Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.2 → 1.4

Time: 2.1min

Precision: binary64

Cost: 14292

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := y + \left(b - y\right) \cdot z\\ t_3 := \frac{\left(t - a\right) \cdot z}{t_2} + \frac{y \cdot x}{t_2}\\ t_4 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_5 := \frac{t}{b - y} - \frac{a}{b - y}\\ t_6 := y \cdot \frac{x}{t_1} + t_5\\ t_7 := \left(-\frac{-1 \cdot \left(y \cdot \left(\frac{x}{b - y} - \frac{t - a}{{\left(b - y\right)}^{2}}\right)\right)}{z}\right) + t_5\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \]

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 (+ y (* (- b y) z)))
        (t_3 (+ (/ (* (- t a) z) t_2) (/ (* y x) t_2)))
        (t_4 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_5 (- (/ t (- b y)) (/ a (- b y))))
        (t_6 (+ (* y (/ x t_1)) t_5))
        (t_7
         (+
          (-
           (/
            (* -1.0 (* y (- (/ x (- b y)) (/ (- t a) (pow (- b y) 2.0)))))
            z))
          t_5)))
   (if (<= t_4 (- INFINITY))
     t_6
     (if (<= t_4 -1e-307)
       t_3
       (if (<= t_4 0.0)
         t_7
         (if (<= t_4 5e+238) t_3 (if (<= t_4 INFINITY) t_6 t_7)))))))

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 = y + ((b - y) * z);
	double t_3 = (((t - a) * z) / t_2) + ((y * x) / t_2);
	double t_4 = ((x * y) + (z * (t - a))) / t_1;
	double t_5 = (t / (b - y)) - (a / (b - y));
	double t_6 = (y * (x / t_1)) + t_5;
	double t_7 = -((-1.0 * (y * ((x / (b - y)) - ((t - a) / pow((b - y), 2.0))))) / z) + t_5;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_4 <= -1e-307) {
		tmp = t_3;
	} else if (t_4 <= 0.0) {
		tmp = t_7;
	} else if (t_4 <= 5e+238) {
		tmp = t_3;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_6;
	} else {
		tmp = t_7;
	}
	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 = y + ((b - y) * z);
	double t_3 = (((t - a) * z) / t_2) + ((y * x) / t_2);
	double t_4 = ((x * y) + (z * (t - a))) / t_1;
	double t_5 = (t / (b - y)) - (a / (b - y));
	double t_6 = (y * (x / t_1)) + t_5;
	double t_7 = -((-1.0 * (y * ((x / (b - y)) - ((t - a) / Math.pow((b - y), 2.0))))) / z) + t_5;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else if (t_4 <= -1e-307) {
		tmp = t_3;
	} else if (t_4 <= 0.0) {
		tmp = t_7;
	} else if (t_4 <= 5e+238) {
		tmp = t_3;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else {
		tmp = t_7;
	}
	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 = y + ((b - y) * z)
	t_3 = (((t - a) * z) / t_2) + ((y * x) / t_2)
	t_4 = ((x * y) + (z * (t - a))) / t_1
	t_5 = (t / (b - y)) - (a / (b - y))
	t_6 = (y * (x / t_1)) + t_5
	t_7 = -((-1.0 * (y * ((x / (b - y)) - ((t - a) / math.pow((b - y), 2.0))))) / z) + t_5
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_6
	elif t_4 <= -1e-307:
		tmp = t_3
	elif t_4 <= 0.0:
		tmp = t_7
	elif t_4 <= 5e+238:
		tmp = t_3
	elif t_4 <= math.inf:
		tmp = t_6
	else:
		tmp = t_7
	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(y + Float64(Float64(b - y) * z))
	t_3 = Float64(Float64(Float64(Float64(t - a) * z) / t_2) + Float64(Float64(y * x) / t_2))
	t_4 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_5 = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)))
	t_6 = Float64(Float64(y * Float64(x / t_1)) + t_5)
	t_7 = Float64(Float64(-Float64(Float64(-1.0 * Float64(y * Float64(Float64(x / Float64(b - y)) - Float64(Float64(t - a) / (Float64(b - y) ^ 2.0))))) / z)) + t_5)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_4 <= -1e-307)
		tmp = t_3;
	elseif (t_4 <= 0.0)
		tmp = t_7;
	elseif (t_4 <= 5e+238)
		tmp = t_3;
	elseif (t_4 <= Inf)
		tmp = t_6;
	else
		tmp = t_7;
	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 = y + ((b - y) * z);
	t_3 = (((t - a) * z) / t_2) + ((y * x) / t_2);
	t_4 = ((x * y) + (z * (t - a))) / t_1;
	t_5 = (t / (b - y)) - (a / (b - y));
	t_6 = (y * (x / t_1)) + t_5;
	t_7 = -((-1.0 * (y * ((x / (b - y)) - ((t - a) / ((b - y) ^ 2.0))))) / z) + t_5;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_6;
	elseif (t_4 <= -1e-307)
		tmp = t_3;
	elseif (t_4 <= 0.0)
		tmp = t_7;
	elseif (t_4 <= 5e+238)
		tmp = t_3;
	elseif (t_4 <= Inf)
		tmp = t_6;
	else
		tmp = t_7;
	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[(y + N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(t - a), $MachinePrecision] * z), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y * N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[((-N[(N[(-1.0 * N[(y * N[(N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t$95$5), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$6, If[LessEqual[t$95$4, -1e-307], t$95$3, If[LessEqual[t$95$4, 0.0], t$95$7, If[LessEqual[t$95$4, 5e+238], t$95$3, If[LessEqual[t$95$4, Infinity], t$95$6, t$95$7]]]]]]]]]]]]

