Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.5 → 5.4

Time: 40.6s

Precision: binary64

Cost: 15380

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y - z \cdot \left(a - t\right)}{t_1}\\ t_3 := \frac{x}{1 - z}\\ t_4 := \frac{t - a}{b - y}\\ t_5 := \frac{y}{b - y}\\ t_6 := t_5 \cdot \left(x + \frac{a - t}{b - y}\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3 + \frac{z}{y} \cdot \left(\frac{t - a}{1 - z} - \frac{x \cdot b}{{\left(1 - z\right)}^{2}}\right)\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_4 + \frac{t_6}{z}\\ \mathbf{elif}\;t_2 \leq 10^{+268}:\\ \;\;\;\;\frac{\left(z \cdot t - z \cdot a\right) + x \cdot y}{t_1}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5 \cdot \left(\frac{x}{z} - \frac{t_6}{z \cdot z}\right) + \left(t_4 + \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\right)\\ \end{array} \]

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 (/ (- (* x y) (* z (- a t))) t_1))
        (t_3 (/ x (- 1.0 z)))
        (t_4 (/ (- t a) (- b y)))
        (t_5 (/ y (- b y)))
        (t_6 (* t_5 (+ x (/ (- a t) (- b y))))))
   (if (<= t_2 (- INFINITY))
     (+
      t_3
      (* (/ z y) (- (/ (- t a) (- 1.0 z)) (/ (* x b) (pow (- 1.0 z) 2.0)))))
     (if (<= t_2 -2e-302)
       t_2
       (if (<= t_2 0.0)
         (+ t_4 (/ t_6 z))
         (if (<= t_2 1e+268)
           (/ (+ (- (* z t) (* z a)) (* x y)) t_1)
           (if (<= t_2 INFINITY)
             t_3
             (+
              (* t_5 (- (/ x z) (/ t_6 (* z z))))
              (+ t_4 (* (/ y (pow (- b y) 2.0)) (/ (- a t) 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 = ((x * y) - (z * (a - t))) / t_1;
	double t_3 = x / (1.0 - z);
	double t_4 = (t - a) / (b - y);
	double t_5 = y / (b - y);
	double t_6 = t_5 * (x + ((a - t) / (b - y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3 + ((z / y) * (((t - a) / (1.0 - z)) - ((x * b) / pow((1.0 - z), 2.0))));
	} else if (t_2 <= -2e-302) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_4 + (t_6 / z);
	} else if (t_2 <= 1e+268) {
		tmp = (((z * t) - (z * a)) + (x * y)) / t_1;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (t_5 * ((x / z) - (t_6 / (z * z)))) + (t_4 + ((y / pow((b - y), 2.0)) * ((a - t) / 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 = ((x * y) - (z * (a - t))) / t_1;
	double t_3 = x / (1.0 - z);
	double t_4 = (t - a) / (b - y);
	double t_5 = y / (b - y);
	double t_6 = t_5 * (x + ((a - t) / (b - y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3 + ((z / y) * (((t - a) / (1.0 - z)) - ((x * b) / Math.pow((1.0 - z), 2.0))));
	} else if (t_2 <= -2e-302) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_4 + (t_6 / z);
	} else if (t_2 <= 1e+268) {
		tmp = (((z * t) - (z * a)) + (x * y)) / t_1;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (t_5 * ((x / z) - (t_6 / (z * z)))) + (t_4 + ((y / Math.pow((b - y), 2.0)) * ((a - t) / 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 = ((x * y) - (z * (a - t))) / t_1
	t_3 = x / (1.0 - z)
	t_4 = (t - a) / (b - y)
	t_5 = y / (b - y)
	t_6 = t_5 * (x + ((a - t) / (b - y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3 + ((z / y) * (((t - a) / (1.0 - z)) - ((x * b) / math.pow((1.0 - z), 2.0))))
	elif t_2 <= -2e-302:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_4 + (t_6 / z)
	elif t_2 <= 1e+268:
		tmp = (((z * t) - (z * a)) + (x * y)) / t_1
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = (t_5 * ((x / z) - (t_6 / (z * z)))) + (t_4 + ((y / math.pow((b - y), 2.0)) * ((a - t) / 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(Float64(x * y) - Float64(z * Float64(a - t))) / t_1)
	t_3 = Float64(x / Float64(1.0 - z))
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	t_5 = Float64(y / Float64(b - y))
	t_6 = Float64(t_5 * Float64(x + Float64(Float64(a - t) / Float64(b - y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_3 + Float64(Float64(z / y) * Float64(Float64(Float64(t - a) / Float64(1.0 - z)) - Float64(Float64(x * b) / (Float64(1.0 - z) ^ 2.0)))));
	elseif (t_2 <= -2e-302)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t_4 + Float64(t_6 / z));
	elseif (t_2 <= 1e+268)
		tmp = Float64(Float64(Float64(Float64(z * t) - Float64(z * a)) + Float64(x * y)) / t_1);
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(t_5 * Float64(Float64(x / z) - Float64(t_6 / Float64(z * z)))) + Float64(t_4 + Float64(Float64(y / (Float64(b - y) ^ 2.0)) * Float64(Float64(a - t) / 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 = ((x * y) - (z * (a - t))) / t_1;
	t_3 = x / (1.0 - z);
	t_4 = (t - a) / (b - y);
	t_5 = y / (b - y);
	t_6 = t_5 * (x + ((a - t) / (b - y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3 + ((z / y) * (((t - a) / (1.0 - z)) - ((x * b) / ((1.0 - z) ^ 2.0))));
	elseif (t_2 <= -2e-302)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_4 + (t_6 / z);
	elseif (t_2 <= 1e+268)
		tmp = (((z * t) - (z * a)) + (x * y)) / t_1;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = (t_5 * ((x / z) - (t_6 / (z * z)))) + (t_4 + ((y / ((b - y) ^ 2.0)) * ((a - t) / 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[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 * N[(x + N[(N[(a - t), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$3 + N[(N[(z / y), $MachinePrecision] * N[(N[(N[(t - a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / N[Power[N[(1.0 - z), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-302], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t$95$4 + N[(t$95$6 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+268], N[(N[(N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(t$95$5 * N[(N[(x / z), $MachinePrecision] - N[(t$95$6 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 + N[(N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Target

