Development.Shake.Progress:decay from shake-0.15.5

Average Error: 22.7 → 9.4

Time: 30.5s

Precision: binary64

Cost: 12044

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{a}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\left(-\frac{x}{z}\right) - t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-270}:\\ \;\;\;\;\left(\frac{t}{b - y} + \left(-\frac{\frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}} + \left(-\frac{y \cdot x}{b - y}\right)}{z}\right)\right) - t_3\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{t_1}{z \cdot b + \left(z - 1\right) \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

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)))))
        (t_3 (/ a (- b y))))
   (if (<= t_2 (- INFINITY))
     (- (- (/ x z)) t_3)
     (if (<= t_2 -2e-307)
       t_2
       (if (<= t_2 5e-270)
         (-
          (+
           (/ t (- b y))
           (-
            (/
             (+ (/ (* (- t a) y) (pow (- b y) 2.0)) (- (/ (* y x) (- b y))))
             z)))
          t_3)
         (if (<= t_2 5e+288)
           (/ t_1 (+ (* z b) (* (- z 1.0) (- y))))
           (/ (- 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 t_3 = a / (b - y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = -(x / z) - t_3;
	} else if (t_2 <= -2e-307) {
		tmp = t_2;
	} else if (t_2 <= 5e-270) {
		tmp = ((t / (b - y)) + -(((((t - a) * y) / pow((b - y), 2.0)) + -((y * x) / (b - y))) / z)) - t_3;
	} else if (t_2 <= 5e+288) {
		tmp = t_1 / ((z * b) + ((z - 1.0) * -y));
	} 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 t_3 = a / (b - y);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = -(x / z) - t_3;
	} else if (t_2 <= -2e-307) {
		tmp = t_2;
	} else if (t_2 <= 5e-270) {
		tmp = ((t / (b - y)) + -(((((t - a) * y) / Math.pow((b - y), 2.0)) + -((y * x) / (b - y))) / z)) - t_3;
	} else if (t_2 <= 5e+288) {
		tmp = t_1 / ((z * b) + ((z - 1.0) * -y));
	} 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)))
	t_3 = a / (b - y)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = -(x / z) - t_3
	elif t_2 <= -2e-307:
		tmp = t_2
	elif t_2 <= 5e-270:
		tmp = ((t / (b - y)) + -(((((t - a) * y) / math.pow((b - y), 2.0)) + -((y * x) / (b - y))) / z)) - t_3
	elif t_2 <= 5e+288:
		tmp = t_1 / ((z * b) + ((z - 1.0) * -y))
	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))))
	t_3 = Float64(a / Float64(b - y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(-Float64(x / z)) - t_3);
	elseif (t_2 <= -2e-307)
		tmp = t_2;
	elseif (t_2 <= 5e-270)
		tmp = Float64(Float64(Float64(t / Float64(b - y)) + Float64(-Float64(Float64(Float64(Float64(Float64(t - a) * y) / (Float64(b - y) ^ 2.0)) + Float64(-Float64(Float64(y * x) / Float64(b - y)))) / z))) - t_3);
	elseif (t_2 <= 5e+288)
		tmp = Float64(t_1 / Float64(Float64(z * b) + Float64(Float64(z - 1.0) * Float64(-y))));
	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)));
	t_3 = a / (b - y);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = -(x / z) - t_3;
	elseif (t_2 <= -2e-307)
		tmp = t_2;
	elseif (t_2 <= 5e-270)
		tmp = ((t / (b - y)) + -(((((t - a) * y) / ((b - y) ^ 2.0)) + -((y * x) / (b - y))) / z)) - t_3;
	elseif (t_2 <= 5e+288)
		tmp = t_1 / ((z * b) + ((z - 1.0) * -y));
	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]}, Block[{t$95$3 = N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[((-N[(x / z), $MachinePrecision]) - t$95$3), $MachinePrecision], If[LessEqual[t$95$2, -2e-307], t$95$2, If[LessEqual[t$95$2, 5e-270], N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + (-N[(N[(N[(N[(N[(t - a), $MachinePrecision] * y), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + (-N[(N[(y * x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision])), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$2, 5e+288], N[(t$95$1 / N[(N[(z * b), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Target