Target

Original	23.2
Target	18.2
Herbie	1.4

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 4.99999999999999995e238 < (/.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 t around 0 55.8

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

   3. Simplified 5.4

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

      [Start] 55.8	\[ -1 \cdot \frac{a \cdot z}{y + \left(b - y\right) \cdot z} + \left(\frac{y \cdot x}{y + \left(b - y\right) \cdot z} + \frac{t \cdot z}{y + \left(b - y\right) \cdot z}\right) \]
      rational.json-simplify-1 [=>] 55.8	\[ -1 \cdot \frac{a \cdot z}{y + \left(b - y\right) \cdot z} + \color{blue}{\left(\frac{t \cdot z}{y + \left(b - y\right) \cdot z} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z}\right)} \]
      rational.json-simplify-41 [<=] 55.8	\[ \color{blue}{\frac{y \cdot x}{y + \left(b - y\right) \cdot z} + \left(-1 \cdot \frac{a \cdot z}{y + \left(b - y\right) \cdot z} + \frac{t \cdot z}{y + \left(b - y\right) \cdot z}\right)} \]
      rational.json-simplify-2 [=>] 55.8	\[ \frac{\color{blue}{x \cdot y}}{y + \left(b - y\right) \cdot z} + \left(-1 \cdot \frac{a \cdot z}{y + \left(b - y\right) \cdot z} + \frac{t \cdot z}{y + \left(b - y\right) \cdot z}\right) \]
      rational.json-simplify-2 [=>] 55.8	\[ \frac{x \cdot y}{y + \color{blue}{z \cdot \left(b - y\right)}} + \left(-1 \cdot \frac{a \cdot z}{y + \left(b - y\right) \cdot z} + \frac{t \cdot z}{y + \left(b - y\right) \cdot z}\right) \]
      rational.json-simplify-49 [=>] 29.3	\[ \color{blue}{y \cdot \frac{x}{y + z \cdot \left(b - y\right)}} + \left(-1 \cdot \frac{a \cdot z}{y + \left(b - y\right) \cdot z} + \frac{t \cdot z}{y + \left(b - y\right) \cdot z}\right) \]
      rational.json-simplify-49 [=>] 20.4	\[ y \cdot \frac{x}{y + z \cdot \left(b - y\right)} + \left(-1 \cdot \color{blue}{\left(z \cdot \frac{a}{y + \left(b - y\right) \cdot z}\right)} + \frac{t \cdot z}{y + \left(b - y\right) \cdot z}\right) \]
      rational.json-simplify-43 [=>] 20.4	\[ y \cdot \frac{x}{y + z \cdot \left(b - y\right)} + \left(\color{blue}{z \cdot \left(\frac{a}{y + \left(b - y\right) \cdot z} \cdot -1\right)} + \frac{t \cdot z}{y + \left(b - y\right) \cdot z}\right) \]
      rational.json-simplify-49 [=>] 5.4	\[ y \cdot \frac{x}{y + z \cdot \left(b - y\right)} + \left(z \cdot \left(\frac{a}{y + \left(b - y\right) \cdot z} \cdot -1\right) + \color{blue}{z \cdot \frac{t}{y + \left(b - y\right) \cdot z}}\right) \]
      rational.json-simplify-2 [=>] 5.4	\[ y \cdot \frac{x}{y + z \cdot \left(b - y\right)} + \left(z \cdot \left(\frac{a}{y + \left(b - y\right) \cdot z} \cdot -1\right) + \color{blue}{\frac{t}{y + \left(b - y\right) \cdot z} \cdot z}\right) \]
      rational.json-simplify-51 [=>] 5.4	\[ y \cdot \frac{x}{y + z \cdot \left(b - y\right)} + \color{blue}{z \cdot \left(\frac{t}{y + \left(b - y\right) \cdot z} + \frac{a}{y + \left(b - y\right) \cdot z} \cdot -1\right)} \]

   4. Taylor expanded in z around inf 5.0

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.99999999999999909e-308 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.99999999999999995e238

   1. Initial program 0.3

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

   2. Taylor expanded in x around inf 0.3

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

   if -9.99999999999999909e-308 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 57.9

