Development.Shake.Progress:decay from shake-0.15.5

Average Accuracy: 62.9% → 91.5%

Time: 36.1s

Precision: binary64

Cost: 12816

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := {\left(b - y\right)}^{2}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_4 := \frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+301}:\\ \;\;\;\;\frac{\frac{a - t}{\frac{z + -1}{z}} - \frac{z}{\frac{{\left(z + -1\right)}^{2}}{x \cdot b}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{-292}:\\ \;\;\;\;\left(\left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \frac{y}{z} \cdot \frac{t - a}{t_2}\right) - \frac{a}{b - y}\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{\frac{t - a}{\frac{t_2}{y}} - \frac{y}{\frac{b - y}{x}}}{z}\\ \end{array} \]

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 (+ y (* z (- b y))))
        (t_2 (pow (- b y) 2.0))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_4 (/ (+ (* x y) (- (* z t) (* z a))) t_1)))
   (if (<= t_3 -1e+301)
     (-
      (/
       (- (/ (- a t) (/ (+ z -1.0) z)) (/ z (/ (pow (+ z -1.0) 2.0) (* x b))))
       y)
      (/ x (+ z -1.0)))
     (if (<= t_3 -2e-296)
       t_4
       (if (<= t_3 4e-292)
         (-
          (-
           (+ (/ t (- b y)) (* (/ y z) (/ x (- b y))))
           (* (/ y z) (/ (- t a) t_2)))
          (/ a (- b y)))
         (if (<= t_3 5e+257)
           t_4
           (-
            (/ (- t a) (- b y))
            (/ (- (/ (- t a) (/ t_2 y)) (/ y (/ (- b y) x))) 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 = y + (z * (b - y));
	double t_2 = pow((b - y), 2.0);
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = ((x * y) + ((z * t) - (z * a))) / t_1;
	double tmp;
	if (t_3 <= -1e+301) {
		tmp = ((((a - t) / ((z + -1.0) / z)) - (z / (pow((z + -1.0), 2.0) / (x * b)))) / y) - (x / (z + -1.0));
	} else if (t_3 <= -2e-296) {
		tmp = t_4;
	} else if (t_3 <= 4e-292) {
		tmp = (((t / (b - y)) + ((y / z) * (x / (b - y)))) - ((y / z) * ((t - a) / t_2))) - (a / (b - y));
	} else if (t_3 <= 5e+257) {
		tmp = t_4;
	} else {
		tmp = ((t - a) / (b - y)) - ((((t - a) / (t_2 / y)) - (y / ((b - y) / x))) / z);
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (b - y) ** 2.0d0
    t_3 = ((x * y) + (z * (t - a))) / t_1
    t_4 = ((x * y) + ((z * t) - (z * a))) / t_1
    if (t_3 <= (-1d+301)) then
        tmp = ((((a - t) / ((z + (-1.0d0)) / z)) - (z / (((z + (-1.0d0)) ** 2.0d0) / (x * b)))) / y) - (x / (z + (-1.0d0)))
    else if (t_3 <= (-2d-296)) then
        tmp = t_4
    else if (t_3 <= 4d-292) then
        tmp = (((t / (b - y)) + ((y / z) * (x / (b - y)))) - ((y / z) * ((t - a) / t_2))) - (a / (b - y))
    else if (t_3 <= 5d+257) then
        tmp = t_4
    else
        tmp = ((t - a) / (b - y)) - ((((t - a) / (t_2 / y)) - (y / ((b - y) / x))) / z)
    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 = Math.pow((b - y), 2.0);
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = ((x * y) + ((z * t) - (z * a))) / t_1;
	double tmp;
	if (t_3 <= -1e+301) {