Original	22.7
Target	17.7
Herbie	9.4

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

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 z around -inf 40.9

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

   3. Simplified 40.9

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

      [Start] 40.9	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]

   4. Taylor expanded in y around inf 41.7

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} - \frac{a}{b - y} \]

   5. Simplified 41.7

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

      [Start] 41.7	\[ -1 \cdot \frac{x}{z} - \frac{a}{b - y} \]
      rational_best.json-simplify-2 [=>] 41.7	\[ \color{blue}{\frac{x}{z} \cdot -1} - \frac{a}{b - y} \]
      rational_best.json-simplify-12 [=>] 41.7	\[ \color{blue}{\left(-\frac{x}{z}\right)} - \frac{a}{b - y} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999982e-307

   1. Initial program 0.3

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

   if -1.99999999999999982e-307 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.9999999999999998e-270

   1. Initial program 44.2

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

   2. Taylor expanded in z around -inf 9.5

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

   3. Simplified 9.5

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

      [Start] 9.5	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]

   if 4.9999999999999998e-270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000003e288

   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 y around -inf 0.3

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

   3. Simplified 0.3

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

      [Start] 0.3	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b + -1 \cdot \left(\left(z - 1\right) \cdot y\right)} \]
      rational_best.json-simplify-44 [=>] 0.3	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b + \color{blue}{\left(z - 1\right) \cdot \left(-1 \cdot y\right)}} \]
      rational_best.json-simplify-2 [=>] 0.3	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot -1\right)}} \]
      rational_best.json-simplify-12 [=>] 0.3	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b + \left(z - 1\right) \cdot \color{blue}{\left(-y\right)}} \]

   if 5.0000000000000003e288 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 62.2

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

   2. Taylor expanded in z around inf 23.5

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

4. Final simplification 9.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\left(-\frac{x}{z}\right) - \frac{a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{-270}:\\ \;\;\;\;\left(\frac{t}{b - y} + \left(-\frac{\frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}} + \left(-\frac{y \cdot x}{b - y}\right)}{z}\right)\right) - \frac{a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b + \left(z - 1\right) \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	10.0
Cost	5904

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(-\frac{x}{z}\right) - \frac{a}{b - y}\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{t_2}{z \cdot b + \left(z - 1\right) \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	10.0
Cost	5712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\left(-\frac{x}{z}\right) - \frac{a}{b - y}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	20.0
Cost	1232

\[\begin{array}{l} t_1 := x + z \cdot \left(x + \frac{t - a}{y}\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.023:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-228}:\\ \;\;\;\;\frac{\left(\frac{y \cdot x}{z} + t\right) - a}{b}\\ \mathbf{elif}\;z \leq 0.15:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	20.8
Cost	1232

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -900000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-260}:\\ \;\;\;\;\frac{y \cdot x + \left(t - a\right) \cdot z}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq 10^{-228}:\\ \;\;\;\;\frac{\left(\frac{y \cdot x}{z} + t\right) - a}{b}\\ \mathbf{elif}\;z \leq 0.15:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	27.1
Cost	976

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 62000:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	19.2
Cost	968

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.023:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.28:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	31.3
Cost	912

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y \cdot x}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+141}:\\ \;\;\;\;-\frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	38.5
Cost	848

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -160000:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -0.425:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.15:\\ \;\;\;\;z \cdot x + x\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]

Alternative 9
Error	24.2
Cost	712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1800000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.15:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	41.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 0.16:\\ \;\;\;\;z \cdot x + x\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]

Alternative 11
Error	38.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]

Alternative 12
Error	30.3
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-53}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	42.8
Cost	520

\[\begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-132}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	41.6
Cost	520

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 0.15:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]

Alternative 15
Error	40.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.175:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16
Error	46.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023088 
(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)))))