Development.Shake.Progress:decay from shake-0.15.5

Average Error: 24.0 → 6.0

Time: 29.9s

Precision: binary64

Cost: 12817

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-261}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t - a, z, x \cdot y\right)}{t_1}\\ \mathbf{elif}\;t_2 \leq 10^{-279} \lor \neg \left(t_2 \leq 2 \cdot 10^{+284}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3
         (+
          (/ (+ (* x (/ y (- b y))) (* y (/ (- a t) (pow (- b y) 2.0)))) z)
          (/ (- t a) (- b y)))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -5e-261)
       (/ (fma (- t a) z (* x y)) t_1)
       (if (or (<= t_2 1e-279) (not (<= t_2 2e+284))) t_3 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 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = (((x * (y / (b - y))) + (y * ((a - t) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -5e-261) {
		tmp = fma((t - a), z, (x * y)) / t_1;
	} else if ((t_2 <= 1e-279) || !(t_2 <= 2e+284)) {
		tmp = t_3;
	} 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(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -5e-261)
		tmp = Float64(fma(Float64(t - a), z, Float64(x * y)) / t_1);
	elseif ((t_2 <= 1e-279) || !(t_2 <= 2e+284))
		tmp = t_3;
	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[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -5e-261], N[(N[(N[(t - a), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[Or[LessEqual[t$95$2, 1e-279], N[Not[LessEqual[t$95$2, 2e+284]], $MachinePrecision]], t$95$3, t$95$2]]]]]]

Target

Original	24.0
Target	18.3
Herbie	6.0

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

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 -4.99999999999999981e-261 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.00000000000000006e-279 or 2.00000000000000016e284 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 57.5

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

   2. Taylor expanded in z around -inf 33.6

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

   3. Simplified 14.0

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

      [Start] 33.6	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      +-commutative [=>] 33.6	\[ \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]
      associate--l+ [=>] 33.6	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999981e-261

   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 0 0.3

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

   3. Simplified 0.3

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

      [Start] 0.3	\[ \frac{y \cdot x + \left(t - a\right) \cdot z}{y + z \cdot \left(b - y\right)} \]
      +-commutative [=>] 0.3	\[ \frac{\color{blue}{\left(t - a\right) \cdot z + y \cdot x}}{y + z \cdot \left(b - y\right)} \]
      *-commutative [=>] 0.3	\[ \frac{\left(t - a\right) \cdot z + \color{blue}{x \cdot y}}{y + z \cdot \left(b - y\right)} \]
      fma-udef [<=] 0.3	\[ \frac{\color{blue}{\mathsf{fma}\left(t - a, z, x \cdot y\right)}}{y + z \cdot \left(b - y\right)} \]
      *-commutative [<=] 0.3	\[ \frac{\mathsf{fma}\left(t - a, z, \color{blue}{y \cdot x}\right)}{y + z \cdot \left(b - y\right)} \]

   if 1.00000000000000006e-279 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000016e284

   1. Initial program 0.3

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 6.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-261}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t - a, z, x \cdot y\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{-279} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+284}\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.0
Cost	12945

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-261}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t - a, z, x \cdot y\right)}{t_1}\\ \mathbf{elif}\;t_2 \leq 10^{-279} \lor \neg \left(t_2 \leq 2 \cdot 10^{+284}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	10.5
Cost	9672

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(t_3 + \frac{a - t}{y \cdot z}\right)\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-261}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t - a, z, x \cdot y\right)}{t_1}\\ \mathbf{elif}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 10^{+235}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	10.3
Cost	5714

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq -5 \cdot 10^{-261} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 10^{+235}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	10.5
Cost	5713

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(t_2 + \frac{a - t}{y \cdot z}\right)\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-261} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 10^{+235}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	18.7
Cost	1360

\[\begin{array}{l} t_1 := x + \frac{z \cdot \left(\left(t - a\right) - x \cdot b\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-116}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	34.1
Cost	1308

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{-a}{b - y}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -150:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	34.6
Cost	1308

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{-a}{b - y}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -500:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-48}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	36.4
Cost	1244

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-9}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	19.6
Cost	1228

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-148}:\\ \;\;\;\;\frac{x \cdot y + t_1}{y}\\ \mathbf{elif}\;z \leq 255000000:\\ \;\;\;\;\frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	12.6
Cost	1225

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-40} \lor \neg \left(z \leq 3.5\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \]

Alternative 11
Error	40.3
Cost	1048

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;z \leq -95:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+161}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	35.9
Cost	980

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -490:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	23.5
Cost	976

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-116}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	23.1
Cost	976

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	24.4
Cost	976

\[\begin{array}{l} t_1 := y + z \cdot b\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-155}:\\ \;\;\;\;\frac{x \cdot y}{t_1}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-109}:\\ \;\;\;\;\frac{z \cdot t}{t_1}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	20.2
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{-40} \lor \neg \left(z \leq 9.8 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 17
Error	40.3
Cost	652

\[\begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;z \leq -95:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+162}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	31.0
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+125} \lor \neg \left(y \leq 2.9 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 19
Error	42.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	47.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023060 
(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)))))