Development.Shake.Progress:decay from shake-0.15.5

Average Error: 36.27% → 4.38%

Time: 37.3s

Precision: binary64

Cost: 12624

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3}{t_1} - x \cdot \left(y \cdot \frac{-1}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ t_5 := \frac{t_3 + x \cdot y}{t_1}\\ t_6 := t_2 - \frac{x}{z + -1}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq -5 \cdot 10^{-262}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 5 \cdot 10^{-306}:\\ \;\;\;\;t_2 - \frac{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}} - x \cdot \frac{y}{b - y}}{z}\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+278}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

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 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (- (/ t_3 t_1) (* x (* y (/ -1.0 (fma z (- b y) y))))))
        (t_5 (/ (+ t_3 (* x y)) t_1))
        (t_6 (- t_2 (/ x (+ z -1.0)))))
   (if (<= t_5 (- INFINITY))
     t_6
     (if (<= t_5 -5e-262)
       t_4
       (if (<= t_5 5e-306)
         (-
          t_2
          (/ (- (* y (/ (- t a) (pow (- b y) 2.0))) (* x (/ y (- b y)))) z))
         (if (<= t_5 2e+278) t_4 t_6))))))

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 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = (t_3 / t_1) - (x * (y * (-1.0 / fma(z, (b - y), y))));
	double t_5 = (t_3 + (x * y)) / t_1;
	double t_6 = t_2 - (x / (z + -1.0));
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_5 <= -5e-262) {
		tmp = t_4;
	} else if (t_5 <= 5e-306) {
		tmp = t_2 - (((y * ((t - a) / pow((b - y), 2.0))) - (x * (y / (b - y)))) / z);
	} else if (t_5 <= 2e+278) {
		tmp = t_4;
	} else {
		tmp = t_6;
	}
	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(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(t_3 / t_1) - Float64(x * Float64(y * Float64(-1.0 / fma(z, Float64(b - y), y)))))
	t_5 = Float64(Float64(t_3 + Float64(x * y)) / t_1)
	t_6 = Float64(t_2 - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_5 <= -5e-262)
		tmp = t_4;
	elseif (t_5 <= 5e-306)
		tmp = Float64(t_2 - Float64(Float64(Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0))) - Float64(x * Float64(y / Float64(b - y)))) / z));
	elseif (t_5 <= 2e+278)
		tmp = t_4;
	else
		tmp = t_6;
	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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 / t$95$1), $MachinePrecision] - N[(x * N[(y * N[(-1.0 / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$6, If[LessEqual[t$95$5, -5e-262], t$95$4, If[LessEqual[t$95$5, 5e-306], N[(t$95$2 - N[(N[(N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 2e+278], t$95$4, t$95$6]]]]]]]]]]

Target

Original	36.27%
Target	28.36%
Herbie	4.38%

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

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 1.99999999999999993e278 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 97.55

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

   2. Taylor expanded in x around inf 97.55

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

   3. Applied egg-rr 70.47

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

   4. Taylor expanded in z around inf 12.49

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

   5. Taylor expanded in y around -inf 8.46

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

   6. Simplified 8.46

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

      [Start] 8.46	\[ \frac{t - a}{b - y} + -1 \cdot \frac{x}{z - 1} \]
      mul-1-neg [=>] 8.46	\[ \frac{t - a}{b - y} + \color{blue}{\left(-\frac{x}{z - 1}\right)} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999992e-262 or 4.99999999999999998e-306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.99999999999999993e278

   1. Initial program 0.49

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

   2. Taylor expanded in x around inf 0.48

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

   3. Applied egg-rr 1.37

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

   if -4.99999999999999992e-262 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.99999999999999998e-306

   1. Initial program 65.8

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

   2. Taylor expanded in z around -inf 19.5

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

   3. Simplified 10.23

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

      [Start] 19.5	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      +-commutative [=>] 19.5	\[ \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]
      associate--l+ [=>] 19.5	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 4.38

