Development.Shake.Progress:decay from shake-0.15.5

Average Accuracy: 64.3% → 97.0%

Time: 34.5s

Precision: binary64

Cost: 19924

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \mathsf{fma}\left(z, b - y, y\right)\\ t_3 := z \cdot \frac{t - a}{t_2} + x \cdot \frac{y}{t_2}\\ t_4 := \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-180}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} + \left(\frac{y}{z} \cdot t_4 - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot t_4}{z} + \frac{t - a}{b - y}\\ \end{array} \]

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 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (fma z (- b y) y))
        (t_3 (+ (* z (/ (- t a) t_2)) (* x (/ y t_2))))
        (t_4 (/ (- a t) (pow (- b y) 2.0))))
   (if (<= t_1 -1e+286)
     t_3
     (if (<= t_1 -4e-294)
       t_1
       (if (<= t_1 2e-180)
         (+
          (* (/ y z) (/ x (- b y)))
          (+ (/ t (- b y)) (- (* (/ y z) t_4) (/ a (- b y)))))
         (if (<= t_1 2e+302)
           t_1
           (if (<= t_1 INFINITY)
             t_3
             (+
              (/ (+ (* x (/ y (- b y))) (* y t_4)) 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 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = fma(z, (b - y), y);
	double t_3 = (z * ((t - a) / t_2)) + (x * (y / t_2));
	double t_4 = (a - t) / pow((b - y), 2.0);
	double tmp;
	if (t_1 <= -1e+286) {
		tmp = t_3;
	} else if (t_1 <= -4e-294) {
		tmp = t_1;
	} else if (t_1 <= 2e-180) {
		tmp = ((y / z) * (x / (b - y))) + ((t / (b - y)) + (((y / z) * t_4) - (a / (b - y))));
	} else if (t_1 <= 2e+302) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (((x * (y / (b - y))) + (y * t_4)) / 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(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = fma(z, Float64(b - y), y)
	t_3 = Float64(Float64(z * Float64(Float64(t - a) / t_2)) + Float64(x * Float64(y / t_2)))
	t_4 = Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))
	tmp = 0.0
	if (t_1 <= -1e+286)
		tmp = t_3;
	elseif (t_1 <= -4e-294)
		tmp = t_1;
	elseif (t_1 <= 2e-180)
		tmp = Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(y / z) * t_4) - Float64(a / Float64(b - y)))));
	elseif (t_1 <= 2e+302)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * t_4)) / 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[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+286], t$95$3, If[LessEqual[t$95$1, -4e-294], t$95$1, If[LessEqual[t$95$1, 2e-180], N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / z), $MachinePrecision] * t$95$4), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+302], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$3, N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$4), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Target

Original	64.3%
Target	72.5%
Herbie	97.0%

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000003e286 or 2.0000000000000002e302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 4.0%

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

   2. Taylor expanded in x around 0 4.0%

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

   3. Simplified 98.5%

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

      [Start] 4.0	\[ \frac{y \cdot x}{y + \left(b - y\right) \cdot z} + \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} \]
      +-commutative [=>] 4.0	\[ \color{blue}{\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z}} \]
      associate-/l* [=>] 46.3	\[ \color{blue}{\frac{t - a}{\frac{y + \left(b - y\right) \cdot z}{z}}} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z} \]
      +-commutative [=>] 46.3	\[ \frac{t - a}{\frac{\color{blue}{\left(b - y\right) \cdot z + y}}{z}} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z} \]
      *-commutative [=>] 46.3	\[ \frac{t - a}{\frac{\color{blue}{z \cdot \left(b - y\right)} + y}{z}} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z} \]
      fma-udef [<=] 46.3	\[ \frac{t - a}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{z}} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z} \]
      associate-/r/ [=>] 45.0	\[ \color{blue}{\frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)} \cdot z} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z} \]
      associate-/l* [=>] 96.5	\[ \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)} \cdot z + \color{blue}{\frac{y}{\frac{y + \left(b - y\right) \cdot z}{x}}} \]
      +-commutative [=>] 96.5	\[ \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)} \cdot z + \frac{y}{\frac{\color{blue}{\left(b - y\right) \cdot z + y}}{x}} \]
      *-commutative [=>] 96.5	\[ \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)} \cdot z + \frac{y}{\frac{\color{blue}{z \cdot \left(b - y\right)} + y}{x}} \]
      fma-udef [<=] 96.5	\[ \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)} \cdot z + \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{x}} \]
      associate-/r/ [=>] 98.5	\[ \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)} \cdot z + \color{blue}{\frac{y}{\mathsf{fma}\left(z, b - y, y\right)} \cdot x} \]

