Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.3 → 8.9

Time: 52.2s

Precision: binary64

Cost: 12044

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x}{\left(-z\right) + 1}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(\frac{t}{b - y} + \left(-\frac{-\left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{z}\right)\right) - \frac{a}{b - y}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

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))) (+ y (* z (- b y))))))
   (if (<= t_1 (- INFINITY))
     (/ x (+ (- z) 1.0))
     (if (<= t_1 -2e-217)
       t_1
       (if (<= t_1 0.0)
         (-
          (+
           (/ t (- b y))
           (-
            (/
             (- (- (/ (* y x) (- b y)) (/ (* (- t a) y) (pow (- b y) 2.0))))
             z)))
          (/ a (- b y)))
         (if (<= t_1 5e+302) t_1 (/ (- 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))) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x / (-z + 1.0);
	} else if (t_1 <= -2e-217) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((t / (b - y)) + -(-(((y * x) / (b - y)) - (((t - a) * y) / pow((b - y), 2.0))) / z)) - (a / (b - y));
	} else if (t_1 <= 5e+302) {
		tmp = t_1;
	} 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))) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x / (-z + 1.0);
	} else if (t_1 <= -2e-217) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((t / (b - y)) + -(-(((y * x) / (b - y)) - (((t - a) * y) / Math.pow((b - y), 2.0))) / z)) - (a / (b - y));
	} else if (t_1 <= 5e+302) {
		tmp = t_1;
	} 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))) / (y + (z * (b - y)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x / (-z + 1.0)
	elif t_1 <= -2e-217:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((t / (b - y)) + -(-(((y * x) / (b - y)) - (((t - a) * y) / math.pow((b - y), 2.0))) / z)) - (a / (b - y))
	elif t_1 <= 5e+302:
		tmp = t_1
	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(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x / Float64(Float64(-z) + 1.0));
	elseif (t_1 <= -2e-217)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(t / Float64(b - y)) + Float64(-Float64(Float64(-Float64(Float64(Float64(y * x) / Float64(b - y)) - Float64(Float64(Float64(t - a) * y) / (Float64(b - y) ^ 2.0)))) / z))) - Float64(a / Float64(b - y)));
	elseif (t_1 <= 5e+302)
		tmp = t_1;
	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))) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x / (-z + 1.0);
	elseif (t_1 <= -2e-217)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((t / (b - y)) + -(-(((y * x) / (b - y)) - (((t - a) * y) / ((b - y) ^ 2.0))) / z)) - (a / (b - y));
	elseif (t_1 <= 5e+302)
		tmp = t_1;
	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[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x / N[((-z) + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-217], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + (-N[((-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]) / z), $MachinePrecision])), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+302], t$95$1, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	23.3
Target	18.0
Herbie	8.9

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

Derivation

1. Split input into 4 regimes

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

   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 34.1

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

   3. Simplified 34.1

      \[\leadsto \color{blue}{\frac{x}{\left(-z\right) + 1}} \]
      Proof

      [Start] 34.1	\[ \frac{x}{-1 \cdot z + 1} \]
      rational.json-simplify-2 [=>] 34.1	\[ \frac{x}{\color{blue}{z \cdot -1} + 1} \]
      rational.json-simplify-9 [=>] 34.1	\[ \frac{x}{\color{blue}{\left(-z\right)} + 1} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000016e-217 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5e302

   1. Initial program 0.3

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

   if -2.00000000000000016e-217 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 39.2

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

   2. Taylor expanded in z around -inf 13.6

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

   3. Simplified 13.6

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

      [Start] 13.6	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      rational.json-simplify-2 [=>] 13.6	\[ \left(\frac{t}{b - y} + \color{blue}{\frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} \cdot -1}\right) - \frac{a}{b - y} \]
      rational.json-simplify-9 [=>] 13.6	\[ \left(\frac{t}{b - y} + \color{blue}{\left(-\frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right)}\right) - \frac{a}{b - y} \]
      rational.json-simplify-2 [=>] 13.6	\[ \left(\frac{t}{b - y} + \left(-\frac{-1 \cdot \frac{y \cdot x}{b - y} - \color{blue}{\frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}} \cdot -1}}{z}\right)\right) - \frac{a}{b - y} \]
      rational.json-simplify-48 [=>] 13.6	\[ \left(\frac{t}{b - y} + \left(-\frac{\color{blue}{-1 \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}}{z}\right)\right) - \frac{a}{b - y} \]
      rational.json-simplify-2 [=>] 13.6	\[ \left(\frac{t}{b - y} + \left(-\frac{\color{blue}{\left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right) \cdot -1}}{z}\right)\right) - \frac{a}{b - y} \]
      rational.json-simplify-9 [=>] 13.6	\[ \left(\frac{t}{b - y} + \left(-\frac{\color{blue}{-\left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}}{z}\right)\right) - \frac{a}{b - y} \]

   if 5e302 < (/.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. Taylor expanded in z around inf 21.3