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-262}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} - x \cdot \left(y \cdot \frac{-1}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{-306}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}} - x \cdot \frac{y}{b - y}}{z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+278}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} - x \cdot \left(y \cdot \frac{-1}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z + -1}\\ \end{array} \]

Alternatives

Alternative 1
Error	4.58%
Cost	12624

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3}{t_1} - x \cdot \left(y \cdot \frac{-1}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ t_5 := \frac{t_3 + x \cdot y}{t_1}\\ t_6 := t_2 - \frac{x}{z + -1}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq -5 \cdot 10^{-262}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 5 \cdot 10^{-306}:\\ \;\;\;\;t_2 + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+278}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 2
Error	4.05%
Cost	11984

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3 + x \cdot y}{t_1}\\ t_5 := t_2 - \frac{x}{z + -1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-262}:\\ \;\;\;\;\frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{-306}:\\ \;\;\;\;t_2 + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+278}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_3\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 3
Error	4.05%
Cost	5712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_3 := t_1 - \frac{x}{z + -1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-306}:\\ \;\;\;\;t_1 + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+278}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	4.05%
Cost	5712

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3 + x \cdot y}{t_1}\\ t_5 := t_2 - \frac{x}{z + -1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-262}:\\ \;\;\;\;\frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{-306}:\\ \;\;\;\;t_2 + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+278}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 5
Error	39.44%
Cost	1764

\[\begin{array}{l} t_1 := \frac{t - a}{\frac{y}{z}}\\ t_2 := \frac{x \cdot y}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-90}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	57.85%
Cost	1704

\[\begin{array}{l} t_1 := \frac{-a}{b - y}\\ t_2 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+140}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+60}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-93}:\\ \;\;\;\;\frac{z}{\frac{y}{t - a}}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-209}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-117}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-25}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	38.68%
Cost	1496

\[\begin{array}{l} t_1 := \frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-88}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-172}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-96}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	57.58%
Cost	1440

\[\begin{array}{l} t_1 := \frac{-a}{b - y}\\ t_2 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+141}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-209}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-111}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-24}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	38.64%
Cost	1368

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-89}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-123}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-172}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-107}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	12.18%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-33} \lor \neg \left(z \leq 1.9 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 11
Error	57.05%
Cost	1308

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t}{b - y}\\ t_3 := \frac{t - a}{b}\\ t_4 := \frac{-a}{b - y}\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-42}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-31}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	57.61%
Cost	1244

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t}{b - y}\\ t_3 := \frac{t - a}{b}\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.3:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 13
Error	40.54%
Cost	1240

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-94}:\\ \;\;\;\;\frac{z}{\frac{y}{t - a}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-209}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-114}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-24}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	40.46%
Cost	1240

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-94}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-209}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-117}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y}\\ \mathbf{elif}\;z \leq 10^{-24}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	32.85%
Cost	1232

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right) + x \cdot y\\ t_2 := \frac{t_1}{y}\\ t_3 := \frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-55}:\\ \;\;\;\;\frac{t_1}{z \cdot b}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 16
Error	18.57%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-25} \lor \neg \left(z \leq 3.4 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 17
Error	29.44%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-33} \lor \neg \left(z \leq 10^{-96}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \end{array} \]

Alternative 18
Error	32.37%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-34} \lor \neg \left(z \leq 3.6 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \end{array} \]

Alternative 19
Error	61.26%
Cost	849

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+121} \lor \neg \left(x \leq 4.8 \cdot 10^{+139}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]

Alternative 20
Error	64.93%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-124} \lor \neg \left(z \leq 2.9 \cdot 10^{-24}\right):\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 21
Error	55.62%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{-82} \lor \neg \left(z \leq 1.12 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 22
Error	47.41%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+52} \lor \neg \left(y \leq 1.3 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 23
Error	64.92%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-124} \lor \neg \left(z \leq 1.9 \cdot 10^{-23}\right):\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Error	73.59%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(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)))))