Development.Shake.Progress:decay from shake-0.15.5

Average Error: 22.9 → 6.9

Time: 29.7s

Precision: binary64

Cost: 14160

Math

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

↓

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{\frac{y}{b - y} \cdot x}{z} + \left(\frac{t - a}{b - y} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{\frac{y}{z}}}\right)\\ \mathbf{if}\;z \leq -24000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-229}:\\ \;\;\;\;\frac{t_1 + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 68000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, t_1\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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 (* z (- t a)))
        (t_2
         (+
          (/ (* (/ y (- b y)) x) z)
          (- (/ (- t a) (- b y)) (/ (- t a) (/ (pow (- b y) 2.0) (/ y z)))))))
   (if (<= z -24000000.0)
     t_2
     (if (<= z -3.8e-229)
       (/ (+ t_1 (* y x)) (+ y (* z (- b y))))
       (if (<= z 2.3e-278)
         x
         (if (<= z 68000000.0) (/ (fma y x t_1) (fma z (- b y) y)) t_2))))))

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 = z * (t - a);
	double t_2 = (((y / (b - y)) * x) / z) + (((t - a) / (b - y)) - ((t - a) / (pow((b - y), 2.0) / (y / z))));
	double tmp;
	if (z <= -24000000.0) {
		tmp = t_2;
	} else if (z <= -3.8e-229) {
		tmp = (t_1 + (y * x)) / (y + (z * (b - y)));
	} else if (z <= 2.3e-278) {
		tmp = x;
	} else if (z <= 68000000.0) {
		tmp = fma(y, x, t_1) / fma(z, (b - y), y);
	} else {
		tmp = t_2;
	}
	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(z * Float64(t - a))
	t_2 = Float64(Float64(Float64(Float64(y / Float64(b - y)) * x) / z) + Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(Float64(t - a) / Float64((Float64(b - y) ^ 2.0) / Float64(y / z)))))
	tmp = 0.0
	if (z <= -24000000.0)
		tmp = t_2;
	elseif (z <= -3.8e-229)
		tmp = Float64(Float64(t_1 + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 2.3e-278)
		tmp = x;
	elseif (z <= 68000000.0)
		tmp = Float64(fma(y, x, t_1) / fma(z, Float64(b - y), y));
	else
		tmp = t_2;
	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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t - a), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -24000000.0], t$95$2, If[LessEqual[z, -3.8e-229], N[(N[(t$95$1 + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-278], x, If[LessEqual[z, 68000000.0], N[(N[(y * x + t$95$1), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Target

Original	22.9
Target	18.1
Herbie	6.9

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

Derivation

1. Split input into 4 regimes

2. if z < -2.4e7 or 6.8e7 < z

   1. Initial program 39.0

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

   2. Taylor expanded in z around inf 21.9

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

   3. Simplified 2.3

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

      [Start] 21.9	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 21.9	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      *-commutative [<=] 21.9	\[ \frac{y \cdot x}{\color{blue}{\left(b - y\right) \cdot z}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      times-frac [=>] 16.4	\[ \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      associate-*r/ [=>] 16.3	\[ \color{blue}{\frac{\frac{y}{b - y} \cdot x}{z}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 16.3	\[ \frac{\frac{y}{b - y} \cdot x}{z} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 16.3	\[ \frac{\frac{y}{b - y} \cdot x}{z} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      associate--r+ [=>] 16.3	\[ \frac{\frac{y}{b - y} \cdot x}{z} + \color{blue}{\left(\left(\frac{t}{b - y} - \frac{a}{b - y}\right) - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right)} \]
      div-sub [<=] 16.3	\[ \frac{\frac{y}{b - y} \cdot x}{z} + \left(\color{blue}{\frac{t - a}{b - y}} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right) \]
      associate-/l* [=>] 2.3	\[ \frac{\frac{y}{b - y} \cdot x}{z} + \left(\frac{t - a}{b - y} - \color{blue}{\frac{t - a}{\frac{{\left(b - y\right)}^{2} \cdot z}{y}}}\right) \]
      associate-/l* [=>] 2.3	\[ \frac{\frac{y}{b - y} \cdot x}{z} + \left(\frac{t - a}{b - y} - \frac{t - a}{\color{blue}{\frac{{\left(b - y\right)}^{2}}{\frac{y}{z}}}}\right) \]

   if -2.4e7 < z < -3.8000000000000002e-229

   1. Initial program 8.9

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

   if -3.8000000000000002e-229 < z < 2.30000000000000003e-278

   1. Initial program 10.0

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

   2. Taylor expanded in z around 0 21.6

      \[\leadsto \color{blue}{x} \]

   if 2.30000000000000003e-278 < z < 6.8e7

   1. Initial program 8.3

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

   2. Simplified 8.3

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

      [Start] 8.3	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      *-commutative [=>] 8.3	\[ \frac{\color{blue}{y \cdot x} + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 8.3	\[ \frac{\color{blue}{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]
      +-commutative [=>] 8.3	\[ \frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\color{blue}{z \cdot \left(b - y\right) + y}} \]
      fma-def [=>] 8.3	\[ \frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 6.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24000000:\\ \;\;\;\;\frac{\frac{y}{b - y} \cdot x}{z} + \left(\frac{t - a}{b - y} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{\frac{y}{z}}}\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-229}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 68000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{b - y} \cdot x}{z} + \left(\frac{t - a}{b - y} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{\frac{y}{z}}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	8.5
Cost	12756

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	6.8
Cost	8848

\[\begin{array}{l} t_1 := \frac{\frac{y}{b - y} \cdot x}{z} + \left(\frac{t - a}{b - y} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{\frac{y}{z}}}\right)\\ t_2 := \frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;z \leq -15500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 21000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	11.6
Cost	1616

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	22.7
Cost	1364

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -50000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-230}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	22.7
Cost	1364

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right) + y \cdot x\\ \mathbf{if}\;z \leq -48000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.77:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{t_2}{z \cdot b}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-231}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-16}:\\ \;\;\;\;\frac{t_2}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	19.2
Cost	1360

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -48000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.61:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{z \cdot b}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} + \left(x - \frac{a}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	23.8
Cost	1236

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -48000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.48:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-15}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	41.0
Cost	1180

\[\begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+50}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -1.1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+169}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+277}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \]

Alternative 9
Error	41.0
Cost	1180

\[\begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+51}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -1.1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -0.00013:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.0001:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+172}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+278}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \]

Alternative 10
Error	36.2
Cost	981

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+71} \lor \neg \left(z \leq 4.8 \cdot 10^{+182}\right) \land z \leq 10^{+245}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	37.0
Cost	981

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+72} \lor \neg \left(z \leq 3.3 \cdot 10^{+186}\right) \land z \leq 6.8 \cdot 10^{+246}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 12
Error	37.7
Cost	980

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{a}{-b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 13
Error	24.8
Cost	978

\[\begin{array}{l} \mathbf{if}\;z \leq -48000000000000 \lor \neg \left(z \leq -1.1\right) \land \left(z \leq -4.2 \cdot 10^{-57} \lor \neg \left(z \leq 6.4 \cdot 10^{+49}\right)\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 14
Error	40.2
Cost	917

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+87} \lor \neg \left(z \leq 5.3 \cdot 10^{+169}\right) \land z \leq 1.6 \cdot 10^{+256}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 15
Error	40.4
Cost	916

\[\begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.00034:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+167}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+275}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \]

Alternative 16
Error	31.6
Cost	780

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+94}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	31.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+119} \lor \neg \left(y \leq 1.25 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 18
Error	42.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 19
Error	39.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 20
Error	47.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023039 
(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)))))