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

   2. Taylor expanded in z around -inf 28.5

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

   3. Simplified 1.7

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

      [Start] 28.5	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      rational.json-simplify-48 [=>] 28.5	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{y + z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-307}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(-\frac{-1 \cdot \left(y \cdot \left(\frac{x}{b - y} - \frac{t - a}{{\left(b - y\right)}^{2}}\right)\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+238}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;y \cdot \frac{x}{y + z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{-1 \cdot \left(y \cdot \left(\frac{x}{b - y} - \frac{t - a}{{\left(b - y\right)}^{2}}\right)\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	4.6
Cost	6224

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := y + \left(b - y\right) \cdot z\\ t_3 := \frac{\left(t - a\right) \cdot z}{t_2} + \frac{y \cdot x}{t_2}\\ t_4 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_5 := y \cdot \frac{x}{t_1} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+238}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 2
Error	4.6
Cost	6096

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := y \cdot \frac{x}{t_1} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+238}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	20.7
Cost	2012

\[\begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{\frac{1}{b - y}}{z} \cdot t_1\\ \mathbf{if}\;z \leq -8 \cdot 10^{+155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-114}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-207}:\\ \;\;\;\;\frac{t_1}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+87}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	20.5
Cost	1880

\[\begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{\frac{1}{b - y}}{z} \cdot t_1\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-207}:\\ \;\;\;\;\frac{t_1}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \left(\left(-x\right) + \frac{a}{y}\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	14.2
Cost	1880

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	14.2
Cost	1880

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ t_4 := x \cdot y + z \cdot \left(t - a\right)\\ t_5 := \frac{t_4}{t_2}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-153}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-260}:\\ \;\;\;\;\frac{1}{t_2} \cdot t_4\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	34.4
Cost	1772

\[\begin{array}{l} t_1 := -\frac{t - a}{y}\\ t_2 := \frac{a}{y - b}\\ t_3 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+261}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+32}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-115}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{t \cdot z}{y}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+235}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 8
Error	19.1
Cost	1748

\[\begin{array}{l} t_1 := \frac{\frac{1}{b - y}}{z} \cdot \left(x \cdot y + z \cdot \left(t - a\right)\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+33}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{t - a}{1 - z} + t_3\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z}{y \cdot \left(1 - z\right)} + t_3\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	20.8
Cost	1688

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{\frac{y + z \cdot \left(b - y\right)}{y}}\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-114}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z + y \cdot x}{z \cdot b}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-207}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-71}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \left(\left(-x\right) + \frac{a}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	20.8
Cost	1688

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{\frac{y + z \cdot \left(b - y\right)}{y}}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-114}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z + y \cdot x}{z \cdot b}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-207}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-71}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \left(\left(-x\right) + \frac{a}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	38.0
Cost	1640

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t}{b - y}\\ t_3 := \frac{a}{y - b}\\ \mathbf{if}\;a \leq -1.58 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	13.9
Cost	1616

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-52}:\\ \;\;\;\;\frac{y \cdot x}{z \cdot b} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	13.9
Cost	1616

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{z}{y} \cdot \frac{t - a}{1 - z} + \frac{x}{1 - z}\\ t_3 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-126}:\\ \;\;\;\;\frac{1}{\frac{t_3}{y \cdot x + t_1}}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{y \cdot x}{z \cdot b} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot y + t_1}{t_3}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	20.9
Cost	1500

\[\begin{array}{l} t_1 := x + \frac{t \cdot z}{y}\\ t_2 := x \cdot \frac{y}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-115}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	20.9
Cost	1500

\[\begin{array}{l} t_1 := x + \frac{t \cdot z}{y}\\ t_2 := x \cdot \frac{y}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-115}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 16
Error	20.9
Cost	1500

\[\begin{array}{l} t_1 := x + \frac{t \cdot z}{y}\\ t_2 := x \cdot \frac{y}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{-9}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{\frac{y + z \cdot \left(b - y\right)}{y}}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-116}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	36.7
Cost	1244

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := -\frac{x}{z}\\ t_3 := \frac{a}{y - b}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-71}:\\ \;\;\;\;z \cdot x + x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+234}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Error	21.0
Cost	1240

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{\frac{y + z \cdot \left(b - y\right)}{y}}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-207}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{t \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	20.8
Cost	1240

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{\frac{y + z \cdot \left(b - y\right)}{y}}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z + y \cdot x}{z \cdot b}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-207}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{t \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	44.4
Cost	980

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+129}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-218}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x + x\\ \end{array} \]

Alternative 21
Error	44.4
Cost	916

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+129}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-221}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	36.0
Cost	848

\[\begin{array}{l} t_1 := \frac{a}{y - b}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{+93}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-28}:\\ \;\;\;\;z \cdot x + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	21.8
Cost	712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{t \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 24
Error	31.3
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 25
Error	42.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-115}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 26
Error	41.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 27
Error	47.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023064 
(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)))))