Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.4 → 1.1

Time: 49.9s

Precision: binary64

Cost: 42772

Math

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

↓

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := {\left(b - y\right)}^{2}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ t_5 := \frac{t_3 + x \cdot y}{t_1}\\ t_6 := \mathsf{fma}\left(z, b - y, y\right)\\ t_7 := x \cdot \frac{y}{t_6} + z \cdot \frac{t - a}{t_6}\\ t_8 := \frac{y}{b - y}\\ t_9 := t_8 \cdot \left(x + \frac{a - t}{b - y}\right)\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-247}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 4 \cdot 10^{-277}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{t_9}{z}\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_8 \cdot \left(\frac{x}{z} - \frac{t_9}{z \cdot z}\right) + \left(\mathsf{fma}\left(\frac{y}{\frac{t_2}{y}}, \frac{t_9}{{z}^{3}}, \frac{t}{b - y}\right) - \mathsf{fma}\left(\frac{t - a}{t_2}, \frac{y}{z}, \frac{a}{b - y}\right)\right)\\ \end{array} \]

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 (* z (- t a)))
        (t_4 (+ (/ t_3 t_1) (/ (* x y) t_1)))
        (t_5 (/ (+ t_3 (* x y)) t_1))
        (t_6 (fma z (- b y) y))
        (t_7 (+ (* x (/ y t_6)) (* z (/ (- t a) t_6))))
        (t_8 (/ y (- b y)))
        (t_9 (* t_8 (+ x (/ (- a t) (- b y))))))
   (if (<= t_5 (- INFINITY))
     t_7
     (if (<= t_5 -2e-247)
       t_4
       (if (<= t_5 4e-277)
         (+ (/ (- t a) (- b y)) (/ t_9 z))
         (if (<= t_5 2e+295)
           t_4
           (if (<= t_5 INFINITY)
             t_7
             (+
              (* t_8 (- (/ x z) (/ t_9 (* z z))))
              (-
               (fma (/ y (/ t_2 y)) (/ t_9 (pow z 3.0)) (/ t (- b y)))
               (fma (/ (- t a) t_2) (/ y z) (/ a (- b y))))))))))))

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 = z * (t - a);
	double t_4 = (t_3 / t_1) + ((x * y) / t_1);
	double t_5 = (t_3 + (x * y)) / t_1;
	double t_6 = fma(z, (b - y), y);
	double t_7 = (x * (y / t_6)) + (z * ((t - a) / t_6));
	double t_8 = y / (b - y);
	double t_9 = t_8 * (x + ((a - t) / (b - y)));
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_7;
	} else if (t_5 <= -2e-247) {
		tmp = t_4;
	} else if (t_5 <= 4e-277) {
		tmp = ((t - a) / (b - y)) + (t_9 / z);
	} else if (t_5 <= 2e+295) {
		tmp = t_4;
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_7;
	} else {
		tmp = (t_8 * ((x / z) - (t_9 / (z * z)))) + (fma((y / (t_2 / y)), (t_9 / pow(z, 3.0)), (t / (b - y))) - fma(((t - a) / t_2), (y / z), (a / (b - y))));
	}
	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(z * Float64(t - a))
	t_4 = Float64(Float64(t_3 / t_1) + Float64(Float64(x * y) / t_1))
	t_5 = Float64(Float64(t_3 + Float64(x * y)) / t_1)
	t_6 = fma(z, Float64(b - y), y)
	t_7 = Float64(Float64(x * Float64(y / t_6)) + Float64(z * Float64(Float64(t - a) / t_6)))
	t_8 = Float64(y / Float64(b - y))
	t_9 = Float64(t_8 * Float64(x + Float64(Float64(a - t) / Float64(b - y))))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_7;
	elseif (t_5 <= -2e-247)
		tmp = t_4;
	elseif (t_5 <= 4e-277)
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(t_9 / z));
	elseif (t_5 <= 2e+295)
		tmp = t_4;
	elseif (t_5 <= Inf)
		tmp = t_7;
	else
		tmp = Float64(Float64(t_8 * Float64(Float64(x / z) - Float64(t_9 / Float64(z * z)))) + Float64(fma(Float64(y / Float64(t_2 / y)), Float64(t_9 / (z ^ 3.0)), Float64(t / Float64(b - y))) - fma(Float64(Float64(t - a) / t_2), Float64(y / z), Float64(a / Float64(b - y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x * N[(y / t$95$6), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(t - a), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$8 * N[(x + N[(N[(a - t), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$7, If[LessEqual[t$95$5, -2e-247], t$95$4, If[LessEqual[t$95$5, 4e-277], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(t$95$9 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 2e+295], t$95$4, If[LessEqual[t$95$5, Infinity], t$95$7, N[(N[(t$95$8 * N[(N[(x / z), $MachinePrecision] - N[(t$95$9 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] * N[(t$95$9 / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision] * N[(y / z), $MachinePrecision] + N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Target

