Development.Shake.Progress:decay from shake-0.15.5

Average Accuracy: 63.2% → 93.1%

Time: 35.9s

Precision: binary64

Cost: 15944

Math

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

↓

\[\begin{array}{l} t_1 := {\left(b - y\right)}^{2}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, t_3\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \left(\frac{a}{b - y} + \frac{y}{z} \cdot \frac{t - a}{t_1}\right)\\ \mathbf{elif}\;t_4 \leq 10^{+297}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_3\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}}}{z} + \left(\frac{t - a}{b - y} + \frac{a - t}{\frac{t_1}{\frac{y}{z}}}\right)\\ \end{array} \]

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 (pow (- b y) 2.0))
        (t_2 (+ y (* z (- b y))))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_2)))
   (if (<= t_4 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_4 -5e-275)
       (/ (fma y x t_3) (fma z (- b y) y))
       (if (<= t_4 0.0)
         (-
          (+ (/ t (- b y)) (* (/ y z) (/ x (- b y))))
          (+ (/ a (- b y)) (* (/ y z) (/ (- t a) t_1))))
         (if (<= t_4 1e+297)
           (/ (fma x y t_3) t_2)
           (+
            (/ (/ x (/ (- b y) y)) z)
            (+ (/ (- t a) (- b y)) (/ (- a t) (/ t_1 (/ y z)))))))))))

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 = pow((b - y), 2.0);
	double t_2 = y + (z * (b - y));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_4 <= -5e-275) {
		tmp = fma(y, x, t_3) / fma(z, (b - y), y);
	} else if (t_4 <= 0.0) {
		tmp = ((t / (b - y)) + ((y / z) * (x / (b - y)))) - ((a / (b - y)) + ((y / z) * ((t - a) / t_1)));
	} else if (t_4 <= 1e+297) {
		tmp = fma(x, y, t_3) / t_2;
	} else {
		tmp = ((x / ((b - y) / y)) / z) + (((t - a) / (b - y)) + ((a - t) / (t_1 / (y / z))));
	}
	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(b - y) ^ 2.0
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_4 <= -5e-275)
		tmp = Float64(fma(y, x, t_3) / fma(z, Float64(b - y), y));
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) - Float64(Float64(a / Float64(b - y)) + Float64(Float64(y / z) * Float64(Float64(t - a) / t_1))));
	elseif (t_4 <= 1e+297)
		tmp = Float64(fma(x, y, t_3) / t_2);
	else
		tmp = Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) / z) + Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(a - t) / Float64(t_1 / Float64(y / z)))));
	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[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -5e-275], N[(N[(y * x + t$95$3), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+297], N[(N[(x * y + t$95$3), $MachinePrecision] / t$95$2), $MachinePrecision], N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(t$95$1 / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Target

Original	63.2%
Target	71.4%
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 32.6%

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

   4. Simplified 57.8%

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

      [Start] 32.6	\[ -1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      mul-1-neg [=>] 32.6	\[ -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]
      unsub-neg [=>] 32.6	\[ \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
      mul-1-neg [=>] 32.6	\[ \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      distribute-neg-frac [=>] 32.6	\[ \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   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)))) < -4.99999999999999983e-275

   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%

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

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

   if -4.99999999999999983e-275 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 30.6%

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

   2. Simplified 30.6%

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

      [Start] 30.6	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 30.6	\[ \frac{\color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]

   3. Taylor expanded in z around inf 70.8%

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

   4. Simplified 90.7%

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

      [Start] 70.8	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      +-commutative [=>] 70.8	\[ \color{blue}{\left(\frac{t}{b - y} + \frac{y \cdot x}{z \cdot \left(b - y\right)}\right)} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      times-frac [=>] 82.5	\[ \left(\frac{t}{b - y} + \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      +-commutative [=>] 82.5	\[ \left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)} \]
      *-commutative [<=] 82.5	\[ \left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right) \]
      times-frac [=>] 90.7	\[ \left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \left(\frac{a}{b - y} + \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right) \]