		tmp = ((((a - t) / ((z + -1.0) / z)) - (z / (Math.pow((z + -1.0), 2.0) / (x * b)))) / y) - (x / (z + -1.0));
	} else if (t_3 <= -2e-296) {
		tmp = t_4;
	} else if (t_3 <= 4e-292) {
		tmp = (((t / (b - y)) + ((y / z) * (x / (b - y)))) - ((y / z) * ((t - a) / t_2))) - (a / (b - y));
	} else if (t_3 <= 5e+257) {
		tmp = t_4;
	} else {
		tmp = ((t - a) / (b - y)) - ((((t - a) / (t_2 / y)) - (y / ((b - y) / x))) / 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 = y + (z * (b - y))
	t_2 = math.pow((b - y), 2.0)
	t_3 = ((x * y) + (z * (t - a))) / t_1
	t_4 = ((x * y) + ((z * t) - (z * a))) / t_1
	tmp = 0
	if t_3 <= -1e+301:
		tmp = ((((a - t) / ((z + -1.0) / z)) - (z / (math.pow((z + -1.0), 2.0) / (x * b)))) / y) - (x / (z + -1.0))
	elif t_3 <= -2e-296:
		tmp = t_4
	elif t_3 <= 4e-292:
		tmp = (((t / (b - y)) + ((y / z) * (x / (b - y)))) - ((y / z) * ((t - a) / t_2))) - (a / (b - y))
	elif t_3 <= 5e+257:
		tmp = t_4
	else:
		tmp = ((t - a) / (b - y)) - ((((t - a) / (t_2 / y)) - (y / ((b - y) / x))) / 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(y + Float64(z * Float64(b - y)))
	t_2 = Float64(b - y) ^ 2.0
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_4 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1)
	tmp = 0.0
	if (t_3 <= -1e+301)
		tmp = Float64(Float64(Float64(Float64(Float64(a - t) / Float64(Float64(z + -1.0) / z)) - Float64(z / Float64((Float64(z + -1.0) ^ 2.0) / Float64(x * b)))) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_3 <= -2e-296)
		tmp = t_4;
	elseif (t_3 <= 4e-292)
		tmp = Float64(Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) - Float64(Float64(y / z) * Float64(Float64(t - a) / t_2))) - Float64(a / Float64(b - y)));
	elseif (t_3 <= 5e+257)
		tmp = t_4;
	else
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(Float64(Float64(Float64(t - a) / Float64(t_2 / y)) - Float64(y / Float64(Float64(b - y) / x))) / 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 = y + (z * (b - y));
	t_2 = (b - y) ^ 2.0;
	t_3 = ((x * y) + (z * (t - a))) / t_1;
	t_4 = ((x * y) + ((z * t) - (z * a))) / t_1;
	tmp = 0.0;
	if (t_3 <= -1e+301)
		tmp = ((((a - t) / ((z + -1.0) / z)) - (z / (((z + -1.0) ^ 2.0) / (x * b)))) / y) - (x / (z + -1.0));
	elseif (t_3 <= -2e-296)
		tmp = t_4;
	elseif (t_3 <= 4e-292)
		tmp = (((t / (b - y)) + ((y / z) * (x / (b - y)))) - ((y / z) * ((t - a) / t_2))) - (a / (b - y));
	elseif (t_3 <= 5e+257)
		tmp = t_4;
	else
		tmp = ((t - a) / (b - y)) - ((((t - a) / (t_2 / y)) - (y / ((b - y) / x))) / 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[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+301], N[(N[(N[(N[(N[(a - t), $MachinePrecision] / N[(N[(z + -1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(z / N[(N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision] / N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-296], t$95$4, If[LessEqual[t$95$3, 4e-292], N[(N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+257], t$95$4, N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t - a), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Target

