Development.Shake.Progress:decay from shake-0.15.5

Average Accuracy: 62.9% → 93.1%

Time: 32.5s

Precision: binary64

Cost: 11916

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t_2 + x \cdot y}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-231}:\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{\frac{x \cdot y}{b - y} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \end{array} \]

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 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ t_2 (* x y)) t_1)))
   (if (<= t_3 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_3 -2e-301)
       (/ (fma x y t_2) t_1)
       (if (<= t_3 2e-231)
         (+
          (/ t (- b y))
          (-
           (/ (+ (/ (* x y) (- b y)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z)
           (/ a (- b y))))
         (if (<= t_3 5e+305)
           t_3
           (+ (* (/ y (- b y)) (/ x z)) (/ (- 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 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (t_2 + (x * y)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_3 <= -2e-301) {
		tmp = fma(x, y, t_2) / t_1;
	} else if (t_3 <= 2e-231) {
		tmp = (t / (b - y)) + (((((x * y) / (b - y)) + ((a - t) / (pow((b - y), 2.0) / y))) / z) - (a / (b - y)));
	} else if (t_3 <= 5e+305) {
		tmp = t_3;
	} else {
		tmp = ((y / (b - y)) * (x / z)) + ((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(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(t_2 + Float64(x * y)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_3 <= -2e-301)
		tmp = Float64(fma(x, y, t_2) / t_1);
	elseif (t_3 <= 2e-231)
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(Float64(Float64(x * y) / Float64(b - y)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z) - Float64(a / Float64(b - y))));
	elseif (t_3 <= 5e+305)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(Float64(t - a) / Float64(b - y)));
	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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-301], N[(N[(x * y + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 2e-231], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+305], t$95$3, N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Target

Original	62.9%
Target	70.9%
Herbie	93.1%

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

Derivation

1. Split input into 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 0.0%

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

   2. Simplified 0.0%

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

      [Start] 0.0	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 0.0	\[ \frac{\color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]

   3. Taylor expanded in y around -inf 34.8%

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

   4. Simplified 58.2%

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

      [Start] 34.8	\[ -1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      mul-1-neg [=>] 34.8	\[ -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]
      unsub-neg [=>] 34.8	\[ \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
      mul-1-neg [=>] 34.8	\[ \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      distribute-neg-frac [=>] 34.8	\[ \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   5. Taylor expanded in z around inf 70.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000013e-301

   1. Initial program 99.5%

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

   2. Simplified 99.5%

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

      [Start] 99.5	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 99.5	\[ \frac{\color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]

   if -2.00000000000000013e-301 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e-231

   1. Initial program 35.3%

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

   2. Applied egg-rr 31.6%

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

   3. Simplified 24.5%

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

      [Start] 31.6	\[ \frac{x \cdot y + \frac{z \cdot \left(t \cdot t - a \cdot a\right)}{t + a}}{y + z \cdot \left(b - y\right)} \]
      *-commutative [<=] 31.6	\[ \frac{x \cdot y + \frac{\color{blue}{\left(t \cdot t - a \cdot a\right) \cdot z}}{t + a}}{y + z \cdot \left(b - y\right)} \]
      associate-/l* [=>] 23.3	\[ \frac{x \cdot y + \color{blue}{\frac{t \cdot t - a \cdot a}{\frac{t + a}{z}}}}{y + z \cdot \left(b - y\right)} \]
      difference-of-squares [=>] 23.3	\[ \frac{x \cdot y + \frac{\color{blue}{\left(t + a\right) \cdot \left(t - a\right)}}{\frac{t + a}{z}}}{y + z \cdot \left(b - y\right)} \]
      associate-/l* [=>] 24.5	\[ \frac{x \cdot y + \color{blue}{\frac{t + a}{\frac{\frac{t + a}{z}}{t - a}}}}{y + z \cdot \left(b - y\right)} \]

