Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Average Error: 20.6 → 6.5

Time: 33.2s

Precision: binary64

Cost: 17484

\[ \begin{array}{c}[t, a] = \mathsf{sort}([t, a])\\ \end{array} \]

Math

\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

↓

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} + t_1}{c}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-9}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0)))
        (t_2 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_2 (- INFINITY))
     (/ (+ (/ (+ b (* 9.0 (* x y))) z) t_1) c)
     (if (<= t_2 -5e+69)
       t_2
       (if (<= t_2 2e-9)
         (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) c)
         (if (<= t_2 5e+296) t_2 (/ (+ t_1 (* 9.0 (* x (/ y z)))) c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (((b + (9.0 * (x * y))) / z) + t_1) / c;
	} else if (t_2 <= -5e+69) {
		tmp = t_2;
	} else if (t_2 <= 2e-9) {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / c;
	} else if (t_2 <= 5e+296) {
		tmp = t_2;
	} else {
		tmp = (t_1 + (9.0 * (x * (y / z)))) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

↓

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) / z) + t_1) / c);
	elseif (t_2 <= -5e+69)
		tmp = t_2;
	elseif (t_2 <= 2e-9)
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	elseif (t_2 <= 5e+296)
		tmp = t_2;
	else
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(x * Float64(y / z)))) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, -5e+69], t$95$2, If[LessEqual[t$95$2, 2e-9], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 5e+296], t$95$2, N[(N[(t$95$1 + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]

Target

Original	20.6
Target	14.4
Herbie	6.5

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -inf.0

   1. Initial program 64.0

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 24.6

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
      Proof
      (/.f64 (+.f64 (/.f64 (fma.f64 (*.f64 x 9) y b) z) (*.f64 t (*.f64 a -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (*.f64 x 9) y) b)) z) (*.f64 t (*.f64 a -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 b (*.f64 (*.f64 x 9) y))) z) (*.f64 t (*.f64 a -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 t (*.f64 a (Rewrite<= metadata-eval (neg.f64 4))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 t (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a 4))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 t (*.f64 a 4))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 t) (*.f64 a 4)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 t (*.f64 a 4)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 t a) 4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 t a)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= metadata-eval (/.f64 4 1)) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 4 (Rewrite<= *-inverses_binary64 (/.f64 z z))) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 4 z) z)) (*.f64 t a))) c): 1 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 z 4)) z) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 z 4) (/.f64 z (*.f64 t a))))) c): 26 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 z 4) (*.f64 t a)) z))) c): 17 points increase in error, 25 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 30 points increase in error, 3 points decrease in error
      (/.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 3 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= associate-+r-_binary64 (+.f64 b (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)))) z) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b)) z) c): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))): 44 points increase in error, 52 points decrease in error

   3. Taylor expanded in z around 0 24.5

      \[\leadsto \frac{\color{blue}{\frac{9 \cdot \left(y \cdot x\right) + b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -5.00000000000000036e69 or 2.00000000000000012e-9 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 5.0000000000000001e296

   1. Initial program 0.7

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   if -5.00000000000000036e69 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 2.00000000000000012e-9

   1. Initial program 12.3

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 1.5

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      Proof
      (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (*.f64 a (Rewrite<= metadata-eval (neg.f64 4))) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a 4))) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 a) 4)) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (Rewrite=> *-commutative_binary64 (*.f64 4 (neg.f64 a))) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (*.f64 4 (neg.f64 a)) (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (*.f64 9 y)) b)) z)) c): 1 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (*.f64 4 (neg.f64 a)) (/.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 9) y)) b) z)) c): 10 points increase in error, 6 points decrease in error
      (/.f64 (fma.f64 t (*.f64 4 (neg.f64 a)) (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 b (*.f64 (*.f64 x 9) y))) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 t (*.f64 4 (neg.f64 a))) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 t 4) (neg.f64 a))) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 t)) (neg.f64 a)) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 (*.f64 4 t) a))) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (neg.f64 (*.f64 (*.f64 4 t) a)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite=> unsub-neg_binary64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (*.f64 4 t) a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite=> associate-*l*_binary64 (*.f64 4 (*.f64 t a)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= metadata-eval (/.f64 4 1)) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 4 (Rewrite<= *-inverses_binary64 (/.f64 z z))) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 4 z) z)) (*.f64 t a))) c): 1 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 z 4)) z) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 z 4) (/.f64 z (*.f64 t a))))) c): 26 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 z 4) (*.f64 t a)) z))) c): 17 points increase in error, 25 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 30 points increase in error, 3 points decrease in error
      (/.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 3 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= associate-+r-_binary64 (+.f64 b (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)))) z) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b)) z) c): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))): 44 points increase in error, 52 points decrease in error

   if 5.0000000000000001e296 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 61.3

