Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.2 → 6.6

Time: 33.7s

Precision: binary64

Cost: 8720

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} - \frac{\frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}} - \frac{y}{b - y} \cdot x}{z}\\ \mathbf{if}\;z \leq -15500000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{-126}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{t_1}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-250}:\\ \;\;\;\;\frac{z \cdot \frac{a - t}{z + -1} - \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(z \cdot x\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+15}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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
         (-
          (/ (- t a) (- b y))
          (/ (- (/ (- t a) (/ (pow (- b y) 2.0) y)) (* (/ y (- b y)) x)) z))))
   (if (<= z -15500000.0)
     t_2
     (if (<= z -9.4e-126)
       (/ (+ (* y x) (* z (- t a))) t_1)
       (if (<= z 2.8e-250)
         (-
          (/
           (-
            (* z (/ (- a t) (+ z -1.0)))
            (* (/ b (pow (+ z -1.0) 2.0)) (* z x)))
           y)
          (/ x (+ z -1.0)))
         (if (<= z 3e+15) (/ (+ (* y x) (- (* z t) (* z a))) t_1) t_2))))))

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 = ((t - a) / (b - y)) - ((((t - a) / (pow((b - y), 2.0) / y)) - ((y / (b - y)) * x)) / z);
	double tmp;
	if (z <= -15500000.0) {
		tmp = t_2;
	} else if (z <= -9.4e-126) {
		tmp = ((y * x) + (z * (t - a))) / t_1;
	} else if (z <= 2.8e-250) {
		tmp = (((z * ((a - t) / (z + -1.0))) - ((b / pow((z + -1.0), 2.0)) * (z * x))) / y) - (x / (z + -1.0));
	} else if (z <= 3e+15) {
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
end function

↓

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = ((t - a) / (b - y)) - ((((t - a) / (((b - y) ** 2.0d0) / y)) - ((y / (b - y)) * x)) / z)
    if (z <= (-15500000.0d0)) then
        tmp = t_2
    else if (z <= (-9.4d-126)) then
        tmp = ((y * x) + (z * (t - a))) / t_1
    else if (z <= 2.8d-250) then
        tmp = (((z * ((a - t) / (z + (-1.0d0)))) - ((b / ((z + (-1.0d0)) ** 2.0d0)) * (z * x))) / y) - (x / (z + (-1.0d0)))
    else if (z <= 3d+15) then
        tmp = ((y * x) + ((z * t) - (z * a))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

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 = y + (z * (b - y));
	double t_2 = ((t - a) / (b - y)) - ((((t - a) / (Math.pow((b - y), 2.0) / y)) - ((y / (b - y)) * x)) / z);
	double tmp;
	if (z <= -15500000.0) {
		tmp = t_2;
	} else if (z <= -9.4e-126) {
		tmp = ((y * x) + (z * (t - a))) / t_1;
	} else if (z <= 2.8e-250) {
		tmp = (((z * ((a - t) / (z + -1.0))) - ((b / Math.pow((z + -1.0), 2.0)) * (z * x))) / y) - (x / (z + -1.0));
	} else if (z <= 3e+15) {
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = t_2;
	}
	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 = y + (z * (b - y))
	t_2 = ((t - a) / (b - y)) - ((((t - a) / (math.pow((b - y), 2.0) / y)) - ((y / (b - y)) * x)) / z)
	tmp = 0
	if z <= -15500000.0:
		tmp = t_2
	elif z <= -9.4e-126:
		tmp = ((y * x) + (z * (t - a))) / t_1
	elif z <= 2.8e-250:
		tmp = (((z * ((a - t) / (z + -1.0))) - ((b / math.pow((z + -1.0), 2.0)) * (z * x))) / y) - (x / (z + -1.0))
	elif z <= 3e+15:
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1
	else:
		tmp = t_2
	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(t - a) / Float64(b - y)) - Float64(Float64(Float64(Float64(t - a) / Float64((Float64(b - y) ^ 2.0) / y)) - Float64(Float64(y / Float64(b - y)) * x)) / z))
	tmp = 0.0
	if (z <= -15500000.0)
		tmp = t_2;
	elseif (z <= -9.4e-126)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / t_1);
	elseif (z <= 2.8e-250)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(a - t) / Float64(z + -1.0))) - Float64(Float64(b / (Float64(z + -1.0) ^ 2.0)) * Float64(z * x))) / y) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 3e+15)
		tmp = Float64(Float64(Float64(y * x) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	else
		tmp = t_2;
	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 = y + (z * (b - y));
	t_2 = ((t - a) / (b - y)) - ((((t - a) / (((b - y) ^ 2.0) / y)) - ((y / (b - y)) * x)) / z);
	tmp = 0.0;
	if (z <= -15500000.0)
		tmp = t_2;
	elseif (z <= -9.4e-126)
		tmp = ((y * x) + (z * (t - a))) / t_1;
	elseif (z <= 2.8e-250)
		tmp = (((z * ((a - t) / (z + -1.0))) - ((b / ((z + -1.0) ^ 2.0)) * (z * x))) / y) - (x / (z + -1.0));
	elseif (z <= 3e+15)
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	else
		tmp = t_2;
	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[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t - a), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -15500000.0], t$95$2, If[LessEqual[z, -9.4e-126], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 2.8e-250], N[(N[(N[(N[(z * N[(N[(a - t), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b / N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+15], N[(N[(N[(y * x), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Target