Original	23.4
Target	18.3
Herbie	1.1

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 2e295 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 62.1

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

   2. Taylor expanded in x around 0 62.1

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

   3. Simplified 0.9

      \[\leadsto \color{blue}{\frac{y}{\mathsf{fma}\left(z, b - y, y\right)} \cdot x + \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)} \cdot z} \]
      Proof
      (+.f64 (*.f64 (/.f64 y (fma.f64 z (-.f64 b y) y)) x) (*.f64 (/.f64 (-.f64 t a) (fma.f64 z (-.f64 b y) y)) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 y (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 b y)) y))) x) (*.f64 (/.f64 (-.f64 t a) (fma.f64 z (-.f64 b y) y)) z)): 0 points increase in error, 1 points decrease in error
      (+.f64 (*.f64 (/.f64 y (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 b y) z)) y)) x) (*.f64 (/.f64 (-.f64 t a) (fma.f64 z (-.f64 b y) y)) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 y (Rewrite<= +-commutative_binary64 (+.f64 y (*.f64 (-.f64 b y) z)))) x) (*.f64 (/.f64 (-.f64 t a) (fma.f64 z (-.f64 b y) y)) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (+.f64 y (*.f64 (-.f64 b y) z)) x))) (*.f64 (/.f64 (-.f64 t a) (fma.f64 z (-.f64 b y) y)) z)): 32 points increase in error, 9 points decrease in error
      (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (+.f64 y (*.f64 (-.f64 b y) z)))) (*.f64 (/.f64 (-.f64 t a) (fma.f64 z (-.f64 b y) y)) z)): 50 points increase in error, 23 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) (+.f64 y (*.f64 (-.f64 b y) z))) (*.f64 (/.f64 (-.f64 t a) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (-.f64 b y)) y))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) (+.f64 y (*.f64 (-.f64 b y) z))) (*.f64 (/.f64 (-.f64 t a) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 b y) z)) y)) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) (+.f64 y (*.f64 (-.f64 b y) z))) (*.f64 (/.f64 (-.f64 t a) (Rewrite<= +-commutative_binary64 (+.f64 y (*.f64 (-.f64 b y) z)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) (+.f64 y (*.f64 (-.f64 b y) z))) (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 t a) (/.f64 (+.f64 y (*.f64 (-.f64 b y) z)) z)))): 13 points increase in error, 38 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) (+.f64 y (*.f64 (-.f64 b y) z))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t a) z) (+.f64 y (*.f64 (-.f64 b y) z))))): 61 points increase in error, 8 points decrease in error

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-247 or 3.99999999999999988e-277 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e295

   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 -2e-247 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 3.99999999999999988e-277

   1. Initial program 40.5

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

   2. Simplified 40.5

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}} \]
      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)): 1 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))): 0 points increase in error, 1 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 20.2