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 27.4

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
      Proof
      (/.f64 (+.f64 (/.f64 (fma.f64 (*.f64 x 9) y b) z) (*.f64 t (*.f64 a -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (*.f64 x 9) y) b)) z) (*.f64 t (*.f64 a -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 b (*.f64 (*.f64 x 9) y))) z) (*.f64 t (*.f64 a -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 t (*.f64 a (Rewrite<= metadata-eval (neg.f64 4))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 t (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a 4))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 t (*.f64 a 4))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 t) (*.f64 a 4)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 t (*.f64 a 4)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 t a) 4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= *-commutative_binary64 (*.f64 4 (*.f64 t a)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= metadata-eval (/.f64 4 1)) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 4 (Rewrite<= *-inverses_binary64 (/.f64 z z))) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 4 z) z)) (*.f64 t a))) c): 1 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 z 4)) z) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 z 4) (/.f64 z (*.f64 t a))))) c): 26 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 z 4) (*.f64 t a)) z))) c): 17 points increase in error, 25 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 30 points increase in error, 3 points decrease in error
      (/.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 3 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= associate-+r-_binary64 (+.f64 b (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)))) z) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b)) z) c): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))): 44 points increase in error, 52 points decrease in error

   3. Taylor expanded in x around inf 31.3

      \[\leadsto \frac{\color{blue}{9 \cdot \frac{y \cdot x}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   4. Simplified 20.7

      \[\leadsto \frac{\color{blue}{9 \cdot \left(\frac{y}{z} \cdot x\right)} + t \cdot \left(a \cdot -4\right)}{c} \]
      Proof
      (*.f64 9 (*.f64 (/.f64 y z) x)): 0 points increase in error, 0 points decrease in error
      (*.f64 9 (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 z x)))): 47 points increase in error, 45 points decrease in error
      (*.f64 9 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) z))): 40 points increase in error, 53 points decrease in error
3. Recombined 4 regimes into one program.

4. Final simplification 6.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{+69}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{-9}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.5
Cost	6352

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} + t_1}{c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-9}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \end{array} \]

Alternative 2
Error	12.1
Cost	2252

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+281}:\\ \;\;\;\;\frac{y}{z} \cdot \left(9 \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-184}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t_1 \leq 10^{+265}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]

Alternative 3
Error	37.4
Cost	1900

\[\begin{array}{l} t_1 := \frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ t_2 := \frac{t \cdot a}{\frac{c}{-4}}\\ t_3 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -1.26 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-258}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-253}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-228}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-140}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 4
Error	37.3
Cost	1900

\[\begin{array}{l} t_1 := 9 \cdot \frac{y}{c}\\ t_2 := \frac{x}{z} \cdot t_1\\ t_3 := \frac{t \cdot a}{\frac{c}{-4}}\\ t_4 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -1.22 \cdot 10^{-115}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-257}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-254}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-226}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-140}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-64}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{x \cdot t_1}{z}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 5
Error	37.3
Cost	1900

\[\begin{array}{l} t_1 := 9 \cdot \frac{y}{c}\\ t_2 := \frac{t \cdot a}{\frac{c}{-4}}\\ t_3 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-257}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-253}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-228}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-140}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{z} \cdot t_1\\ \mathbf{elif}\;a \leq 10^{-63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{c}{\frac{y}{0.1111111111111111}}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{x \cdot t_1}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 6
Error	37.7
Cost	1896

\[\begin{array}{l} t_1 := \frac{t \cdot a}{\frac{c}{-4}}\\ t_2 := 9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ t_3 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-243}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 3.65 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+108}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	37.8
Cost	1896

\[\begin{array}{l} t_1 := \frac{t \cdot a}{\frac{c}{-4}}\\ t_2 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ t_3 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;y \leq -7.9 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-243}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-10}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+109}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	37.6
Cost	1896

\[\begin{array}{l} t_1 := \frac{t \cdot a}{\frac{c}{-4}}\\ t_2 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ t_3 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-240}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 950:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+111}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	37.5
Cost	1896

\[\begin{array}{l} t_1 := \frac{t \cdot a}{\frac{c}{-4}}\\ t_2 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ t_3 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-238}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 840:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+107}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	38.4
Cost	1632

\[\begin{array}{l} t_1 := \frac{t \cdot a}{\frac{c}{-4}}\\ t_2 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{-63}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 880:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+108}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 11
Error	38.6
Cost	1632

\[\begin{array}{l} t_1 := \frac{t \cdot a}{\frac{c}{-4}}\\ t_2 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-67}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 920:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+108}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 12
Error	31.7
Cost	1628

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+111}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 13
Error	35.6
Cost	1372

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ t_2 := \frac{-4}{\frac{c}{t \cdot a}}\\ t_3 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-253}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	35.7
Cost	1372

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ t_3 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-253}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	35.8
Cost	1372

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{t \cdot a}{\frac{c}{-4}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-253}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-224}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 16
Error	24.5
Cost	1364

\[\begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;y \leq -8 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 740:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+216}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 17
Error	20.4
Cost	1356

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{t_1 + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+226}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+93}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	11.9
Cost	1352

\[\begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ t_2 := \frac{\frac{t_1}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;z \leq -3 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{t_1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	34.7
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ t_2 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -1.22 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+92}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	34.6
Cost	1108

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+92}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	34.7
Cost	1108

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -9.6 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+92}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	34.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+34}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 23
Error	34.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 24
Error	42.5
Cost	584

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 25
Error	43.4
Cost	320

\[\frac{b}{z \cdot c} \]

Reproduce

herbie shell --seed 2022338 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))