Original	62.9%
Target	71.3%
Herbie	91.5%

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

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)))) < -1.00000000000000005e301

   1. Initial program 2.0%

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

   2. Taylor expanded in y around -inf 37.0%

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

   3. Simplified 59.7%

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

      [Start] 37.0	\[ -1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      mul-1-neg [=>] 37.0	\[ -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]
      unsub-neg [=>] 37.0	\[ \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
      mul-1-neg [=>] 37.0	\[ \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      distribute-neg-frac [=>] 37.0	\[ \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      cancel-sign-sub-inv [=>] 37.0	\[ \frac{-x}{z - 1} - \frac{\color{blue}{\frac{\left(t - a\right) \cdot z}{z - 1} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]
      associate-/l* [=>] 56.7	\[ \frac{-x}{z - 1} - \frac{\color{blue}{\frac{t - a}{\frac{z - 1}{z}}} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      metadata-eval [=>] 56.7	\[ \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{1} \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]
      *-lft-identity [=>] 56.7	\[ \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]
      associate-/l* [=>] 59.7	\[ \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}}{y} \]

   if -1.00000000000000005e301 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-296 or 4.0000000000000002e-292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000028e257

   1. Initial program 99.5%

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

   2. Taylor expanded in t around 0 99.5%

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

   if -2e-296 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.0000000000000002e-292

   1. Initial program 29.8%

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

   2. Simplified 29.8%

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

      [Start] 29.8	\[ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
      fma-def [=>] 29.8	\[ \frac{\color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}}{y + z \cdot \left(b - y\right)} \]
      +-commutative [=>] 29.8	\[ \frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\color{blue}{z \cdot \left(b - y\right) + y}} \]
      fma-def [=>] 29.8	\[ \frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}} \]

   3. Taylor expanded in z around inf 69.7%

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

   4. Simplified 91.4%

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

      [Start] 69.7	\[ \left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right) \]
      associate--r+ [=>] 69.7	\[ \color{blue}{\left(\left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right) - \frac{a}{b - y}} \]
      +-commutative [=>] 69.7	\[ \left(\color{blue}{\left(\frac{t}{b - y} + \frac{y \cdot x}{z \cdot \left(b - y\right)}\right)} - \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right) - \frac{a}{b - y} \]
      times-frac [=>] 81.7	\[ \left(\left(\frac{t}{b - y} + \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}}\right) - \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right) - \frac{a}{b - y} \]
      *-commutative [<=] 81.7	\[ \left(\left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \frac{\left(t - a\right) \cdot y}{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}\right) - \frac{a}{b - y} \]
      times-frac [=>] 91.4	\[ \left(\left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}}\right) - \frac{a}{b - y} \]

   if 5.00000000000000028e257 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 6.4%

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

   2. Taylor expanded in z around -inf 35.6%

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

   3. Simplified 82.5%

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

      [Start] 35.6	\[ \left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y} \]
      +-commutative [=>] 35.6	\[ \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]
      associate--l+ [=>] 35.6	\[ \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+301}:\\ \;\;\;\;\frac{\frac{a - t}{\frac{z + -1}{z}} - \frac{z}{\frac{{\left(z + -1\right)}^{2}}{x \cdot b}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-296}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{-292}:\\ \;\;\;\;\left(\left(\frac{t}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right) - \frac{a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{\frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}} - \frac{y}{\frac{b - y}{x}}}{z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.4%
Cost	12817

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+301}:\\ \;\;\;\;\frac{\frac{a - t}{\frac{z + -1}{z}} - \frac{z}{\frac{{\left(z + -1\right)}^{2}}{x \cdot b}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-296} \lor \neg \left(t_2 \leq 4 \cdot 10^{-292}\right) \land t_2 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{\frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}} - \frac{y}{\frac{b - y}{x}}}{z}\\ \end{array} \]

Alternative 2
Accuracy	88.6%
Cost	9348

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+301}:\\ \;\;\;\;\frac{\frac{a - t}{\frac{z + -1}{z}} - \frac{z}{\frac{{\left(z + -1\right)}^{2}}{x \cdot b}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{-292}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 3
Accuracy	88.5%
Cost	8132

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{-292}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 4
Accuracy	88.0%
Cost	5840

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+301}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{-292}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 5
Accuracy	88.0%
Cost	5712

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+301}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{-292}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 6
Accuracy	42.4%
Cost	1112

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{a - t}{y}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+168}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	70.2%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-33} \lor \neg \left(z \leq 1.16 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 8
Accuracy	52.3%
Cost	912

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6500000:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+89}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	68.4%
Cost	836

\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10
Accuracy	68.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-35} \lor \neg \left(z \leq 1.46 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 11
Accuracy	45.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-71} \lor \neg \left(z \leq 7.1 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	43.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+43} \lor \neg \left(y \leq 3.5 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 13
Accuracy	52.3%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+43} \lor \neg \left(y \leq 7.5 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 14
Accuracy	35.0%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-11}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 15
Accuracy	35.9%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-36} \lor \neg \left(z \leq 6.2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Accuracy	34.9%
Cost	520

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 17
Accuracy	25.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023147 
(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)))))