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e297

   1. Initial program 99.5%

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

   2. Simplified 99.6%

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

      [Start] 99.5	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 99.6	\[ \frac{\color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]

   if 1e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 1.6%

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

   2. Taylor expanded in z around inf 35.7%

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

   3. Simplified 84.7%

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

      [Start] 35.7	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 35.7	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      *-commutative [<=] 35.7	\[ \frac{\color{blue}{x \cdot y}}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      associate-/l/ [<=] 35.7	\[ \color{blue}{\frac{\frac{x \cdot y}{b - y}}{z}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      associate-/l* [=>] 48.8	\[ \frac{\color{blue}{\frac{x}{\frac{b - y}{y}}}}{z} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 48.8	\[ \frac{\frac{x}{\frac{b - y}{y}}}{z} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 48.8	\[ \frac{\frac{x}{\frac{b - y}{y}}}{z} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      associate--r+ [=>] 48.8	\[ \frac{\frac{x}{\frac{b - y}{y}}}{z} + \color{blue}{\left(\left(\frac{t}{b - y} - \frac{a}{b - y}\right) - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right)} \]
      div-sub [<=] 48.8	\[ \frac{\frac{x}{\frac{b - y}{y}}}{z} + \left(\color{blue}{\frac{t - a}{b - y}} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right) \]
      associate-/l* [=>] 84.8	\[ \frac{\frac{x}{\frac{b - y}{y}}}{z} + \left(\frac{t - a}{b - y} - \color{blue}{\frac{t - a}{\frac{{\left(b - y\right)}^{2} \cdot z}{y}}}\right) \]
      associate-/l* [=>] 84.7	\[ \frac{\frac{x}{\frac{b - y}{y}}}{z} + \left(\frac{t - a}{b - y} - \frac{t - a}{\color{blue}{\frac{{\left(b - y\right)}^{2}}{\frac{y}{z}}}}\right) \]

3. Recombined 5 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \left(\frac{a}{b - y} + \frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+297}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}}}{z} + \left(\frac{t - a}{b - y} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{\frac{y}{z}}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	93.3%
Cost	12945

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t_2}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-275}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0 \lor \neg \left(t_3 \leq 10^{+297}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}}}{z} + \left(\frac{t - a}{b - y} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{\frac{y}{z}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \end{array} \]

Alternative 2
Accuracy	93.1%
Cost	12944

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t_2}{t_1}\\ t_4 := {\left(b - y\right)}^{2}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-275}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \left(\frac{a}{b - y} + \frac{y}{z} \cdot \frac{t - a}{t_4}\right)\\ \mathbf{elif}\;t_3 \leq 10^{+297}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}}}{z} + \left(\frac{t - a}{b - y} + \frac{a - t}{\frac{t_4}{\frac{y}{z}}}\right)\\ \end{array} \]

Alternative 3
Accuracy	87.6%
Cost	11985

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t_2}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-275}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0 \lor \neg \left(t_3 \leq 10^{+302}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \end{array} \]

Alternative 4
Accuracy	88.3%
Cost	11984

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-275}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2 + \frac{\frac{x \cdot y}{b - y} + \frac{y \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;t_4 \leq 10^{+302}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_3\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	87.6%
Cost	5713

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-275} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6
Accuracy	43.8%
Cost	1245

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-7}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+115}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+178}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+224} \lor \neg \left(z \leq 6.2 \cdot 10^{+256}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 7
Accuracy	44.3%
Cost	1244

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+124}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+190}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	66.4%
Cost	1100

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-108}:\\ \;\;\;\;\frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-238}:\\ \;\;\;\;\frac{x \cdot y + t_1}{y}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	65.1%
Cost	968

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-238}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	44.5%
Cost	849

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -3 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-11}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+224} \lor \neg \left(z \leq 6.2 \cdot 10^{+256}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 11
Accuracy	62.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-77} \lor \neg \left(z \leq 3.1 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 12
Accuracy	52.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-21} \lor \neg \left(y \leq 9.6 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 13
Accuracy	36.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -16500000000:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-8}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 14
Accuracy	33.3%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -13.5:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 15
Accuracy	36.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -24000000000:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16
Accuracy	26.1%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(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)))))