Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.1 → 4.9

Time: 25.9s

Precision: binary64

Cost: 15944

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-271}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, t_2\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{y}{z} \cdot \frac{x}{b - y}\\ \end{array} \]

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 (/ (- t a) (- b y)))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) (+ y (* z (- b y))))))
   (if (<= t_3 (- INFINITY))
     (- t_1 (/ x z))
     (if (<= t_3 -2e-271)
       (/ (fma y x t_2) (fma z (- b y) y))
       (if (<= t_3 4e-279)
         (+
          (/ (/ (* x y) z) (- b y))
          (+
           (/ t (- b y))
           (- (* (/ y z) (/ (- a t) (pow (- b y) 2.0))) (/ a (- b y)))))
         (if (<= t_3 5e+296) t_3 (+ t_1 (* (/ y z) (/ x (- 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 = (t - a) / (b - y);
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / (y + (z * (b - y)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_1 - (x / z);
	} else if (t_3 <= -2e-271) {
		tmp = fma(y, x, t_2) / fma(z, (b - y), y);
	} else if (t_3 <= 4e-279) {
		tmp = (((x * y) / z) / (b - y)) + ((t / (b - y)) + (((y / z) * ((a - t) / pow((b - y), 2.0))) - (a / (b - y))));
	} else if (t_3 <= 5e+296) {
		tmp = t_3;
	} else {
		tmp = t_1 + ((y / z) * (x / (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(Float64(t - a) / Float64(b - y))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(t_1 - Float64(x / z));
	elseif (t_3 <= -2e-271)
		tmp = Float64(fma(y, x, t_2) / fma(z, Float64(b - y), y));
	elseif (t_3 <= 4e-279)
		tmp = Float64(Float64(Float64(Float64(x * y) / z) / Float64(b - y)) + Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))) - Float64(a / Float64(b - y)))));
	elseif (t_3 <= 5e+296)
		tmp = t_3;
	else
		tmp = Float64(t_1 + Float64(Float64(y / z) * Float64(x / 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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-271], N[(N[(y * x + t$95$2), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e-279], N[(N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+296], t$95$3, N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Target

Original	23.1
Target	17.6
Herbie	4.9

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

Derivation

1. Split input into 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 64.0

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

   2. Taylor expanded in z around inf 41.7

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

   3. Simplified 33.0

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

      [Start] 41.7	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 41.7	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      times-frac [=>] 38.5	\[ \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 38.5	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 38.5	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      associate--r+ [=>] 38.5	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\left(\left(\frac{t}{b - y} - \frac{a}{b - y}\right) - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right)} \]
      div-sub [<=] 38.5	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\color{blue}{\frac{t - a}{b - y}} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right) \]
      times-frac [=>] 33.0	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t - a}{b - y} - \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right) \]

   4. Taylor expanded in z around inf 28.6

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

   5. Simplified 28.6

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

      [Start] 28.6	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]
      div-sub [<=] 28.6	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\frac{t - a}{b - y}} \]

   6. Taylor expanded in y around inf 29.7

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

   7. Simplified 29.7

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

      [Start] 29.7	\[ -1 \cdot \frac{x}{z} + \frac{t - a}{b - y} \]
      associate-*r/ [=>] 29.7	\[ \color{blue}{\frac{-1 \cdot x}{z}} + \frac{t - a}{b - y} \]
      neg-mul-1 [<=] 29.7	\[ \frac{\color{blue}{-x}}{z} + \frac{t - a}{b - y} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999993e-271

   1. Initial program 0.3

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

   2. Simplified 0.3

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

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

   if -1.99999999999999993e-271 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.00000000000000022e-279

   1. Initial program 41.2

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

   2. Taylor expanded in z around inf 19.5

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

   3. Simplified 4.3

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

      [Start] 19.5	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 19.5	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      *-commutative [=>] 19.5	\[ \frac{\color{blue}{x \cdot y}}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      associate-/r* [=>] 10.5	\[ \color{blue}{\frac{\frac{x \cdot y}{z}}{b - y}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      *-commutative [<=] 10.5	\[ \frac{\frac{\color{blue}{y \cdot x}}{z}}{b - y} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 10.5	\[ \frac{\frac{y \cdot x}{z}}{b - y} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 10.5	\[ \frac{\frac{y \cdot x}{z}}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      times-frac [=>] 4.3	\[ \frac{\frac{y \cdot x}{z}}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right)\right) \]

   if 4.00000000000000022e-279 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000001e296

   1. Initial program 0.3

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

   if 5.0000000000000001e296 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 63.2

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

   2. Taylor expanded in z around inf 39.0

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

   3. Simplified 10.5

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

      [Start] 39.0	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 39.0	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      times-frac [=>] 31.7	\[ \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 31.7	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 31.7	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      associate--r+ [=>] 31.7	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\left(\left(\frac{t}{b - y} - \frac{a}{b - y}\right) - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right)} \]
      div-sub [<=] 31.7	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\color{blue}{\frac{t - a}{b - y}} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right) \]
      times-frac [=>] 10.5	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t - a}{b - y} - \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right) \]

   4. Taylor expanded in z around inf 8.8

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

   5. Simplified 8.8

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

      [Start] 8.8	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]
      div-sub [<=] 8.8	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\frac{t - a}{b - y}} \]

3. Recombined 5 regimes into one program.

4. Final simplification 4.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-271}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	4.9
Cost	12044

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2 - \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{y}{z} \cdot \frac{x}{b - y}\\ \end{array} \]

Alternative 2
Error	5.2
Cost	5713

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2 - \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-271} \lor \neg \left(t_1 \leq 4 \cdot 10^{-279}\right) \land t_1 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{y}{z} \cdot \frac{x}{b - y}\\ \end{array} \]

Alternative 3
Error	15.5
Cost	1616

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ t_2 := \frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\\ \mathbf{if}\;z \leq -7.7 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-306}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	39.7
Cost	1245

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.9 \cdot 10^{+82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+128} \lor \neg \left(y \leq 3.5 \cdot 10^{+224}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	22.2
Cost	1241

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+136} \lor \neg \left(z \leq 2.15 \cdot 10^{+173}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 6
Error	19.6
Cost	1232

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ t_2 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	24.9
Cost	977

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+136} \lor \neg \left(z \leq 2.15 \cdot 10^{+173}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 8
Error	41.3
Cost	916

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+178}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	36.9
Cost	849

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-5}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+55} \lor \neg \left(z \leq 2.9 \cdot 10^{+174}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 10
Error	32.6
Cost	849

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-14}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+128} \lor \neg \left(y \leq 3.5 \cdot 10^{+224}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 11
Error	41.2
Cost	785

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-81} \lor \neg \left(z \leq 2.7 \cdot 10^{-12}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	41.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 13
Error	47.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023016 
(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)))))