Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.3 → 8.0

Time: 21.2s

Precision: binary64

Cost: 13972

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_2}\\ t_5 := \frac{t_3}{t_2} + \frac{x \cdot y}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;x\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-197}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+287}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \end{array} \]

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 (+ y (* z (- b y))))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_2))
        (t_5 (+ (/ t_3 t_2) (/ (* x y) t_2))))
   (if (<= t_4 (- INFINITY))
     x
     (if (<= t_4 -5e-197)
       t_5
       (if (<= t_4 0.0)
         t_1
         (if (<= t_4 5e+287)
           t_5
           (if (<= t_4 INFINITY)
             (/ x (- 1.0 z))
             (+
              t_1
              (/
               (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0))))
               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 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_2;
	double t_5 = (t_3 / t_2) + ((x * y) / t_2);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = x;
	} else if (t_4 <= -5e-197) {
		tmp = t_5;
	} else if (t_4 <= 0.0) {
		tmp = t_1;
	} else if (t_4 <= 5e+287) {
		tmp = t_5;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1 + (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
}

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_2;
	double t_5 = (t_3 / t_2) + ((x * y) / t_2);
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = x;
	} else if (t_4 <= -5e-197) {
		tmp = t_5;
	} else if (t_4 <= 0.0) {
		tmp = t_1;
	} else if (t_4 <= 5e+287) {
		tmp = t_5;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1 + (((x * (y / (b - y))) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return ((x * y) + (z * (t - a))) / (y + (z * (b - y)))

↓

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = y + (z * (b - y))
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_2
	t_5 = (t_3 / t_2) + ((x * y) / t_2)
	tmp = 0
	if t_4 <= -math.inf:
		tmp = x
	elif t_4 <= -5e-197:
		tmp = t_5
	elif t_4 <= 0.0:
		tmp = t_1
	elif t_4 <= 5e+287:
		tmp = t_5
	elif t_4 <= math.inf:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1 + (((x * (y / (b - y))) - (y * ((t - a) / math.pow((b - y), 2.0)))) / 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(Float64(t - a) / Float64(b - y))
	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)
	t_5 = Float64(Float64(t_3 / t_2) + Float64(Float64(x * y) / t_2))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = x;
	elseif (t_4 <= -5e-197)
		tmp = t_5;
	elseif (t_4 <= 0.0)
		tmp = t_1;
	elseif (t_4 <= 5e+287)
		tmp = t_5;
	elseif (t_4 <= Inf)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = y + (z * (b - y));
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_2;
	t_5 = (t_3 / t_2) + ((x * y) / t_2);
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = x;
	elseif (t_4 <= -5e-197)
		tmp = t_5;
	elseif (t_4 <= 0.0)
		tmp = t_1;
	elseif (t_4 <= 5e+287)
		tmp = t_5;
	elseif (t_4 <= Inf)
		tmp = x / (1.0 - z);
	else
		tmp = t_1 + (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z);
	end
	tmp_2 = 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[(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]}, Block[{t$95$5 = N[(N[(t$95$3 / t$95$2), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], x, If[LessEqual[t$95$4, -5e-197], t$95$5, If[LessEqual[t$95$4, 0.0], t$95$1, If[LessEqual[t$95$4, 5e+287], t$95$5, If[LessEqual[t$95$4, Infinity], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + 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]), $MachinePrecision]]]]]]]]]]]

Target

Original	23.3
Target	17.7
Herbie	8.0

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

Derivation

1. Split input into 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 0 37.3

      \[\leadsto \color{blue}{x} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000002e-197 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5e287

   1. Initial program 0.3

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

   2. Taylor expanded in x around inf 0.3

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

   if -5.0000000000000002e-197 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 37.3

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

   2. Taylor expanded in z around inf 18.9

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if 5e287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 59.6

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

   2. Taylor expanded in y around inf 34.5

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot z + 1}} \]

   3. Simplified 34.5

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
      Proof
      (/.f64 x (-.f64 1 z)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= unsub-neg_binary64 (+.f64 1 (neg.f64 z)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 z) 1))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (+.f64 (Rewrite=> neg-mul-1_binary64 (*.f64 -1 z)) 1)): 0 points increase in error, 0 points decrease in error

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

   1. Initial program 64.0

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

   2. Simplified 64.0

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}} \]
      Proof
      (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a)))) (+.f64 y (*.f64 z (-.f64 b y)))): 1 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around -inf 38.9

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

   4. Simplified 0.1

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{b - y} \cdot x - \frac{t - a}{{\left(b - y\right)}^{2}} \cdot y\right)}{z} + \frac{t - a}{b - y}} \]
      Proof
      (+.f64 (/.f64 (*.f64 1 (-.f64 (*.f64 (/.f64 y (-.f64 b y)) x) (*.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) y))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 -1 -1)) (-.f64 (*.f64 (/.f64 y (-.f64 b y)) x) (*.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) y))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (*.f64 -1 -1) (-.f64 (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (-.f64 b y) x))) (*.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) y))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 9 points increase in error, 18 points decrease in error
      (+.f64 (/.f64 (*.f64 (*.f64 -1 -1) (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) y))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 34 points increase in error, 10 points decrease in error
      (+.f64 (/.f64 (*.f64 (*.f64 -1 -1) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 t a) (/.f64 (pow.f64 (-.f64 b y) 2) y))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 2 points increase in error, 10 points decrease in error
      (+.f64 (/.f64 (*.f64 (*.f64 -1 -1) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 42 points increase in error, 3 points decrease in error
      (+.f64 (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 -1 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 -1 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z))) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 t (-.f64 b y)) (/.f64 a (-.f64 b y))))): 3 points increase in error, 1 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)) (/.f64 t (-.f64 b y))) (/.f64 a (-.f64 b y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 t (-.f64 b y)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 -1 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) z)))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
3. Recombined 5 regimes into one program.

4. Final simplification 8.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-197}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+287}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	9.8
Cost	6224

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_2}\\ t_5 := \frac{t_3}{t_2} + \frac{x \cdot y}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;x\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-197}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+287}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	9.8
Cost	5712

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	33.0
Cost	1176

\[\begin{array}{l} t_1 := \frac{-a}{b - y}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-30}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 4
Error	32.1
Cost	1176

\[\begin{array}{l} t_1 := \frac{-a}{b - y}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.00018:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{t}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 5
Error	31.6
Cost	1176

\[\begin{array}{l} t_1 := \frac{-a}{b - y}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+207}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 6
Error	37.1
Cost	1112

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	41.3
Cost	1048

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+131}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	37.1
Cost	980

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+208}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	31.2
Cost	848

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.78 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+62}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+94}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	30.9
Cost	848

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.78 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+94}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	17.8
Cost	840

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	17.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 13
Error	20.6
Cost	712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.04 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	30.3
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+94}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	40.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16
Error	46.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022330 
(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)))))