Development.Shake.Progress:decay from shake-0.15.5

Average Error: 22.8 → 8.4

Time: 23.4s

Precision: binary64

Cost: 12108

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-243}:\\ \;\;\;\;\left(-\frac{-1 \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;t_2 \leq 10^{+303}:\\ \;\;\;\;\frac{t_1}{\left(y + z \cdot b\right) - y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

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 (+ (* x y) (* z (- t a)))) (t_2 (/ t_1 (+ y (* z (- b y))))))
   (if (<= t_2 (- INFINITY))
     (/ x (- 1.0 z))
     (if (<= t_2 -4e-293)
       t_2
       (if (<= t_2 2e-243)
         (+
          (-
           (/
            (*
             -1.0
             (- (/ (* y x) (- b y)) (/ (* (- t a) y) (pow (- b y) 2.0))))
            z))
          (- (/ t (- b y)) (/ a (- b y))))
         (if (<= t_2 1e+303)
           (/ t_1 (- (+ y (* z b)) (* y z)))
           (/ (- t a) (- b y))))))))

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 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x / (1.0 - z);
	} else if (t_2 <= -4e-293) {
		tmp = t_2;
	} else if (t_2 <= 2e-243) {
		tmp = -((-1.0 * (((y * x) / (b - y)) - (((t - a) * y) / pow((b - y), 2.0)))) / z) + ((t / (b - y)) - (a / (b - y)));
	} else if (t_2 <= 1e+303) {
		tmp = t_1 / ((y + (z * b)) - (y * z));
	} else {
		tmp = (t - a) / (b - y);
	}
	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 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = x / (1.0 - z);
	} else if (t_2 <= -4e-293) {
		tmp = t_2;
	} else if (t_2 <= 2e-243) {
		tmp = -((-1.0 * (((y * x) / (b - y)) - (((t - a) * y) / Math.pow((b - y), 2.0)))) / z) + ((t / (b - y)) - (a / (b - y)));
	} else if (t_2 <= 1e+303) {
		tmp = t_1 / ((y + (z * b)) - (y * z));
	} else {
		tmp = (t - a) / (b - y);
	}
	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 = (x * y) + (z * (t - a))
	t_2 = t_1 / (y + (z * (b - y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = x / (1.0 - z)
	elif t_2 <= -4e-293:
		tmp = t_2
	elif t_2 <= 2e-243:
		tmp = -((-1.0 * (((y * x) / (b - y)) - (((t - a) * y) / math.pow((b - y), 2.0)))) / z) + ((t / (b - y)) - (a / (b - y)))
	elif t_2 <= 1e+303:
		tmp = t_1 / ((y + (z * b)) - (y * z))
	else:
		tmp = (t - a) / (b - y)
	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(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x / Float64(1.0 - z));
	elseif (t_2 <= -4e-293)
		tmp = t_2;
	elseif (t_2 <= 2e-243)
		tmp = Float64(Float64(-Float64(Float64(-1.0 * Float64(Float64(Float64(y * x) / Float64(b - y)) - Float64(Float64(Float64(t - a) * y) / (Float64(b - y) ^ 2.0)))) / z)) + Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y))));
	elseif (t_2 <= 1e+303)
		tmp = Float64(t_1 / Float64(Float64(y + Float64(z * b)) - Float64(y * z)));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	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 = (x * y) + (z * (t - a));
	t_2 = t_1 / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = x / (1.0 - z);
	elseif (t_2 <= -4e-293)
		tmp = t_2;
	elseif (t_2 <= 2e-243)
		tmp = -((-1.0 * (((y * x) / (b - y)) - (((t - a) * y) / ((b - y) ^ 2.0)))) / z) + ((t / (b - y)) - (a / (b - y)));
	elseif (t_2 <= 1e+303)
		tmp = t_1 / ((y + (z * b)) - (y * z));
	else
		tmp = (t - a) / (b - y);
	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[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-293], t$95$2, If[LessEqual[t$95$2, 2e-243], N[((-N[(N[(-1.0 * N[(N[(N[(y * x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t - a), $MachinePrecision] * y), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+303], N[(t$95$1 / N[(N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	22.8
Target	17.8
Herbie	8.4

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

Derivation

1. Split input into 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 31.0

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

   3. Simplified 31.0

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

      [Start] 31.0	\[ \frac{x}{-1 \cdot z + 1} \]
      rational_best_oopsla_all_46_json_45_simplify-11 [=>] 31.0	\[ \frac{x}{\color{blue}{-1 \cdot z - -1}} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 31.0	\[ \frac{x}{\color{blue}{z \cdot -1} - -1} \]
      rational_best_oopsla_all_46_json_45_simplify-94 [<=] 31.0	\[ \frac{x}{\color{blue}{\left(-z\right)} - -1} \]
      rational_best_oopsla_all_46_json_45_simplify-97 [=>] 31.0	\[ \frac{x}{\color{blue}{\left(0 - z\right)} - -1} \]
      rational_best_oopsla_all_46_json_45_simplify-105 [=>] 31.0	\[ \frac{x}{\color{blue}{\left(0 - -1\right) - z}} \]
      metadata-eval [=>] 31.0	\[ \frac{x}{\color{blue}{1} - z} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.0000000000000002e-293

   1. Initial program 0.3

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

   if -4.0000000000000002e-293 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.99999999999999999e-243

   1. Initial program 40.6

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

   2. Taylor expanded in z around -inf 12.2

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

   3. Simplified 12.2

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

      [Start] 12.2	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      rational_best_oopsla_all_46_json_45_simplify-107 [=>] 12.2	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 12.2	\[ \color{blue}{\frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} \cdot -1} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-92 [=>] 12.2	\[ \color{blue}{\left(-\frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 12.2	\[ \left(-\frac{\color{blue}{\frac{y \cdot x}{b - y} \cdot -1} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-102 [=>] 12.2	\[ \left(-\frac{\color{blue}{-1 \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

   if 1.99999999999999999e-243 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e303

   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

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

   if 1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 63.6

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

   2. Taylor expanded in z around inf 21.6

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 8.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-293}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{-243}:\\ \;\;\;\;\left(-\frac{-1 \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{\left(y + z \cdot b\right) - y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	8.5
Cost	5840

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-304}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 10^{+303}:\\ \;\;\;\;\frac{t_2}{\left(y + z \cdot b\right) - y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	8.5
Cost	5712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+303}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	22.6
Cost	1492

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{y \cdot x + \left(t - a\right) \cdot z}{z \cdot b}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+23}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-202}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;z \cdot \frac{t}{y} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	22.6
Cost	1492

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{y \cdot x + \left(t - a\right) \cdot z}{z \cdot b}\\ \mathbf{if}\;z \leq -9.4 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+22}:\\ \;\;\;\;-1 \cdot \left(\frac{t}{y} + \frac{x - \left(-\frac{t}{y}\right)}{z}\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-202}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;z \cdot \frac{t}{y} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	44.4
Cost	1312

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-238}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+220}:\\ \;\;\;\;-\frac{t}{y}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+220}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+298}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z}\\ \end{array} \]

Alternative 6
Error	44.2
Cost	1116

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+78}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+219}:\\ \;\;\;\;-\frac{t}{y}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+220}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	38.7
Cost	1112

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := -\frac{a}{b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -80000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+220}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	21.7
Cost	976

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+23}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-99}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	44.8
Cost	852

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-237}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+220}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	36.4
Cost	848

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-74}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;z \cdot x + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	29.8
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+79}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	41.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-74}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 13
Error	46.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(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)))))