Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.5 → 4.2

Time: 31.4s

Precision: binary64

Cost: 20372

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z}, \frac{x}{b - y}, \frac{t - a}{b - y} + \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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
         (fma
          (/ y z)
          (/ x (- b y))
          (+ (/ (- t a) (- b y)) (* (/ y (pow (- b y) 2.0)) (/ (- a t) z)))))
        (t_2 (/ (+ (* x y) (* z (- t a))) (- y (* z (- y b))))))
   (if (<= t_2 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_2 -5e-256)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 5e+305)
           (/ (fma z (- t a) (* x y)) (fma z (- b y) y))
           (if (<= t_2 INFINITY) (- (/ (- x) (+ z -1.0)) (/ t 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 = fma((y / z), (x / (b - y)), (((t - a) / (b - y)) + ((y / pow((b - y), 2.0)) * ((a - t) / z))));
	double t_2 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -5e-256) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+305) {
		tmp = fma(z, (t - a), (x * y)) / fma(z, (b - y), y);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (-x / (z + -1.0)) - (t / y);
	} else {
		tmp = 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 = fma(Float64(y / z), Float64(x / Float64(b - y)), Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(y / (Float64(b - y) ^ 2.0)) * Float64(Float64(a - t) / z))))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y - Float64(z * Float64(y - b))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_2 <= -5e-256)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+305)
		tmp = Float64(fma(z, Float64(t - a), Float64(x * y)) / fma(z, Float64(b - y), y));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(Float64(-x) / Float64(z + -1.0)) - Float64(t / y));
	else
		tmp = 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[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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, -5e-256], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 5e+305], N[(N[(z * N[(t - a), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[((-x) / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] - N[(t / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Target

Original	23.5
Target	18.5
Herbie	4.2

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

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 y around -inf 41.5

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

   3. Simplified 26.5

      \[\leadsto \color{blue}{\left(-\frac{x}{z + -1}\right) - \frac{\frac{t - a}{\frac{z + -1}{z}} + \frac{z}{{\left(z + -1\right)}^{2}} \cdot \left(b \cdot x\right)}{y}} \]
      Proof
      (-.f64 (neg.f64 (/.f64 x (+.f64 z -1))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z -1) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (neg.f64 (/.f64 x (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z -1) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (neg.f64 (/.f64 x (Rewrite<= sub-neg_binary64 (-.f64 z 1)))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z -1) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 x (-.f64 z 1)))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z -1) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1))) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 45 points increase in error, 5 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 (/.f64 z (pow.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 (/.f64 z (pow.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (Rewrite<= associate-/r/_binary64 (/.f64 z (/.f64 (pow.f64 (-.f64 z 1) 2) (*.f64 b x))))) y)): 3 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2)))) y)): 8 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2))))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2)))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 -1 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2))))) y)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (neg.f64 (/.f64 (-.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 -1 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2)))) y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 -1 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2)))) y)))): 0 points increase in error, 0 points decrease in error

   4. Taylor expanded in z around inf 16.5

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5e-256

   1. Initial program 0.3

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

   if -5e-256 < (/.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 55.1

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

   2. Simplified 55.1

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}} \]
      Proof
      (/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 t a)) (*.f64 x y))) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 b y)) y))): 1 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (Rewrite<= +-commutative_binary64 (+.f64 y (*.f64 z (-.f64 b y))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 31.1

