\\ \;\;\;\;t_1 + \frac{\frac{x \cdot y}{b}}{z}\\ \mathbf{elif}\;z \leq -1.0155610056099877 \cdot 10^{-96}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{elif}\;z \leq -1.4936361278257272 \cdot 10^{-149}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.257302903750043 \cdot 10^{-176}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 5.02301431478943 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.5853537157929192 \cdot 10^{+118}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	15.7
Cost	1752

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := t_1 - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.2235532495334988 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.78901551646289 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq -1.1901853585280145 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.138142619996208 \cdot 10^{-28}:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq 5.02301431478943 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.5853537157929192 \cdot 10^{+118}:\\ \;\;\;\;t_1 + \frac{\frac{x}{\frac{b}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	11.3
Cost	1488

\[\begin{array}{l} t_1 := \frac{t}{b - y} - \frac{a}{b - y}\\ t_2 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.2235532495334988 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.78901551646289 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1901853585280145 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.093591776000166 \cdot 10^{-14}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	16.1
Cost	1364

\[\begin{array}{l} t_1 := \frac{t}{b - y} - \frac{a}{b - y}\\ t_2 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.2235532495334988 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.78901551646289 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1901853585280145 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.138142619996208 \cdot 10^{-28}:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq 5.02301431478943 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	42.3
Cost	1116

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;y \leq -0.21442047730615205:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.829392475477247 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-176}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3069806811946198 \cdot 10^{-117}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.9630458268527656 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.203221487169794 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	30.2
Cost	976

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.1132531577291003 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9378221328220755 \cdot 10^{-21}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -2.8062437526856307 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5457278961271474 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	16.5
Cost	968

\[\begin{array}{l} t_1 := \frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{if}\;z \leq -1.7777172608601702 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.02301431478943 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	30.2
Cost	848

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.1132531577291003 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9378221328220755 \cdot 10^{-21}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -2.8062437526856307 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5457278961271474 \cdot 10^{+32}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	16.5
Cost	840

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.7777172608601702 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.02301431478943 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	25.8
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.1132531577291003 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.265013883181821 \cdot 10^{+128}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	34.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -0.21442047730615205:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.499286626571263 \cdot 10^{+123}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	29.8
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -0.21442047730615205:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5457278961271474 \cdot 10^{+32}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	42.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4588510418971544 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.203221487169794 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	46.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022316 
(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)))))