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

Average Error: 7.8 → 4.3

Time: 11.2s

Precision: binary64

Cost: 2248

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

↓

\[\begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;\frac{\frac{x \cdot y}{2}}{a} + \frac{\left(z \cdot t\right) \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* 0.5 (* y (/ x a)))
     (if (<= t_1 4e+307)
       (+ (/ (/ (* x y) 2.0) a) (/ (* (* z t) -4.5) a))
       (* -4.5 (* z (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = 0.5 * (y * (x / a));
	} else if (t_1 <= 4e+307) {
		tmp = (((x * y) / 2.0) / a) + (((z * t) * -4.5) / a);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (y * (x / a));
	} else if (t_1 <= 4e+307) {
		tmp = (((x * y) / 2.0) / a) + (((z * t) * -4.5) / a);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

↓

def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = 0.5 * (y * (x / a))
	elif t_1 <= 4e+307:
		tmp = (((x * y) / 2.0) / a) + (((z * t) * -4.5) / a)
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (t_1 <= 4e+307)
		tmp = Float64(Float64(Float64(Float64(x * y) / 2.0) / a) + Float64(Float64(Float64(z * t) * -4.5) / a));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = 0.5 * (y * (x / a));
	elseif (t_1 <= 4e+307)
		tmp = (((x * y) / 2.0) / a) + (((z * t) * -4.5) / a);
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+307], N[(N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] / a), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	7.8
Target	5.6
Herbie	4.3

\[\begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -inf.0

   1. Initial program 64.0

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Simplified 63.6

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
      Proof
      (/.f64 (fma.f64 x y (*.f64 z (*.f64 t -9))) (*.f64 a 2)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 x y (*.f64 z (*.f64 t (Rewrite<= metadata-eval (neg.f64 9))))) (*.f64 a 2)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 x y (*.f64 z (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 t 9))))) (*.f64 a 2)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 x y (*.f64 z (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 9 t))))) (*.f64 a 2)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 x y (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 z (*.f64 9 t))))) (*.f64 a 2)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 x y (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 z 9) t)))) (*.f64 a 2)): 17 points increase in error, 8 points decrease in error
      (/.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (*.f64 a 2)): 2 points increase in error, 1 points decrease in error
      (/.f64 (-.f64 (Rewrite<= +-rgt-identity_binary64 (+.f64 (*.f64 x y) 0)) (*.f64 (*.f64 z 9) t)) (*.f64 a 2)): 0 points increase in error, 0 points decrease in error
      (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (+.f64 (*.f64 x y) 0) (*.f64 a 2)) (/.f64 (*.f64 (*.f64 z 9) t) (*.f64 a 2)))): 2 points increase in error, 3 points decrease in error
      (-.f64 (/.f64 (Rewrite=> +-rgt-identity_binary64 (*.f64 x y)) (*.f64 a 2)) (/.f64 (*.f64 (*.f64 z 9) t) (*.f64 a 2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))): 3 points increase in error, 2 points decrease in error

   3. Taylor expanded in x around inf 63.1

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]

   4. Simplified 32.2

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]
      Proof
      (*.f64 1/2 (*.f64 (/.f64 x a) y)): 0 points increase in error, 0 points decrease in error
      (*.f64 1/2 (Rewrite<= associate-/r/_binary64 (/.f64 x (/.f64 a y)))): 54 points increase in error, 45 points decrease in error
      (*.f64 1/2 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x y) a))): 51 points increase in error, 55 points decrease in error
      (*.f64 1/2 (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 y x)) a)): 0 points increase in error, 0 points decrease in error

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 3.99999999999999994e307

   1. Initial program 0.9

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Applied egg-rr 5.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{a + a}, -\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\right)} \]

