Development.Shake.Progress:decay from shake-0.15.5

Average Error: 35.48% → 8.1%

Time: 33.2s

Precision: binary64

Cost: 12817

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0 \lor \neg \left(t_2 \leq \infty\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\left(t - a\right) \cdot \left(z \cdot \frac{1}{\mathsf{fma}\left(z, b - y, y\right)}\right) + \frac{x \cdot y}{t_1}\\ \end{array} \]

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)) (* x y)) t_1)))
   (if (<= t_2 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_2 -2e-307)
       t_2
       (if (or (<= t_2 0.0) (not (<= t_2 INFINITY)))
         (+
          (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z)
          (/ (- t a) (- b y)))
         (+ (* (- t a) (* z (/ 1.0 (fma z (- b y) y)))) (/ (* x y) t_1)))))))

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)) + (x * y)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -2e-307) {
		tmp = t_2;
	} else if ((t_2 <= 0.0) || !(t_2 <= ((double) INFINITY))) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	} else {
		tmp = ((t - a) * (z * (1.0 / fma(z, (b - y), y)))) + ((x * y) / t_1);
	}
	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(Float64(z * Float64(t - a)) + Float64(x * y)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_2 <= -2e-307)
		tmp = t_2;
	elseif ((t_2 <= 0.0) || !(t_2 <= Inf))
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(t - a) * Float64(z * Float64(1.0 / fma(z, Float64(b - y), y)))) + Float64(Float64(x * y) / t_1));
	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[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-307], t$95$2, If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, Infinity]], $MachinePrecision]], N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t - a), $MachinePrecision] * N[(z * N[(1.0 / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	35.48%
Target	27.63%
Herbie	8.1%

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

Derivation

1. Split input into 4 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 100

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

   2. Simplified 100

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

      [Start] 100	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 100	\[ \frac{\color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]

   3. Taylor expanded in y around -inf 68.31

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

   4. Simplified 43.05

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

      [Start] 68.31	\[ -1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      mul-1-neg [=>] 68.31	\[ -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]
      unsub-neg [=>] 68.31	\[ \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
      mul-1-neg [=>] 68.31	\[ \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      distribute-neg-frac [=>] 68.31	\[ \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   5. Taylor expanded in z around inf 28.15

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999982e-307

   1. Initial program 0.53

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

   if -1.99999999999999982e-307 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 90.21

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

   2. Taylor expanded in z around -inf 43.36

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

   3. Simplified 2.13

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

      [Start] 43.36	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      +-commutative [=>] 43.36	\[ \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]
      associate--l+ [=>] 43.36	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 19.92

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

   2. Taylor expanded in x around inf 19.92

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

   3. Applied egg-rr 13.35

      \[\leadsto \color{blue}{\left(t - a\right) \cdot \left(z \cdot \frac{1}{\mathsf{fma}\left(z, b - y, y\right)}\right)} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 8.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq \infty\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\left(t - a\right) \cdot \left(z \cdot \frac{1}{\mathsf{fma}\left(z, b - y, y\right)}\right) + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	12.77%
Cost	11985

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t_2 + x \cdot y}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{-270} \lor \neg \left(t_3 \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \end{array} \]

Alternative 2
Error	12.77%
Cost	5841

\[\begin{array}{l} t_1 := z \cdot \left(t - a\right) + x \cdot y\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-270} \lor \neg \left(t_2 \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{z \cdot b - y \cdot \left(z + -1\right)}\\ \end{array} \]

Alternative 3
Error	12.77%
Cost	5713

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-307} \lor \neg \left(t_1 \leq 5 \cdot 10^{-270}\right) \land t_1 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4
Error	30.29%
Cost	1488

\[\begin{array}{l} t_1 := \frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-281}:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{z + -1} \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 280000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	35.42%
Cost	1228

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-260}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{elif}\;z \leq 10^{-228}:\\ \;\;\;\;\frac{t - a}{b} + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;z \leq 0.18:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	30.13%
Cost	1224

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+92}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	35.49%
Cost	1100

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-260}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{elif}\;z \leq 10^{-228}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 0.15:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	39.25%
Cost	1036

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2300000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 0.3:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	39.25%
Cost	1036

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{1 - z \cdot z} \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-196}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 0.42:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	49.06%
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-55}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+141}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{1 - z}\\ \end{array} \]

Alternative 11
Error	42.83%
Cost	976

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 900000:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{1 - z}\\ \end{array} \]

Alternative 12
Error	32.46%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-9} \lor \neg \left(z \leq 0.15\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \end{array} \]

Alternative 13
Error	60.34%
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -0.000215:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 0.15:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 14
Error	60.36%
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 0.15:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 15
Error	48.99%
Cost	848

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-53}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+141}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	37.81%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1700000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 17
Error	47.48%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+46} \lor \neg \left(y \leq 1.95 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 18
Error	64.83%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 0.15:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 19
Error	59.71%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 20
Error	66.89%
Cost	520

\[\begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-133}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	64.94%
Cost	520

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 22
Error	63.47%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 23
Error	73.31%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023088 
(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)))))