Original	23.5
Target	18.1
Herbie	5.4

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

Derivation

1. Split input into 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 y around inf 36.7

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

   3. Simplified 27.2

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.9999999999999999e-302

   1. Initial program 0.3

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

   if -1.9999999999999999e-302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 46.5

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

   2. Taylor expanded in z around inf 20.4

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

   3. Simplified 3.1

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.9999999999999997e267

   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 9.9999999999999997e267 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 55.8

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

   2. Taylor expanded in y around inf 32.0

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

   3. Simplified 32.0

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

   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 39.9

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

   3. Simplified 0.0

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \left(\frac{x}{z} - \frac{\frac{y}{b - y} \cdot \left(x - \frac{t - a}{b - y}\right)}{z \cdot z}\right) + \left(\frac{t - a}{b - y} - \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 5.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z}{y} \cdot \left(\frac{t - a}{1 - z} - \frac{x \cdot b}{{\left(1 - z\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-302}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+268}:\\ \;\;\;\;\frac{\left(z \cdot t - z \cdot a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{b - y} \cdot \left(\frac{x}{z} - \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z \cdot z}\right) + \left(\frac{t - a}{b - y} + \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	5.4
Cost	9220

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y - z \cdot \left(a - t\right)}{t_1}\\ t_3 := \frac{x}{1 - z}\\ t_4 := \frac{t - a}{b - y} + \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3 + \frac{z}{y} \cdot \left(\frac{t - a}{1 - z} - \frac{x \cdot b}{{\left(1 - z\right)}^{2}}\right)\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 10^{+268}:\\ \;\;\;\;\frac{\left(z \cdot t - z \cdot a\right) + x \cdot y}{t_1}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Error	5.5
Cost	7380

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} + \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z}\\ t_3 := \frac{x \cdot y - z \cdot \left(a - t\right)}{t_1}\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 10^{+268}:\\ \;\;\;\;\frac{\left(z \cdot t - z \cdot a\right) + x \cdot y}{t_1}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	7.6
Cost	6484

\[\begin{array}{l} t_1 := \frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := t_2 - \frac{x}{z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	7.6
Cost	6484