Original	23.2
Target	17.7
Herbie	6.6

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

Derivation

1. Split input into 4 regimes

2. if z < -1.55e7 or 3e15 < z

   1. Initial program 38.7

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

   2. Taylor expanded in z around -inf 20.4

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

   3. Simplified 2.1

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

      [Start] 20.4	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      +-commutative [=>] 20.4	\[ \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]
      associate--l+ [=>] 20.4	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   if -1.55e7 < z < -9.40000000000000035e-126

   1. Initial program 9.0

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

   if -9.40000000000000035e-126 < z < 2.80000000000000028e-250

   1. Initial program 9.2

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

   2. Simplified 9.2

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

      [Start] 9.2	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      *-commutative [=>] 9.2	\[ \frac{\color{blue}{y \cdot x} + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 9.2	\[ \frac{\color{blue}{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]
      +-commutative [=>] 9.2	\[ \frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\color{blue}{z \cdot \left(b - y\right) + y}} \]
      fma-def [=>] 9.2	\[ \frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}} \]

   3. Taylor expanded in y around -inf 18.2

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

   4. Simplified 13.8

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

      [Start] 18.2	\[ -1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      mul-1-neg [=>] 18.2	\[ -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]
      unsub-neg [=>] 18.2	\[ \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
      mul-1-neg [=>] 18.2	\[ \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      distribute-neg-frac [=>] 18.2	\[ \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      sub-neg [=>] 18.2	\[ \frac{-x}{\color{blue}{z + \left(-1\right)}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      metadata-eval [=>] 18.2	\[ \frac{-x}{z + \color{blue}{-1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   if 2.80000000000000028e-250 < z < 3e15

   1. Initial program 8.8

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

   2. Applied egg-rr 8.8

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

4. Final simplification 6.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15500000:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{\frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}} - \frac{y}{b - y} \cdot x}{z}\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{-126}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-250}:\\ \;\;\;\;\frac{z \cdot \frac{a - t}{z + -1} - \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(z \cdot x\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+15}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{\frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}} - \frac{y}{b - y} \cdot x}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	9.2
Cost	11404

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := y \cdot x + z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t_1}{y}}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-298}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+256}:\\ \;\;\;\;\frac{t_2}{y \cdot \left(1 - z\right) + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 2
Error	9.2
Cost	5841

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := y \cdot x + z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t_1}{y}}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-298}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq 0 \lor \neg \left(t_3 \leq 2 \cdot 10^{+256}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{y \cdot \left(1 - z\right) + z \cdot b}\\ \end{array} \]

Alternative 3
Error	9.2
Cost	5713

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{y \cdot x + z \cdot \left(t - a\right)}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t_1}{y}}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-298} \lor \neg \left(t_2 \leq 0\right) \land t_2 \leq 2 \cdot 10^{+256}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4
Error	9.2
Cost	5713

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{y \cdot x + z \cdot \left(t - a\right)}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t_1}{y}}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-298}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2 \cdot 10^{+256}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	18.4
Cost	2012

\[\begin{array}{l} t_1 := y \cdot x + z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{t_1}{y}\\ t_4 := x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;t_1 \cdot \frac{\frac{1}{z}}{b - y}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-216}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-251}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-150}:\\ \;\;\;\;\frac{1}{\frac{y + z \cdot \left(b - y\right)}{y \cdot x + z \cdot t}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-143}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-10}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	18.8
Cost	1496

\[\begin{array}{l} t_1 := y \cdot x + z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-38}:\\ \;\;\;\;\frac{t_1}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-204}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{t_1}{y}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	18.7
Cost	1496

\[\begin{array}{l} t_1 := y \cdot x + z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \mathbf{if}\;z \leq -1.36 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-41}:\\ \;\;\;\;t_1 \cdot \frac{\frac{1}{z}}{b - y}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-276}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-143}:\\ \;\;\;\;\frac{t_1}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-15}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	42.4
Cost	1312

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+275}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	19.4
Cost	1232

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-279}:\\ \;\;\;\;\frac{x}{\frac{y + z \cdot \left(b - y\right)}{y}}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-143}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-11}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	36.6
Cost	1112

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	19.3
Cost	1100

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	19.3
Cost	1100

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-142}:\\ \;\;\;\;\frac{x}{\frac{y + z \cdot \left(b - y\right)}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} - \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	30.3
Cost	980

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -900:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-71}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	20.0
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-20} \lor \neg \left(z \leq 5.1 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \end{array} \]

Alternative 15
Error	43.6
Cost	784

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+180}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+274}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	19.7
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{-26} \lor \neg \left(z \leq 4.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 17
Error	40.0
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-26} \lor \neg \left(z \leq 3.9 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	47.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(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)))))