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

   4. Simplified 3.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z}, \frac{x}{b - y}, \frac{t - a}{b - y} - \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\right)} \]
      Proof
      (fma.f64 (/.f64 y z) (/.f64 x (-.f64 b y)) (-.f64 (/.f64 (-.f64 t a) (-.f64 b y)) (*.f64 (/.f64 (-.f64 t a) z) (/.f64 y (pow.f64 (-.f64 b y) 2))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 y z) (/.f64 x (-.f64 b y)) (-.f64 (Rewrite=> div-sub_binary64 (-.f64 (/.f64 t (-.f64 b y)) (/.f64 a (-.f64 b y)))) (*.f64 (/.f64 (-.f64 t a) z) (/.f64 y (pow.f64 (-.f64 b y) 2))))): 1 points increase in error, 1 points decrease in error
      (fma.f64 (/.f64 y z) (/.f64 x (-.f64 b y)) (-.f64 (-.f64 (/.f64 t (-.f64 b y)) (/.f64 a (-.f64 b y))) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 z (pow.f64 (-.f64 b y) 2)))))): 37 points increase in error, 13 points decrease in error
      (fma.f64 (/.f64 y z) (/.f64 x (-.f64 b y)) (-.f64 (-.f64 (/.f64 t (-.f64 b y)) (/.f64 a (-.f64 b y))) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite=> *-commutative_binary64 (*.f64 (pow.f64 (-.f64 b y) 2) z))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 y z) (/.f64 x (-.f64 b y)) (Rewrite<= associate--r+_binary64 (-.f64 (/.f64 t (-.f64 b y)) (+.f64 (/.f64 a (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 y z) (/.f64 x (-.f64 b y)) (-.f64 (/.f64 t (-.f64 b y)) (+.f64 (/.f64 a (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite<= *-commutative_binary64 (*.f64 z (pow.f64 (-.f64 b y) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (/.f64 y z) (/.f64 x (-.f64 b y)) (-.f64 (/.f64 t (-.f64 b y)) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 z (pow.f64 (-.f64 b y) 2))) (/.f64 a (-.f64 b y)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 y z) (/.f64 x (-.f64 b y))) (-.f64 (/.f64 t (-.f64 b y)) (+.f64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 z (pow.f64 (-.f64 b y) 2))) (/.f64 a (-.f64 b y)))))): 1 points increase in error, 1 points decrease in error
      (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y)))) (-.f64 (/.f64 t (-.f64 b y)) (+.f64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 z (pow.f64 (-.f64 b y) 2))) (/.f64 a (-.f64 b y))))): 21 points increase in error, 21 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (/.f64 t (-.f64 b y))) (+.f64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 z (pow.f64 (-.f64 b y) 2))) (/.f64 a (-.f64 b y))))): 1 points increase in error, 0 points decrease in error

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000009e305

   1. Initial program 0.3

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

   2. Simplified 0.3

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}} \]
      Proof
      (/.f64 (fma.f64 z (-.f64 t a) (*.f64 x y)) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 t a)) (*.f64 x y))) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a)))) (fma.f64 z (-.f64 b y) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 b y)) y))): 1 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (Rewrite<= +-commutative_binary64 (+.f64 y (*.f64 z (-.f64 b y))))): 0 points increase in error, 0 points decrease in error

   if 5.00000000000000009e305 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 63.5

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

   2. Taylor expanded in y around -inf 43.2

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

   3. Simplified 26.3

      \[\leadsto \color{blue}{\left(-\frac{x}{z + -1}\right) - \frac{\frac{t - a}{\frac{z + -1}{z}} + \frac{z}{{\left(z + -1\right)}^{2}} \cdot \left(b \cdot x\right)}{y}} \]
      Proof
      (-.f64 (neg.f64 (/.f64 x (+.f64 z -1))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z -1) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (neg.f64 (/.f64 x (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z -1) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (neg.f64 (/.f64 x (Rewrite<= sub-neg_binary64 (-.f64 z 1)))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z -1) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 x (-.f64 z 1)))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z -1) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (-.f64 t a) (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) z)) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1))) (*.f64 (/.f64 z (pow.f64 (+.f64 z -1) 2)) (*.f64 b x))) y)): 45 points increase in error, 5 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 (/.f64 z (pow.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 (/.f64 z (pow.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) 2)) (*.f64 b x))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (Rewrite<= associate-/r/_binary64 (/.f64 z (/.f64 (pow.f64 (-.f64 z 1) 2) (*.f64 b x))))) y)): 3 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2)))) y)): 8 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2))))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (+.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2)))) y)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 -1 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2))))) y)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (neg.f64 (/.f64 (-.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 -1 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2)))) y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 x (-.f64 z 1))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 (/.f64 (*.f64 (-.f64 t a) z) (-.f64 z 1)) (*.f64 -1 (/.f64 (*.f64 z (*.f64 b x)) (pow.f64 (-.f64 z 1) 2)))) y)))): 0 points increase in error, 0 points decrease in error

