Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.5 → 9.1

Time: 2.1min

Precision: binary64

Cost: 17100

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-243}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + x \cdot \frac{y}{\mathsf{fma}\left(b - y, z, y\right)}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot x}{b - y} + \frac{y \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{t - a}{z - 1} \cdot \frac{z}{y}\right) + \frac{x}{\left(-z\right) + 1}\\ \end{array} \]

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 -5e-243)
     (+ (/ (* (- t a) z) (+ y (* (- b y) z))) (* x (/ y (fma (- b y) z y))))
     (if (<= t_1 0.0)
       (+
        (/ (+ (/ (* y x) (- b y)) (/ (* y (- a t)) (pow (- b y) 2.0))) z)
        (- (/ t (- b y)) (/ a (- b y))))
       (if (<= t_1 5e+280)
         (/ (fma z (- t a) (* x y)) (fma z (- b y) y))
         (+ (- (* (/ (- t a) (- z 1.0)) (/ z y))) (/ x (+ (- z) 1.0))))))))

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 <= -5e-243) {
		tmp = (((t - a) * z) / (y + ((b - y) * z))) + (x * (y / fma((b - y), z, y)));
	} else if (t_1 <= 0.0) {
		tmp = ((((y * x) / (b - y)) + ((y * (a - t)) / pow((b - y), 2.0))) / z) + ((t / (b - y)) - (a / (b - y)));
	} else if (t_1 <= 5e+280) {
		tmp = fma(z, (t - a), (x * y)) / fma(z, (b - y), y);
	} else {
		tmp = -(((t - a) / (z - 1.0)) * (z / y)) + (x / (-z + 1.0));
	}
	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 <= -5e-243)
		tmp = Float64(Float64(Float64(Float64(t - a) * z) / Float64(y + Float64(Float64(b - y) * z))) + Float64(x * Float64(y / fma(Float64(b - y), z, y))));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(y * x) / Float64(b - y)) + Float64(Float64(y * Float64(a - t)) / (Float64(b - y) ^ 2.0))) / z) + Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y))));
	elseif (t_1 <= 5e+280)
		tmp = Float64(fma(z, Float64(t - a), Float64(x * y)) / fma(z, Float64(b - y), y));
	else
		tmp = Float64(Float64(-Float64(Float64(Float64(t - a) / Float64(z - 1.0)) * Float64(z / y))) + Float64(x / Float64(Float64(-z) + 1.0)));
	end
	return 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, -5e-243], N[(N[(N[(N[(t - a), $MachinePrecision] * z), $MachinePrecision] / N[(y + N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(N[(y * x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $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$1, 5e+280], N[(N[(z * N[(t - a), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], N[((-N[(N[(N[(t - a), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]) + N[(x / N[((-z) + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	23.5
Target	18.4
Herbie	9.1

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

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)))) < -5e-243

   1. Initial program 14.0

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

   2. Taylor expanded in x around inf 14.0

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

   3. Applied egg-rr 6.8

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

   if -5e-243 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 41.5

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

   2. Simplified 41.5

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

   3. Taylor expanded in z around -inf 10.6

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

   4. Simplified 10.6

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000002e280

   1. Initial program 0.4

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

   2. Simplified 0.3

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

   if 5.0000000000000002e280 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 62.5

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

   2. Taylor expanded in x around inf 62.5

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

   3. Taylor expanded in y around -inf 62.7

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

   4. Simplified 46.9

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

   5. Taylor expanded in y around inf 24.0

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

   6. Simplified 24.0

      \[\leadsto \left(-\frac{t - a}{z - 1} \cdot \frac{z}{y}\right) + \color{blue}{\frac{x}{\left(-z\right) + 1}} \]
      Proof
3. Recombined 4 regimes into one program.