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

   4. Simplified 7.6

      \[\leadsto \color{blue}{\frac{\frac{y}{b - y} \cdot \left(x - \frac{t - a}{b - y}\right)}{z} + \frac{t - a}{b - y}} \]
      Proof
      (+.f64 (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 y (-.f64 b y)) x) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (-.f64 (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (-.f64 b y) x))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 13 points increase in error, 13 points decrease in error
      (+.f64 (/.f64 (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 31 points increase in error, 10 points decrease in error
      (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y (-.f64 t a)) (*.f64 (-.f64 b y) (-.f64 b y))))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 47 points increase in error, 3 points decrease in error
      (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 t a) y)) (*.f64 (-.f64 b y) (-.f64 b y)))) z) (/.f64 (-.f64 t a) (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite<= unpow2_binary64 (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 (Rewrite<= *-lft-identity_binary64 (*.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 (Rewrite<= metadata-eval (*.f64 -1 -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 (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))))): 2 points increase in error, 0 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
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 -1 (-.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
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 -1 (Rewrite=> distribute-lft-out--_binary64 (*.f64 -1 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.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
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 -1 -1) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.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
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 (Rewrite=> metadata-eval 1) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.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
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (Rewrite=> *-lft-identity_binary64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.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
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (/.f64 (*.f64 y x) (-.f64 b y)) z) (/.f64 (/.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
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (-.f64 (Rewrite<= associate-/r*_binary64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z))) (/.f64 (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)) z))) (/.f64 a (-.f64 b y))): 15 points increase in error, 12 points decrease in error
      (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (-.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (Rewrite<= associate-/r*_binary64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))))) (/.f64 a (-.f64 b y))): 3 points increase in error, 4 points decrease in error
      (-.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z))) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z)))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 t (-.f64 b y)) (/.f64 (*.f64 y x) (Rewrite<= *-commutative_binary64 (*.f64 z (-.f64 b y))))) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (/.f64 t (-.f64 b y)))) (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (/.f64 t (-.f64 b y))) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite<= *-commutative_binary64 (*.f64 z (pow.f64 (-.f64 b y) 2))))) (/.f64 a (-.f64 b y))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--r+_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))))): 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

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}} \]
      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)): 1 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))): 0 points increase in error, 1 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 43.7

      \[\leadsto \color{blue}{\left(\frac{y \cdot x}{\left(b - y\right) \cdot z} + \left(-1 \cdot \frac{y \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{\left(b - y\right) \cdot {z}^{2}} + \left(\frac{{y}^{2} \cdot \left(\frac{y \cdot x}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{{\left(b - y\right)}^{2} \cdot {z}^{3}} + \frac{t}{b - y}\right)\right)\right) - \left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2} \cdot z}\right)} \]