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y - z \cdot \left(a - t\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := t_3 - \frac{x}{z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{+268}:\\ \;\;\;\;\frac{\left(z \cdot t - z \cdot a\right) + x \cdot y}{t_1}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 5
Error	32.8
Cost	2024

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ t_3 := \frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{if}\;b \leq -3.654972589874852 \cdot 10^{+167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.4052489573751775 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.2890869621714186 \cdot 10^{+57}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;b \leq -4.559655352727158 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.2009235020724028 \cdot 10^{-90}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-297}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.4271474821727136 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 7.937048505341241 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	36.7
Cost	1768

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t}{b} - \frac{a}{b}\\ t_3 := \frac{t - a}{b}\\ \mathbf{if}\;b \leq -3.654972589874852 \cdot 10^{+167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.4052489573751775 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.2890869621714186 \cdot 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4.559655352727158 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.180942286449343 \cdot 10^{-61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-245}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;b \leq 2.9839297202058544 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.4271474821727136 \cdot 10^{-41}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;b \leq 7.937048505341241 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	25.0
Cost	1692

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -52575845168204186000:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.2379975047595025 \cdot 10^{-41}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq -8.691685425764886 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -2.6390614061319587 \cdot 10^{-132}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -6.719592165656619 \cdot 10^{-207}:\\ \;\;\;\;\frac{z}{\frac{y}{t - a}}\\ \mathbf{elif}\;z \leq 4.9413934927420964 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.250371942634462 \cdot 10^{-151}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.3420504197139172 \cdot 10^{-140}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	36.7
Cost	1640

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b}\\ \mathbf{if}\;b \leq -3.654972589874852 \cdot 10^{+167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.4052489573751775 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.2890869621714186 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.559655352727158 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.180942286449343 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-245}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;b \leq 2.9839297202058544 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.4271474821727136 \cdot 10^{-41}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;b \leq 7.937048505341241 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	17.2
Cost	1360

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot b\\ t_3 := \frac{x \cdot y - z \cdot a}{t_2}\\ \mathbf{if}\;z \leq -52575845168204186000:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.250371942634462 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.5161682976688696 \cdot 10^{-87}:\\ \;\;\;\;\frac{z \cdot t + x \cdot y}{t_2}\\ \mathbf{elif}\;z \leq 0.003719011125572515:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	24.3
Cost	1240

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -52575845168204186000:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.2379975047595025 \cdot 10^{-41}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq -8.691685425764886 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -2.6390614061319587 \cdot 10^{-132}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -6.719592165656619 \cdot 10^{-207}:\\ \;\;\;\;\frac{z}{\frac{y}{t - a}}\\ \mathbf{elif}\;z \leq 1.3420504197139172 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	17.7
Cost	1228

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -52575845168204186000:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5368363919914827 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 260.27317661279193:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	17.7
Cost	1228

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -4.532130861020604 \cdot 10^{+33}:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5368363919914827 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{t_2}\\ \mathbf{elif}\;z \leq 260.27317661279193:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	24.7
Cost	1100

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.906993193599403 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -52575845168204186000:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -2.2379975047595025 \cdot 10^{-41}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 1.3420504197139172 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	17.3
Cost	1096

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -52575845168204186000:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.003719011125572515:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	24.5
Cost	976

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.906993193599403 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.532130861020604 \cdot 10^{+33}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -9.836472812199658 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3420504197139172 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	41.5
Cost	784

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -4.906993193599403 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -52575845168204186000:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -2.2379975047595025 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.188049304493856 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	39.0
Cost	784

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -4.906993193599403 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -52575845168204186000:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -2.2379975047595025 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.188049304493856 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	34.3
Cost	716

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -5.471131070110481 \cdot 10^{+182}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -2.2379975047595025 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.188049304493856 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	42.3
Cost	652

\[\begin{array}{l} \mathbf{if}\;y \leq -6.698186629273234 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.451493712755089 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.7234136143962801 \cdot 10^{-50}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	30.4
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -6.698186629273234 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2160711171421739 \cdot 10^{+26}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	41.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -5.387341739395733 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.188049304493856 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 22
Error	47.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022216 
(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)))))