   4. Taylor expanded in z around -inf 79.6%

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

   5. Simplified 89.8%

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

      [Start] 79.6	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      associate--l+ [=>] 79.6	\[ \color{blue}{\frac{t}{b - y} + \left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} - \frac{a}{b - y}\right)} \]
      mul-1-neg [=>] 79.6	\[ \frac{t}{b - y} + \left(\color{blue}{\left(-\frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right)} - \frac{a}{b - y}\right) \]
      distribute-lft-out-- [=>] 79.6	\[ \frac{t}{b - y} + \left(\left(-\frac{\color{blue}{-1 \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}}{z}\right) - \frac{a}{b - y}\right) \]
      associate-/l* [=>] 89.8	\[ \frac{t}{b - y} + \left(\left(-\frac{-1 \cdot \left(\frac{y \cdot x}{b - y} - \color{blue}{\frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}}\right)}{z}\right) - \frac{a}{b - y}\right) \]

   if 2e-231 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000009e305

   1. Initial program 99.5%

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

   if 5.00000000000000009e305 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 0.2%

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

   2. Applied egg-rr 0.1%

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

   3. Simplified 0.2%

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

      [Start] 0.1	\[ \frac{x \cdot y + \frac{z \cdot \left(t \cdot t - a \cdot a\right)}{t + a}}{y + z \cdot \left(b - y\right)} \]
      *-commutative [<=] 0.1	\[ \frac{x \cdot y + \frac{\color{blue}{\left(t \cdot t - a \cdot a\right) \cdot z}}{t + a}}{y + z \cdot \left(b - y\right)} \]
      associate-/l* [=>] 0.1	\[ \frac{x \cdot y + \color{blue}{\frac{t \cdot t - a \cdot a}{\frac{t + a}{z}}}}{y + z \cdot \left(b - y\right)} \]
      difference-of-squares [=>] 0.1	\[ \frac{x \cdot y + \frac{\color{blue}{\left(t + a\right) \cdot \left(t - a\right)}}{\frac{t + a}{z}}}{y + z \cdot \left(b - y\right)} \]
      associate-/l* [=>] 0.2	\[ \frac{x \cdot y + \color{blue}{\frac{t + a}{\frac{\frac{t + a}{z}}{t - a}}}}{y + z \cdot \left(b - y\right)} \]

   4. Taylor expanded in z around -inf 37.8%

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

   5. Simplified 85.3%

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

      [Start] 37.8	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      +-commutative [=>] 37.8	\[ \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]
      associate--l+ [=>] 37.8	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   6. Taylor expanded in x around inf 59.0%

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

   7. Simplified 85.2%

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

      [Start] 59.0	\[ \frac{y \cdot x}{\left(b - y\right) \cdot z} + \frac{t - a}{b - y} \]
      times-frac [=>] 85.2	\[ \color{blue}{\frac{y}{b - y} \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

3. Recombined 5 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{-231}:\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{\frac{x \cdot y}{b - y} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	93.0%
Cost	9672

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t_2 + x \cdot y}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-231} \lor \neg \left(t_3 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Accuracy	93.0%
Cost	5713

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-301} \lor \neg \left(t_1 \leq 2 \cdot 10^{-231}\right) \land t_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3
Accuracy	65.6%
Cost	1888

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot b}\\ t_3 := y + z \cdot \left(b - y\right)\\ t_4 := \frac{t_1}{t_3}\\ t_5 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+76}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-29}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-158}:\\ \;\;\;\;\frac{x \cdot y}{t_3}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+20}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 4
Accuracy	65.3%
Cost	1628

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ t_2 := \frac{t - a}{b - y} - \frac{x}{z}\\ t_3 := \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.024:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	70.9%
Cost	1356

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;t_2 - \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_1}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	80.9%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-28} \lor \neg \left(z \leq 3 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 7
Accuracy	63.2%
Cost	1100

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.024:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	32.2%
Cost	784

\[\begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-39}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+244}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+301}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Accuracy	52.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+24} \lor \neg \left(y \leq 2.3 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \end{array} \]

Alternative 10
Accuracy	62.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-17} \lor \neg \left(z \leq 2.8 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	41.1%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-103} \lor \neg \left(y \leq 9.5 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 12
Accuracy	52.3%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+24} \lor \neg \left(y \leq 1.75 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 13
Accuracy	36.1%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-6} \lor \neg \left(z \leq 2.2 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Accuracy	36.2%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 15
Accuracy	25.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023141 
(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)))))