   4. Simplified 0.0

      \[\leadsto \color{blue}{\frac{y}{b - y} \cdot \left(\frac{x}{z} - \frac{\frac{y}{b - y} \cdot \left(x - \frac{t - a}{b - y}\right)}{z \cdot z}\right) + \left(\mathsf{fma}\left(\frac{y}{\frac{{\left(b - y\right)}^{2}}{y}}, \frac{\frac{y}{b - y} \cdot \left(x - \frac{t - a}{b - y}\right)}{{z}^{3}}, \frac{t}{b - y}\right) - \mathsf{fma}\left(\frac{t - a}{{\left(b - y\right)}^{2}}, \frac{y}{z}, \frac{a}{b - y}\right)\right)} \]
      Proof
      (+.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 (/.f64 x z) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (*.f64 z z)))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 (/.f64 x z) (/.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 y (-.f64 b y)) x) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y))))) (*.f64 z z)))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 (/.f64 x z) (/.f64 (-.f64 (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (-.f64 b y) x))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) (*.f64 z z)))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 2 points decrease in error
      (+.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 (/.f64 x z) (/.f64 (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) (*.f64 z z)))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 19 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 (/.f64 x z) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y (-.f64 t a)) (*.f64 (-.f64 b y) (-.f64 b y))))) (*.f64 z z)))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 23 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 (/.f64 x z) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 t a) y)) (*.f64 (-.f64 b y) (-.f64 b y)))) (*.f64 z z)))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 (/.f64 x z) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 b y) 2)))) (*.f64 z z)))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 (/.f64 x z) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))) (Rewrite<= unpow2_binary64 (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 y (-.f64 b y)) (/.f64 x z)) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))) (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))) (pow.f64 z 2)))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 6 points increase in error, 3 points decrease in error
      (+.f64 (-.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (neg.f64 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2)))))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2)))))) (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 b y) 2) y)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (fma.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y y) (pow.f64 (-.f64 b y) 2))) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 10 points increase in error, 1 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 y 2)) (pow.f64 (-.f64 b y) 2)) (/.f64 (*.f64 (/.f64 y (-.f64 b y)) (-.f64 x (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 (pow.f64 y 2) (pow.f64 (-.f64 b y) 2)) (/.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 y (-.f64 b y)) x) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y))))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 (pow.f64 y 2) (pow.f64 (-.f64 b y) 2)) (/.f64 (-.f64 (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (-.f64 b y) x))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 1 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 (pow.f64 y 2) (pow.f64 (-.f64 b y) 2)) (/.f64 (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (-.f64 b y))) (*.f64 (/.f64 y (-.f64 b y)) (/.f64 (-.f64 t a) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 1 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 (pow.f64 y 2) (pow.f64 (-.f64 b y) 2)) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y (-.f64 t a)) (*.f64 (-.f64 b y) (-.f64 b y))))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 1 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 (pow.f64 y 2) (pow.f64 (-.f64 b y) 2)) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 t a) y)) (*.f64 (-.f64 b y) (-.f64 b y)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (fma.f64 (/.f64 (pow.f64 y 2) (pow.f64 (-.f64 b y) 2)) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (Rewrite<= unpow2_binary64 (pow.f64 (-.f64 b y) 2)))) (pow.f64 z 3)) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (pow.f64 y 2) (pow.f64 (-.f64 b y) 2)) (/.f64 (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2))) (pow.f64 z 3))) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (pow.f64 y 2) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (pow.f64 (-.f64 b y) 2) (pow.f64 z 3)))) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 a (-.f64 b y))))): 4 points increase in error, 4 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 y 2) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (pow.f64 (-.f64 b y) 2) (pow.f64 z 3))) (/.f64 t (-.f64 b y))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z)) (/.f64 a (-.f64 b y)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 y 2) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (pow.f64 (-.f64 b y) 2) (pow.f64 z 3))) (/.f64 t (-.f64 b y))) (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z))) (/.f64 a (-.f64 b y))))): 0 points increase in error, 4 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 y 2) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (pow.f64 (-.f64 b y) 2) (pow.f64 z 3))) (/.f64 t (-.f64 b y))) (Rewrite<= +-commutative_binary64 (+.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
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2))))) (+.f64 (/.f64 (*.f64 (pow.f64 y 2) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (pow.f64 (-.f64 b y) 2) (pow.f64 z 3))) (/.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
      (-.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 (*.f64 y x) (*.f64 (-.f64 b y) z)) (+.f64 (*.f64 -1 (/.f64 (*.f64 y (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (-.f64 b y) (pow.f64 z 2)))) (+.f64 (/.f64 (*.f64 (pow.f64 y 2) (-.f64 (/.f64 (*.f64 y x) (-.f64 b y)) (/.f64 (*.f64 (-.f64 t a) y) (pow.f64 (-.f64 b y) 2)))) (*.f64 (pow.f64 (-.f64 b y) 2) (pow.f64 z 3))) (/.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
3. Recombined 4 regimes into one program.

