Development.Shake.Progress:decay from shake-0.15.5

Average Error: 22.9 → 4.5

Time: 32.7s

Precision: binary64

Cost: 14100

Math

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

↓

\[\begin{array}{l} t_1 := \frac{a - t}{{\left(b - y\right)}^{2}}\\ t_2 := y - z \cdot \left(y - b\right)\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_2}\\ t_4 := \frac{t - a}{b - y}\\ t_5 := t_4 + \frac{y}{z} \cdot t_1\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot \left(b - y\right)}{x}} + t_5\\ \mathbf{elif}\;t_3 \leq -4 \cdot 10^{-295}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_5 + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x \cdot y}{t_2} + \left(\frac{z \cdot t}{t_2} - \frac{z \cdot a}{t_2}\right)\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \left(\frac{t - a}{1 - z} \cdot \frac{z}{y} - \frac{z \cdot \frac{b}{\frac{y}{x}}}{{\left(1 - z\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_4 + \frac{x \cdot \frac{y}{b - y} + y \cdot t_1}{z}\\ \end{array} \]

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 (/ (- a t) (pow (- b y) 2.0)))
        (t_2 (- y (* z (- y b))))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_2))
        (t_4 (/ (- t a) (- b y)))
        (t_5 (+ t_4 (* (/ y z) t_1))))
   (if (<= t_3 (- INFINITY))
     (+ (/ y (/ (* z (- b y)) x)) t_5)
     (if (<= t_3 -4e-295)
       t_3
       (if (<= t_3 0.0)
         (+ t_5 (* (/ y z) (/ x (- b y))))
         (if (<= t_3 2e+307)
           (+ (/ (* x y) t_2) (- (/ (* z t) t_2) (/ (* z a) t_2)))
           (if (<= t_3 INFINITY)
             (+
              (/ x (- 1.0 z))
              (-
               (* (/ (- t a) (- 1.0 z)) (/ z y))
               (/ (* z (/ b (/ y x))) (pow (- 1.0 z) 2.0))))
             (+ t_4 (/ (+ (* x (/ y (- b y))) (* y t_1)) 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 = (a - t) / pow((b - y), 2.0);
	double t_2 = y - (z * (y - b));
	double t_3 = ((x * y) + (z * (t - a))) / t_2;
	double t_4 = (t - a) / (b - y);
	double t_5 = t_4 + ((y / z) * t_1);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (y / ((z * (b - y)) / x)) + t_5;
	} else if (t_3 <= -4e-295) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_5 + ((y / z) * (x / (b - y)));
	} else if (t_3 <= 2e+307) {
		tmp = ((x * y) / t_2) + (((z * t) / t_2) - ((z * a) / t_2));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = (x / (1.0 - z)) + ((((t - a) / (1.0 - z)) * (z / y)) - ((z * (b / (y / x))) / pow((1.0 - z), 2.0)));
	} else {
		tmp = t_4 + (((x * (y / (b - y))) + (y * t_1)) / 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 = (a - t) / Math.pow((b - y), 2.0);
	double t_2 = y - (z * (y - b));
	double t_3 = ((x * y) + (z * (t - a))) / t_2;
	double t_4 = (t - a) / (b - y);
	double t_5 = t_4 + ((y / z) * t_1);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / ((z * (b - y)) / x)) + t_5;
	} else if (t_3 <= -4e-295) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_5 + ((y / z) * (x / (b - y)));
	} else if (t_3 <= 2e+307) {
		tmp = ((x * y) / t_2) + (((z * t) / t_2) - ((z * a) / t_2));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = (x / (1.0 - z)) + ((((t - a) / (1.0 - z)) * (z / y)) - ((z * (b / (y / x))) / Math.pow((1.0 - z), 2.0)));
	} else {
		tmp = t_4 + (((x * (y / (b - y))) + (y * t_1)) / 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 = (a - t) / math.pow((b - y), 2.0)
	t_2 = y - (z * (y - b))
	t_3 = ((x * y) + (z * (t - a))) / t_2
	t_4 = (t - a) / (b - y)
	t_5 = t_4 + ((y / z) * t_1)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (y / ((z * (b - y)) / x)) + t_5
	elif t_3 <= -4e-295:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = t_5 + ((y / z) * (x / (b - y)))
	elif t_3 <= 2e+307:
		tmp = ((x * y) / t_2) + (((z * t) / t_2) - ((z * a) / t_2))
	elif t_3 <= math.inf:
		tmp = (x / (1.0 - z)) + ((((t - a) / (1.0 - z)) * (z / y)) - ((z * (b / (y / x))) / math.pow((1.0 - z), 2.0)))
	else:
		tmp = t_4 + (((x * (y / (b - y))) + (y * t_1)) / 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(Float64(a - t) / (Float64(b - y) ^ 2.0))
	t_2 = Float64(y - Float64(z * Float64(y - b)))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_2)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	t_5 = Float64(t_4 + Float64(Float64(y / z) * t_1))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(y / Float64(Float64(z * Float64(b - y)) / x)) + t_5);
	elseif (t_3 <= -4e-295)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(t_5 + Float64(Float64(y / z) * Float64(x / Float64(b - y))));
	elseif (t_3 <= 2e+307)
		tmp = Float64(Float64(Float64(x * y) / t_2) + Float64(Float64(Float64(z * t) / t_2) - Float64(Float64(z * a) / t_2)));
	elseif (t_3 <= Inf)
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(Float64(Float64(t - a) / Float64(1.0 - z)) * Float64(z / y)) - Float64(Float64(z * Float64(b / Float64(y / x))) / (Float64(1.0 - z) ^ 2.0))));
	else
		tmp = Float64(t_4 + Float64(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * t_1)) / 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 = (a - t) / ((b - y) ^ 2.0);
	t_2 = y - (z * (y - b));
	t_3 = ((x * y) + (z * (t - a))) / t_2;
	t_4 = (t - a) / (b - y);
	t_5 = t_4 + ((y / z) * t_1);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (y / ((z * (b - y)) / x)) + t_5;
	elseif (t_3 <= -4e-295)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_5 + ((y / z) * (x / (b - y)));
	elseif (t_3 <= 2e+307)
		tmp = ((x * y) / t_2) + (((z * t) / t_2) - ((z * a) / t_2));
	elseif (t_3 <= Inf)
		tmp = (x / (1.0 - z)) + ((((t - a) / (1.0 - z)) * (z / y)) - ((z * (b / (y / x))) / ((1.0 - z) ^ 2.0)));
	else
		tmp = t_4 + (((x * (y / (b - y))) + (y * t_1)) / 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[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + N[(N[(y / z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(y / N[(N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision], If[LessEqual[t$95$3, -4e-295], t$95$3, If[LessEqual[t$95$3, 0.0], N[(t$95$5 + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+307], N[(N[(N[(x * y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / t$95$2), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(t - a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(b / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[N[(1.0 - z), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$4 + N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Target

Original	22.9
Target	17.8
Herbie	4.5

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

Derivation

1. Split input into 6 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 z around inf 41.8

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

   3. Simplified 29.0

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

      [Start] 41.8	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 41.8	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      times-frac [=>] 36.4	\[ \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 36.4	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 36.4	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      associate--r+ [=>] 36.4	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\left(\left(\frac{t}{b - y} - \frac{a}{b - y}\right) - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right)} \]
      div-sub [<=] 36.4	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\color{blue}{\frac{t - a}{b - y}} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right) \]
      times-frac [=>] 29.0	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t - a}{b - y} - \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right) \]

   4. Applied egg-rr 28.8

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.00000000000000024e-295

   1. Initial program 0.4

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

   if -4.00000000000000024e-295 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 45.1