Alternatives

Alternative 1
Error	9.1
Cost	10760

\[\begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-243}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + x \cdot \frac{y}{\mathsf{fma}\left(b - y, z, y\right)}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot x}{b - y} + \frac{y \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{t_1}{y + \left(\left(-y\right) \cdot z + b \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{t - a}{z - 1} \cdot \frac{z}{y}\right) + \frac{x}{\left(-z\right) + 1}\\ \end{array} \]

Alternative 2
Error	10.6
Cost	9028

\[\begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-243}:\\ \;\;\;\;\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + x \cdot \frac{y}{\mathsf{fma}\left(b - y, z, y\right)}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{\left(y \cdot \frac{x}{z} + t\right) - a}{b}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{t_1}{y + \left(\left(-y\right) \cdot z + b \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{t - a}{z - 1} \cdot \frac{z}{y}\right) + \frac{x}{\left(-z\right) + 1}\\ \end{array} \]

Alternative 3
Error	9.9
Cost	8964

\[\begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + \left(\left(-y\right) \cdot z + b \cdot z\right)}\\ t_3 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ t_4 := -\frac{t - a}{z - 1} \cdot \frac{z}{y}\\ \mathbf{if}\;t_3 \leq -4 \cdot 10^{+226}:\\ \;\;\;\;t_4 + x \cdot \frac{y}{\mathsf{fma}\left(b - y, z, y\right)}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{\left(y \cdot \frac{x}{z} + t\right) - a}{b}\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4 + \frac{x}{\left(-z\right) + 1}\\ \end{array} \]

Alternative 4
Error	10.1
Cost	5904

\[\begin{array}{l} t_1 := \left(-\frac{t - a}{z - 1} \cdot \frac{z}{y}\right) + \frac{x}{\left(-z\right) + 1}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{y + \left(\left(-y\right) \cdot z + b \cdot z\right)}\\ t_4 := \frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_4 \leq -4 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-243}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\frac{\left(y \cdot \frac{x}{z} + t\right) - a}{b}\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	10.1
Cost	5840

\[\begin{array}{l} t_1 := \left(-\frac{t - a}{z - 1} \cdot \frac{z}{y}\right) + \frac{x}{\left(-z\right) + 1}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{\left(y \cdot \frac{x}{z} + t\right) - a}{b}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	14.5
Cost	5712

\[\begin{array}{l} t_1 := \frac{\left(y \cdot \frac{x}{z} + t\right) - a}{b}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	30.6
Cost	1496

\[\begin{array}{l} t_1 := \frac{\left(y \cdot \frac{x}{z} + t\right) - a}{b}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+156}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+75}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-32}:\\ \;\;\;\;\left(-\frac{a \cdot z}{y}\right) + x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	30.6
Cost	1496

\[\begin{array}{l} t_1 := \frac{\left(y \cdot \frac{x}{z} + t\right) - a}{b}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+157}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+78}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-97}:\\ \;\;\;\;\frac{a - t}{-b} - \frac{\frac{y \cdot x}{z}}{-b}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-32}:\\ \;\;\;\;\left(-\frac{a \cdot z}{y}\right) + x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	22.6
Cost	1488

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+157}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+75}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+100}:\\ \;\;\;\;\frac{y \cdot x + t \cdot z}{z \cdot \left(b - y\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot \frac{x}{z} + t\right) - a}{b}\\ \end{array} \]

Alternative 10
Error	23.1
Cost	1356

\[\begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+155}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+37}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot \frac{x}{z} + t\right) - a}{b}\\ \end{array} \]

Alternative 11
Error	33.2
Cost	1240

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+74}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{t}{y} + x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \end{array} \]

Alternative 12
Error	32.0
Cost	1240

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+74}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-22}:\\ \;\;\;\;\left(-\frac{a \cdot z}{y}\right) + x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \end{array} \]

Alternative 13
Error	37.6
Cost	1112

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{a - t}{y}\\ \mathbf{if}\;y \leq -1.28 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-278}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 10^{-58}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	34.8
Cost	1112

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+74}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	33.2
Cost	1112

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \frac{t}{y} + x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	40.8
Cost	720

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-65}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 17
Error	36.9
Cost	716

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-278}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	40.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 19
Error	47.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(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)))))