   4. Taylor expanded in t around inf 32.4

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

   5. Simplified 25.4

      \[\leadsto \left(-\frac{x}{z + -1}\right) - \color{blue}{\frac{\frac{t}{\frac{z + -1}{z}}}{y}} \]
      Proof
      (/.f64 (/.f64 t (/.f64 (+.f64 z -1) z)) y): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 t (+.f64 z -1)) z)) y): 28 points increase in error, 21 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 (/.f64 t (+.f64 z -1)) (/.f64 z y))): 51 points increase in error, 39 points decrease in error
      (Rewrite<= times-frac_binary64 (/.f64 (*.f64 t z) (*.f64 (+.f64 z -1) y))): 62 points increase in error, 54 points decrease in error
      (/.f64 (*.f64 t z) (*.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) y)): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 t z) (*.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) y)): 0 points increase in error, 0 points decrease in error

   6. Taylor expanded in z around inf 25.6

      \[\leadsto \left(-\frac{x}{z + -1}\right) - \color{blue}{\frac{t}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 4.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -5 \cdot 10^{-256}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, \frac{x}{b - y}, \frac{t - a}{b - y} + \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq \infty:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, \frac{x}{b - y}, \frac{t - a}{b - y} + \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	7.3
Cost	18256

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	7.3
Cost	6420

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	21.4
Cost	1892

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{b \cdot \frac{z}{x}} - \frac{a}{b}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-227}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-251}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	24.0
Cost	1760

\[\begin{array}{l} t_1 := x + z \cdot \left(x + \frac{t}{y}\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.82 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{b \cdot \frac{z}{x}} - \frac{a}{b}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	21.3
Cost	1760

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{y + z \cdot b}\\ t_4 := \frac{x \cdot y + t_2}{y}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{b \cdot \frac{z}{x}} - \frac{a}{b}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-227}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-181}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-70}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	36.7
Cost	1640

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b}\\ t_3 := \frac{a - t}{y}\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-251}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{+188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+207}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	19.4
Cost	1624

\[\begin{array}{l} t_1 := x - \frac{z \cdot \left(x \cdot b + \left(a - t\right)\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -0.3:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{b \cdot \frac{z}{x}} - \frac{a}{b}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	19.2
Cost	1624

\[\begin{array}{l} t_1 := x - \frac{z \cdot \left(x \cdot b + \left(a - t\right)\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b} + \frac{t - a}{b}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-134}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	23.4
Cost	1500

\[\begin{array}{l} t_1 := x + z \cdot \left(x + \frac{t}{y}\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-21}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	23.4
Cost	1500

\[\begin{array}{l} t_1 := x + z \cdot \left(x + \frac{t}{y}\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -0.36:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{b \cdot \frac{z}{x}} - \frac{a}{b}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	22.6
Cost	1496

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{b \cdot \frac{z}{x}} - \frac{a}{b}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-168}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	11.9
Cost	1356

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.02:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 1800000000:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	12.0
Cost	1356

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.82 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{z \cdot t}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 1450000000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	25.2
Cost	1240

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.82 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7200:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	25.2
Cost	1240

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := y + z \cdot b\\ \mathbf{if}\;z \leq -1.82 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{t_3}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 16500:\\ \;\;\;\;\frac{z \cdot t}{t_3}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	37.5
Cost	1112

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	42.2
Cost	984

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-142}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1950000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	25.2
Cost	976

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.82 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	41.3
Cost	784

\[\begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+49}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -0.24:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.85 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-\frac{t}{y}\\ \end{array} \]

Alternative 20
Error	41.3
Cost	784

\[\begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -0.24:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-29}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-\frac{t}{y}\\ \end{array} \]

Alternative 21
Error	30.2
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-48}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	41.5
Cost	520

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-20}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\frac{t}{y}\\ \end{array} \]

Alternative 23
Error	40.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 24
Error	47.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022325 
(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)))))