   if -1.00000000000000003e286 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.00000000000000007e-294 or 2e-180 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000002e302

   1. Initial program 99.5%

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

   if -4.00000000000000007e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e-180

   1. Initial program 44.5%

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

   2. Taylor expanded in z around inf 64.6%

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

   3. Simplified 79.6%

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

      [Start] 64.6	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--l+ [=>] 64.6	\[ \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]
      times-frac [=>] 71.9	\[ \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]
      +-commutative [=>] 71.9	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]
      *-commutative [<=] 71.9	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right)\right) \]
      times-frac [=>] 79.6	\[ \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right)\right) \]

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around -inf 38.7%

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

   3. Simplified 99.9%

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

      [Start] 38.7	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      +-commutative [=>] 38.7	\[ \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]
      associate--l+ [=>] 38.7	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+286}:\\ \;\;\;\;z \cdot \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)} + x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-294}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{-180}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;z \cdot \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)} + x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	95.9%
Cost	13972

\[\begin{array}{l} t_1 := \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := x + z \cdot \frac{t - a}{t_2}\\ t_4 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_2}\\ \mathbf{if}\;t_4 \leq -1 \cdot 10^{+286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq -4 \cdot 10^{-294}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	93.9%
Cost	13972

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := x + z \cdot \frac{t - a}{t_1}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_4 := \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -4 \cdot 10^{-294}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-180}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} + \left(\frac{y}{z} \cdot t_4 - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot t_4}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3
Accuracy	91.0%
Cost	6740

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := x + z \cdot \frac{t - a}{t_2}\\ t_4 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_2}\\ \mathbf{if}\;t_4 \leq -1 \cdot 10^{+286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq -4 \cdot 10^{-294}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	44.3%
Cost	1705

\[\begin{array}{l} t_1 := \left(t - a\right) \cdot \frac{z}{y}\\ t_2 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-154}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+33} \lor \neg \left(z \leq 4 \cdot 10^{+45}\right) \land z \leq 8 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b - y}\\ \end{array} \]

Alternative 5
Accuracy	75.0%
Cost	1364

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -90:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-154}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{t_2}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-80}:\\ \;\;\;\;\frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;x + t_2 \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	75.2%
Cost	1364

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -65000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-154}:\\ \;\;\;\;x + z \cdot \frac{t - a}{t_1}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{t_3}{y}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{t_3}{t_1}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;x + t_3 \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	37.4%
Cost	1244

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+264}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+223}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 8
Accuracy	75.6%
Cost	1100

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -90:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-154}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-15}:\\ \;\;\;\;x + \left(z \cdot \left(t - a\right)\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	36.8%
Cost	1048

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+264}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 10
Accuracy	74.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -0.0019 \lor \neg \left(z \leq 9.1 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(t - a\right)\right) \cdot \frac{1}{y}\\ \end{array} \]

Alternative 11
Accuracy	74.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -0.0019 \lor \neg \left(z \leq 1.2 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 12
Accuracy	52.6%
Cost	780

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b - y}\\ \end{array} \]

Alternative 13
Accuracy	68.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-59} \lor \neg \left(z \leq 8.5 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 14
Accuracy	53.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -105000000 \lor \neg \left(y \leq 8.8 \cdot 10^{-61}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 15
Accuracy	35.1%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16
Accuracy	27.1%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023135 
(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)))))