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)} + z \cdot \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-247}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{-277}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)} + z \cdot \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{b - y} \cdot \left(\frac{x}{z} - \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z \cdot z}\right) + \left(\mathsf{fma}\left(\frac{y}{\frac{{\left(b - y\right)}^{2}}{y}}, \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{{z}^{3}}, \frac{t}{b - y}\right) - \mathsf{fma}\left(\frac{t - a}{{\left(b - y\right)}^{2}}, \frac{y}{z}, \frac{a}{b - y}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.1
Cost	19924

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} + \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ t_5 := \mathsf{fma}\left(z, b - y, y\right)\\ t_6 := \frac{t_3 + x \cdot y}{t_1}\\ t_7 := x \cdot \frac{y}{t_5} + z \cdot \frac{t - a}{t_5}\\ \mathbf{if}\;t_6 \leq -\infty:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t_6 \leq -2 \cdot 10^{-247}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_6 \leq 4 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_6 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_6 \leq \infty:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	3.2
Cost	13012

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} + \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ t_5 := \frac{t_3 + x \cdot y}{t_1}\\ t_6 := x + z \cdot \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-247}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 4 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	3.6
Cost	13012

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} + \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z}\\ t_3 := x + \left(t - a\right) \cdot \frac{z}{\mathsf{fma}\left(z, b - y, y\right)}\\ t_4 := z \cdot \left(t - a\right)\\ t_5 := \frac{t_4 + x \cdot y}{t_1}\\ t_6 := \frac{t_4}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{if}\;t_5 \leq -1 \cdot 10^{+252}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-247}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq 4 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_5 \leq 10^{+178}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	5.4
Cost	6224

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} + \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z}\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_3 := y - y \cdot z\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;x + \frac{t - a}{t_3} \cdot \left(z - \frac{b}{\frac{\frac{t_3}{z}}{z}}\right)\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-247}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	5.3
Cost	6224

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := y - y \cdot z\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ t_5 := \frac{t_3 + x \cdot y}{t_1}\\ t_6 := \frac{t - a}{b - y} + \frac{\frac{y}{b - y} \cdot \left(x + \frac{a - t}{b - y}\right)}{z}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;x + \frac{t - a}{t_2} \cdot \left(z - \frac{b}{\frac{\frac{t_2}{z}}{z}}\right)\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-247}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 4 \cdot 10^{-277}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 6
Error	12.5
Cost	5712

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;x\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-323}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t - a}{1 - z} \cdot \frac{z}{y}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

Alternative 7
Error	11.8
Cost	5712

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{t_1}\\ t_3 := y - y \cdot z\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;x + \frac{t - a}{t_3} \cdot \left(z - \frac{b}{\frac{\frac{t_3}{z}}{z}}\right)\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-323}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t - a}{1 - z} \cdot \frac{z}{y}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

Alternative 8
Error	12.5
Cost	3400

\[\begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

Alternative 9
Error	16.9
Cost	1224

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4992881303286762 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq -3.035660573733431 \cdot 10^{-161}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10
Error	34.7
Cost	848

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -6.775905354502759 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.98568307092475 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.007791934819775 \cdot 10^{+252}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	34.7
Cost	848

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -6.775905354502759 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 4.98568307092475 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.007791934819775 \cdot 10^{+252}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	24.7
Cost	844

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6.775905354502759 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.0357633152577107 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{t - a}{y}\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	19.7
Cost	840

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6.775905354502759 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	17.7
Cost	840

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6.775905354502759 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	17.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -6.775905354502759 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 16
Error	37.7
Cost	716

\[\begin{array}{l} t_1 := \frac{a - t}{y}\\ \mathbf{if}\;z \leq -25040526703795212000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2573041633902153 \cdot 10^{+65}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	30.7
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.705033687718346 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5256976457659228 \cdot 10^{-96}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	22.0
Cost	712

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6.775905354502759 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	35.5
Cost	584

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -6.775905354502759 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 68.06354020415596:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	30.7
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.705033687718346 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5256976457659228 \cdot 10^{-96}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	40.6
Cost	520

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -1.4992881303286762 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6008448824059525 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	47.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022300 
(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)))))