Average Error: 22.8 → 7.0
Time: 34.4s
Precision: binary64
Cost: 18256
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ t_2 := \frac{y}{z} \cdot \frac{x}{b - y} - \left(\left(\frac{a}{b - y} - \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right) - \frac{t}{b - y}\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+280}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
(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 (/ (+ (* x y) (* z (- t a))) (- y (* z (- y b)))))
        (t_2
         (-
          (* (/ y z) (/ x (- b y)))
          (-
           (- (/ a (- b y)) (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))
           (/ t (- b y))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -1e-239)
       t_1
       (if (<= t_1 5e-243)
         t_2
         (if (<= t_1 2e+280)
           (/ (fma z (- t a) (* x y)) (fma z (- b y) y))
           t_2))))))
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 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)));
	double t_2 = ((y / z) * (x / (b - y))) - (((a / (b - y)) - ((y / z) * ((a - t) / pow((b - y), 2.0)))) - (t / (b - y)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -1e-239) {
		tmp = t_1;
	} else if (t_1 <= 5e-243) {
		tmp = t_2;
	} else if (t_1 <= 2e+280) {
		tmp = fma(z, (t - a), (x * y)) / fma(z, (b - y), y);
	} else {
		tmp = t_2;
	}
	return tmp;
}
function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
end
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y - Float64(z * Float64(y - b))))
	t_2 = Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) - Float64(Float64(Float64(a / Float64(b - y)) - Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) - Float64(t / Float64(b - y))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -1e-239)
		tmp = t_1;
	elseif (t_1 <= 5e-243)
		tmp = t_2;
	elseif (t_1 <= 2e+280)
		tmp = Float64(fma(z, Float64(t - a), Float64(x * y)) / fma(z, Float64(b - y), y));
	else
		tmp = t_2;
	end
	return tmp
end
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[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -1e-239], t$95$1, If[LessEqual[t$95$1, 5e-243], t$95$2, If[LessEqual[t$95$1, 2e+280], N[(N[(z * N[(t - a), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}
\begin{array}{l}
t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\
t_2 := \frac{y}{z} \cdot \frac{x}{b - y} - \left(\left(\frac{a}{b - y} - \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right) - \frac{t}{b - y}\right)\\
\mathbf{if}\;t_1 \leq -\infty:\\
\;\;\;\;t_2\\

\mathbf{elif}\;t_1 \leq -1 \cdot 10^{-239}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t_1 \leq 5 \cdot 10^{-243}:\\
\;\;\;\;t_2\\

\mathbf{elif}\;t_1 \leq 2 \cdot 10^{+280}:\\
\;\;\;\;\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\

\mathbf{else}:\\
\;\;\;\;t_2\\


\end{array}

Error

Target

Original22.8
Target17.7
Herbie7.0
\[\frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}} \]

Derivation

  1. Split input into 3 regimes
  2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or -1.0000000000000001e-239 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5e-243 or 2.0000000000000001e280 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

    1. Initial program 54.8

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
    2. Taylor expanded in z around inf 34.8

      \[\leadsto \color{blue}{\left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)} \]
    3. Simplified16.4

      \[\leadsto \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}\right)\right)} \]
      Proof
      (+.f64 (*.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) (pow.f64 (-.f64 b y) 2)) (/.f64 y z))))): 0 points increase in error, 0 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 a (-.f64 b y)) (*.f64 (/.f64 (-.f64 t a) (pow.f64 (-.f64 b y) 2)) (/.f64 y z))))): 34 points increase in error, 14 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.f64 b y))) (-.f64 (/.f64 t (-.f64 b y)) (+.f64 (/.f64 a (-.f64 b y)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (-.f64 t a) y) (*.f64 (pow.f64 (-.f64 b y) 2) z)))))): 44 points increase in error, 17 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.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
      (+.f64 (/.f64 (*.f64 y x) (*.f64 z (-.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<= 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))))): 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)))) < -1.0000000000000001e-239

    1. Initial program 0.3

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

    if 5e-243 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e280

    1. Initial program 0.3

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
    2. Simplified0.3

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}} \]
      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, 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. Recombined 3 regimes into one program.
  4. Final simplification7.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} - \left(\left(\frac{a}{b - y} - \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right) - \frac{t}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -1 \cdot 10^{-239}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 5 \cdot 10^{-243}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} - \left(\left(\frac{a}{b - y} - \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right) - \frac{t}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{+280}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t - a, x \cdot y\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} - \left(\left(\frac{a}{b - y} - \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right) - \frac{t}{b - y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error7.0
Cost13200
\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ t_2 := \frac{y}{z} \cdot \frac{x}{b - y} - \left(\left(\frac{a}{b - y} - \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\right) - \frac{t}{b - y}\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+280}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 2
Error10.5
Cost5712
\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-243}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;t_1 \leq 10^{+249}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error44.2
Cost1840
\[\begin{array}{l} t_1 := -\frac{a}{b}\\ t_2 := \frac{-x}{z}\\ t_3 := \frac{t}{b - y}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -10000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-258}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-173}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 4
Error45.3
Cost1508
\[\begin{array}{l} t_1 := -\frac{a}{b}\\ t_2 := \frac{-x}{z}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-258}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-177}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+211}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 5
Error21.7
Cost1496
\[\begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-116}:\\ \;\;\;\;\frac{t_1}{z \cdot b}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 6
Error45.3
Cost1444
\[\begin{array}{l} t_1 := -\frac{a}{b}\\ t_2 := \frac{-x}{z}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-258}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-175}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 7
Error38.7
Cost1376
\[\begin{array}{l} t_1 := -\frac{a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-261}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-176}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 8
Error25.4
Cost1368
\[\begin{array}{l} t_1 := \frac{x \cdot y - z \cdot a}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{1 - z} - \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 9
Error23.4
Cost1364
\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{z}{y} \cdot \frac{t}{1 - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error23.4
Cost1364
\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-93}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-207}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{z}{y} \cdot \frac{t}{1 - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 11
Error19.8
Cost1356
\[\begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-76}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-122}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{t_1}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{z}{\frac{1}{t - a}}}{t_1}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
Alternative 12
Error23.5
Cost1236
\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z}{y} \cdot \frac{t}{1 - z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{1 - z} - \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Error21.3
Cost1232
\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-77}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error19.3
Cost1224
\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-76}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 80000:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
Alternative 15
Error25.0
Cost1104
\[\begin{array}{l} t_1 := \frac{x \cdot y - z \cdot a}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-97}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 16
Error30.9
Cost976
\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+51}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 17
Error31.1
Cost848
\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -55000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 18
Error30.9
Cost848
\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+53}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 19
Error40.7
Cost784
\[\begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+276}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 20
Error25.1
Cost712
\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 21
Error41.8
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
Alternative 22
Error47.2
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022329 
(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)))))