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 8.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{\left(-z\right) + 1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-217}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t}{b - y} + \left(-\frac{-\left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{z}\right)\right) - \frac{a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	9.5
Cost	5712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x}{\left(-z\right) + 1}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	36.0
Cost	1640

\[\begin{array}{l} t_1 := \frac{x}{\left(-z\right) + 1}\\ t_2 := \frac{t - a}{b}\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.48 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-285}:\\ \;\;\;\;-\frac{t - a}{y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \frac{t}{y} + x\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-26}:\\ \;\;\;\;-\frac{a}{b - y}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+208}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	19.3
Cost	1624

\[\begin{array}{l} t_1 := \frac{y \cdot x + t \cdot z}{y + z \cdot b}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-47}:\\ \;\;\;\;\left(-\frac{z \cdot a}{y}\right) + x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{\left(\frac{y \cdot x}{z} + t\right) - a}{b}\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-252}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	33.4
Cost	1572

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{\left(-z\right) + 1}\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+18}:\\ \;\;\;\;-\frac{t - a}{y}\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \frac{t}{y} + x\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-137}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+152}:\\ \;\;\;\;-\frac{a}{b - y}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+152}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	21.3
Cost	1496

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-51}:\\ \;\;\;\;\left(-\frac{z \cdot a}{y}\right) + x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-104}:\\ \;\;\;\;\frac{y \cdot x}{y + \left(b - y\right) \cdot z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-206}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	18.8
Cost	1492

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot b\\ t_3 := \frac{y \cdot x + a \cdot \left(-z\right)}{t_2}\\ \mathbf{if}\;z \leq -880000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-245}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-29}:\\ \;\;\;\;\frac{y \cdot x + t \cdot z}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	21.3
Cost	1364

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-45}:\\ \;\;\;\;\left(-\frac{z \cdot a}{y}\right) + x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-135}:\\ \;\;\;\;\frac{\left(\frac{y \cdot x}{z} + t\right) - a}{b}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-250}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{\left(-z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	34.5
Cost	1308

\[\begin{array}{l} t_1 := -\frac{x}{z}\\ t_2 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 800000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+130}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{+274}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b - y}\\ \end{array} \]

Alternative 9
Error	32.7
Cost	1308

\[\begin{array}{l} t_1 := \frac{x}{\left(-z\right) + 1}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+18}:\\ \;\;\;\;-\frac{t - a}{y}\\ \mathbf{elif}\;y \leq -7600:\\ \;\;\;\;z \cdot x + x\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-48}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+152}:\\ \;\;\;\;-\frac{a}{b - y}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+152}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	34.6
Cost	1244

\[\begin{array}{l} t_1 := -\frac{x}{z}\\ t_2 := \frac{t - a}{b}\\ t_3 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 900000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+130}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+271}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	11.6
Cost	1224

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4100000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	21.1
Cost	1100

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-47}:\\ \;\;\;\;\left(-\frac{z \cdot a}{y}\right) + x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-117}:\\ \;\;\;\;\frac{y \cdot x}{y + \left(b - y\right) \cdot z}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-74}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	21.1
Cost	976

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-50}:\\ \;\;\;\;\left(-\frac{z \cdot a}{y}\right) + x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-76}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	40.5
Cost	784

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+83}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 14200:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+143}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 15
Error	40.5
Cost	784

\[\begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-18}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 14200:\\ \;\;\;\;z \cdot x + x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+144}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16
Error	35.9
Cost	716

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-18}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	20.8
Cost	712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-74}:\\ \;\;\;\;\frac{z \cdot t}{y} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	41.0
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+87}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-19}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 19
Error	40.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 20
Error	47.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023077 
(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)))))