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

Average Error: 20.8 → 9.9

Time: 42.6s

Precision: binary64

Cost: 2184

Math

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

↓

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+212}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(-9 \cdot \left(y \cdot x\right) - b\right)}{-z} - \frac{4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{\frac{y}{c}}{z} \cdot x\right)\\ \end{array} \]

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 (* (* x 9.0) y)))
   (if (<= t_1 (- INFINITY))
     (* y (* 9.0 (/ (/ x z) c)))
     (if (<= t_1 5e+212)
       (- (/ (* (/ 1.0 c) (- (* -9.0 (* y x)) b)) (- z)) (/ (* 4.0 (* a t)) c))
       (* 9.0 (* (/ (/ y c) z) x))))))

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 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (9.0 * ((x / z) / c));
	} else if (t_1 <= 5e+212) {
		tmp = (((1.0 / c) * ((-9.0 * (y * x)) - b)) / -z) - ((4.0 * (a * t)) / c);
	} else {
		tmp = 9.0 * (((y / c) / z) * x);
	}
	return tmp;
}

Java

public static 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);
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (9.0 * ((x / z) / c));
	} else if (t_1 <= 5e+212) {
		tmp = (((1.0 / c) * ((-9.0 * (y * x)) - b)) / -z) - ((4.0 * (a * t)) / c);
	} else {
		tmp = 9.0 * (((y / c) / z) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

↓

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (9.0 * ((x / z) / c))
	elif t_1 <= 5e+212:
		tmp = (((1.0 / c) * ((-9.0 * (y * x)) - b)) / -z) - ((4.0 * (a * t)) / c)
	else:
		tmp = 9.0 * (((y / c) / z) * x)
	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(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(9.0 * Float64(Float64(x / z) / c)));
	elseif (t_1 <= 5e+212)
		tmp = Float64(Float64(Float64(Float64(1.0 / c) * Float64(Float64(-9.0 * Float64(y * x)) - b)) / Float64(-z)) - Float64(Float64(4.0 * Float64(a * t)) / c));
	else
		tmp = Float64(9.0 * Float64(Float64(Float64(y / c) / z) * x));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

↓

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (9.0 * ((x / z) / c));
	elseif (t_1 <= 5e+212)
		tmp = (((1.0 / c) * ((-9.0 * (y * x)) - b)) / -z) - ((4.0 * (a * t)) / c);
	else
		tmp = 9.0 * (((y / c) / z) * x);
	end
	tmp_2 = 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[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(9.0 * N[(N[(x / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+212], N[(N[(N[(N[(1.0 / c), $MachinePrecision] * N[(N[(-9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision] - N[(N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	20.8
Target	14.4
Herbie	9.9

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x 9) y) < -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 63.2

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

   3. Taylor expanded in y around inf 63.5

      \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} \]

   4. Applied egg-rr 14.8

      \[\leadsto \color{blue}{y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)} \]

   if -inf.0 < (*.f64 (*.f64 x 9) y) < 4.99999999999999992e212

   1. Initial program 17.7

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

   2. Applied egg-rr 16.1

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

   3. Taylor expanded in z around 0 8.1

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

   4. Simplified 8.1

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

   5. Applied egg-rr 9.0

      \[\leadsto \color{blue}{\frac{\frac{1}{c} \cdot \left(-9 \cdot \left(y \cdot x\right) - b\right)}{-z}} - \frac{4 \cdot \left(a \cdot t\right)}{c} \]

   if 4.99999999999999992e212 < (*.f64 (*.f64 x 9) y)

   1. Initial program 40.9

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

   2. Simplified 39.5

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

   3. Taylor expanded in y around inf 42.6

      \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} \]

   4. Applied egg-rr 19.5

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)} \]

   5. Applied egg-rr 19.5

      \[\leadsto \color{blue}{9 \cdot \left(\frac{\frac{y}{c}}{z} \cdot x\right)} \]
3. Recombined 3 regimes into one program.

Alternatives

Alternative 1
Error	28.4
Cost	2256

\[\begin{array}{l} t_1 := \frac{9 \cdot \left(y \cdot x\right) + b}{z \cdot c}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{-208}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t_2 \leq 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{\frac{y}{c}}{z} \cdot x\right)\\ \end{array} \]

Alternative 2
Error	18.8
Cost	2256

\[\begin{array}{l} t_1 := \frac{9 \cdot \left(y \cdot x\right) + b}{z \cdot c}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{b}{c}}{z} - \frac{4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t_2 \leq 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{\frac{y}{c}}{z} \cdot x\right)\\ \end{array} \]

Alternative 3
Error	17.7
Cost	2256

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 9\right)}{c \cdot z} - t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{b}{c}}{z} - t_2\\ \mathbf{elif}\;t_1 \leq 10^{+177}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{\frac{y}{c}}{z} \cdot x\right)\\ \end{array} \]

Alternative 4
Error	9.7
Cost	1992

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+212}:\\ \;\;\;\;\frac{b + \left(y \cdot x\right) \cdot 9}{z \cdot c} - \frac{4}{c} \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{\frac{y}{c}}{z} \cdot x\right)\\ \end{array} \]

Alternative 5
Error	9.7
Cost	1992

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+212}:\\ \;\;\;\;\frac{b + \left(y \cdot x\right) \cdot 9}{z \cdot c} - \frac{4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{\frac{y}{c}}{z} \cdot x\right)\\ \end{array} \]

Alternative 6
Error	35.9
Cost	1636

\[\begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c}\\ t_2 := 9 \cdot \frac{y \cdot x}{c \cdot z}\\ \mathbf{if}\;b \leq -2.55 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 510000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 7
Error	35.9
Cost	1636

\[\begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c}\\ t_2 := 9 \cdot \frac{y \cdot x}{c \cdot z}\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \left(\frac{x}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 66000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 8
Error	36.0
Cost	1636

\[\begin{array}{l} t_1 := \frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ t_2 := \frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-115}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{c \cdot z}\\ \mathbf{elif}\;b \leq 740000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 9
Error	36.1
Cost	1636

\[\begin{array}{l} t_1 := \frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ t_2 := \frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -0.011:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-114}:\\ \;\;\;\;\frac{y \cdot x}{\frac{c \cdot z}{9}}\\ \mathbf{elif}\;b \leq 215000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 10
Error	36.2
Cost	1632

\[\begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c}\\ t_2 := 9 \cdot \left(\frac{\frac{y}{c}}{z} \cdot x\right)\\ t_3 := \frac{b}{c \cdot z}\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 540000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	35.7
Cost	1240

\[\begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c}\\ t_2 := 9 \cdot \frac{y \cdot x}{c \cdot z}\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 50000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 12
Error	34.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 1050000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 13
Error	42.5
Cost	584

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;c \leq -1.7 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 10^{-49}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	42.4
Cost	584

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+138}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	43.6
Cost	320

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

Alternative 16
Error	59.8
Cost	192

\[3 - 3 \]

Reproduce

herbie shell --seed 2023010 
(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)))