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

   2. Taylor expanded in z around inf 20.2

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

   3. Simplified 5.9

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

      [Start] 20.2	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 20.2	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      times-frac [=>] 11.5	\[ \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 11.5	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 11.5	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      associate--r+ [=>] 11.5	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\left(\left(\frac{t}{b - y} - \frac{a}{b - y}\right) - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right)} \]
      div-sub [<=] 11.5	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\color{blue}{\frac{t - a}{b - y}} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right) \]
      times-frac [=>] 5.9	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t - a}{b - y} - \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right) \]

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.99999999999999997e307

   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. Taylor expanded in a around inf 0.3

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

   if 1.99999999999999997e307 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 63.8

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

   2. Simplified 63.8

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

      [Start] 63.8	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      *-commutative [=>] 63.8	\[ \frac{\color{blue}{y \cdot x} + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 63.8	\[ \frac{\color{blue}{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]
      +-commutative [=>] 63.8	\[ \frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\color{blue}{z \cdot \left(b - y\right) + y}} \]
      fma-def [=>] 63.8	\[ \frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}} \]

   3. Taylor expanded in y around inf 42.4

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

   4. Simplified 21.5

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

      [Start] 42.4	\[ \left(\frac{\left(t - a\right) \cdot z}{\left(-1 \cdot z + 1\right) \cdot y} + \frac{x}{-1 \cdot z + 1}\right) - \frac{z \cdot \left(b \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y} \]
      +-commutative [=>] 42.4	\[ \color{blue}{\left(\frac{x}{-1 \cdot z + 1} + \frac{\left(t - a\right) \cdot z}{\left(-1 \cdot z + 1\right) \cdot y}\right)} - \frac{z \cdot \left(b \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y} \]
      associate-*r* [=>] 34.6	\[ \left(\frac{x}{-1 \cdot z + 1} + \frac{\left(t - a\right) \cdot z}{\left(-1 \cdot z + 1\right) \cdot y}\right) - \frac{\color{blue}{\left(z \cdot b\right) \cdot x}}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y} \]
      *-commutative [=>] 34.6	\[ \left(\frac{x}{-1 \cdot z + 1} + \frac{\left(t - a\right) \cdot z}{\left(-1 \cdot z + 1\right) \cdot y}\right) - \frac{\color{blue}{\left(b \cdot z\right)} \cdot x}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y} \]
      associate-*r* [<=] 36.2	\[ \left(\frac{x}{-1 \cdot z + 1} + \frac{\left(t - a\right) \cdot z}{\left(-1 \cdot z + 1\right) \cdot y}\right) - \frac{\color{blue}{b \cdot \left(z \cdot x\right)}}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y} \]
      associate--l+ [=>] 36.2	\[ \color{blue}{\frac{x}{-1 \cdot z + 1} + \left(\frac{\left(t - a\right) \cdot z}{\left(-1 \cdot z + 1\right) \cdot y} - \frac{b \cdot \left(z \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y}\right)} \]
      +-commutative [=>] 36.2	\[ \frac{x}{\color{blue}{1 + -1 \cdot z}} + \left(\frac{\left(t - a\right) \cdot z}{\left(-1 \cdot z + 1\right) \cdot y} - \frac{b \cdot \left(z \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y}\right) \]
      mul-1-neg [=>] 36.2	\[ \frac{x}{1 + \color{blue}{\left(-z\right)}} + \left(\frac{\left(t - a\right) \cdot z}{\left(-1 \cdot z + 1\right) \cdot y} - \frac{b \cdot \left(z \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y}\right) \]
      unsub-neg [=>] 36.2	\[ \frac{x}{\color{blue}{1 - z}} + \left(\frac{\left(t - a\right) \cdot z}{\left(-1 \cdot z + 1\right) \cdot y} - \frac{b \cdot \left(z \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y}\right) \]
      times-frac [=>] 27.1	\[ \frac{x}{1 - z} + \left(\color{blue}{\frac{t - a}{-1 \cdot z + 1} \cdot \frac{z}{y}} - \frac{b \cdot \left(z \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y}\right) \]
      +-commutative [=>] 27.1	\[ \frac{x}{1 - z} + \left(\frac{t - a}{\color{blue}{1 + -1 \cdot z}} \cdot \frac{z}{y} - \frac{b \cdot \left(z \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y}\right) \]
      mul-1-neg [=>] 27.1	\[ \frac{x}{1 - z} + \left(\frac{t - a}{1 + \color{blue}{\left(-z\right)}} \cdot \frac{z}{y} - \frac{b \cdot \left(z \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y}\right) \]
      unsub-neg [=>] 27.1	\[ \frac{x}{1 - z} + \left(\frac{t - a}{\color{blue}{1 - z}} \cdot \frac{z}{y} - \frac{b \cdot \left(z \cdot x\right)}{{\left(-1 \cdot z + 1\right)}^{2} \cdot y}\right) \]

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

   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 z around -inf 39.0

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

   3. Simplified 0.0

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

      [Start] 39.0	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      +-commutative [=>] 39.0	\[ \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]
      associate--l+ [=>] 39.0	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

3. Recombined 6 regimes into one program.

4. Final simplification 4.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot \left(b - y\right)}{x}} + \left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -4 \cdot 10^{-295}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 0:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right) + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)} + \left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \left(\frac{t - a}{1 - z} \cdot \frac{z}{y} - \frac{z \cdot \frac{b}{\frac{y}{x}}}{{\left(1 - z\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	5.6
Cost	14100

\[\begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \left(t_3 + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right) + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 10^{+299}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \left(\frac{z \cdot t}{t_1} - \frac{z \cdot a}{t_1}\right)\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;x \cdot \frac{1}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Error	4.8
Cost	14100

\[\begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \left(t_3 + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right) + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \left(\frac{z \cdot t}{t_1} - \frac{z \cdot a}{t_1}\right)\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \left(\frac{t - a}{1 - z} \cdot \frac{z}{y} - \frac{z \cdot \frac{b}{\frac{y}{x}}}{{\left(1 - z\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	4.5
Cost	14100

\[\begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ t_4 := t_3 + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot \left(b - y\right)}{x}} + t_3\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \left(\frac{z \cdot t}{t_1} - \frac{z \cdot a}{t_1}\right)\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \left(\frac{t - a}{1 - z} \cdot \frac{z}{y} - \frac{z \cdot \frac{b}{\frac{y}{x}}}{{\left(1 - z\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 4
Error	12.1
Cost	2504

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y - z \cdot \left(y - b\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y}{t_2} + \left(\frac{z \cdot t}{t_2} - \frac{z \cdot a}{t_2}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-146}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{x \cdot y + t_1}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	16.8
Cost	1620

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot t}{y - z \cdot \left(y - b\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.0195:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	12.0
Cost	1616

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{x \cdot y + t_1}{y - z \cdot \left(y - b\right)}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-146}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	18.2
Cost	1492

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-62}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y + t_1}{z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	17.8
Cost	1492

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y + t_1}{z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	32.3
Cost	1242

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-11} \lor \neg \left(z \leq -8 \cdot 10^{-30} \lor \neg \left(z \leq -1.75 \cdot 10^{-78}\right) \land z \leq 1.85 \cdot 10^{-79}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 10
Error	30.3
Cost	1112

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -118000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-74}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+30}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq 7.9 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	17.8
Cost	1104

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-62}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	30.4
Cost	980

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -280000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{+88}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	21.0
Cost	978

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-12} \lor \neg \left(z \leq -6.4 \cdot 10^{-31}\right) \land \left(z \leq -5.2 \cdot 10^{-80} \lor \neg \left(z \leq 1.7 \cdot 10^{-79}\right)\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 14
Error	29.6
Cost	849

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -32500000 \lor \neg \left(y \leq 4.5 \cdot 10^{-48}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 15
Error	40.4
Cost	848

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+17}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-5}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16
Error	40.4
Cost	720

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -32500000000:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.00037:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 17
Error	35.8
Cost	716

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-62}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-7}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	35.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+25} \lor \neg \left(z \leq 0.053\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 19
Error	40.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 20
Error	40.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-62}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 0.0116:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 21
Error	47.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023057 
(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)))))