   3. Simplified 5.4

      \[\leadsto \color{blue}{y \cdot \frac{x}{a + a} - \frac{\left(t \cdot z\right) \cdot 4.5}{a}} \]
      Proof
      (-.f64 (*.f64 y (/.f64 x (+.f64 a a))) (/.f64 (*.f64 (*.f64 t z) 9/2) a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 y x) (+.f64 a a))) (/.f64 (*.f64 (*.f64 t z) 9/2) a)): 35 points increase in error, 31 points decrease in error
      (-.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 x y)) (+.f64 a a)) (/.f64 (*.f64 (*.f64 t z) 9/2) a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 x (/.f64 y (+.f64 a a)))) (/.f64 (*.f64 (*.f64 t z) 9/2) a)): 33 points increase in error, 38 points decrease in error
      (-.f64 (*.f64 x (/.f64 y (+.f64 a a))) (/.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 z t)) 9/2) a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (/.f64 y (+.f64 a a))) (/.f64 (*.f64 (*.f64 z t) (Rewrite<= metadata-eval (*.f64 9 1/2))) a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (/.f64 y (+.f64 a a))) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 z t) 9) 1/2)) a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (/.f64 y (+.f64 a a))) (/.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 9 (*.f64 z t))) 1/2) a)): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (/.f64 y (+.f64 a a))) (Rewrite<= associate-*r/_binary64 (*.f64 (*.f64 9 (*.f64 z t)) (/.f64 1/2 a)))): 19 points increase in error, 9 points decrease in error
      (Rewrite=> fma-neg_binary64 (fma.f64 x (/.f64 y (+.f64 a a)) (neg.f64 (*.f64 (*.f64 9 (*.f64 z t)) (/.f64 1/2 a))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (Rewrite<= /-rgt-identity_binary64 (/.f64 x 1)) (/.f64 y (+.f64 a a)) (neg.f64 (*.f64 (*.f64 9 (*.f64 z t)) (/.f64 1/2 a)))): 0 points increase in error, 0 points decrease in error

   4. Applied egg-rr 0.9

      \[\leadsto \color{blue}{\frac{\frac{y \cdot x}{2}}{a}} - \frac{\left(t \cdot z\right) \cdot 4.5}{a} \]

   if 3.99999999999999994e307 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 63.4

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around 0 61.8

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   3. Simplified 30.5

      \[\leadsto \color{blue}{-4.5 \cdot \left(\frac{t}{a} \cdot z\right)} \]
      Proof
      (*.f64 -9/2 (*.f64 (/.f64 t a) z)): 0 points increase in error, 0 points decrease in error
      (*.f64 -9/2 (Rewrite<= associate-/r/_binary64 (/.f64 t (/.f64 a z)))): 47 points increase in error, 47 points decrease in error
      (*.f64 -9/2 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 t z) a))): 42 points increase in error, 48 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 4.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+307}:\\ \;\;\;\;\frac{\frac{x \cdot y}{2}}{a} + \frac{\left(z \cdot t\right) \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	4.3
Cost	2120

\[\begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t\right) \cdot -9}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 2
Error	19.6
Cost	1748

\[\begin{array}{l} t_1 := \frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-201}:\\ \;\;\;\;\frac{z \cdot t}{\frac{a}{-4.5}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-112}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-52}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+223}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	24.2
Cost	1108

\[\begin{array}{l} t_1 := -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ t_2 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-101}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	24.0
Cost	1108

\[\begin{array}{l} t_1 := -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ t_2 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-101}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	24.0
Cost	1108

\[\begin{array}{l} t_1 := -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ t_2 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-102}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6
Error	24.1
Cost	1108

\[\begin{array}{l} t_1 := -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+71}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-42}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-103}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 7
Error	24.1
Cost	1108

\[\begin{array}{l} t_1 := -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{if}\;x \leq -2.05 \cdot 10^{+71}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-42}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-105}:\\ \;\;\;\;\frac{z \cdot t}{\frac{a}{-4.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 8
Error	31.7
Cost	844

\[\begin{array}{l} t_1 := -4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+112}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]

Alternative 9
Error	32.9
Cost	712

\[\begin{array}{l} t_1 := -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-129}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	32.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-289}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-127}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 11
Error	32.7
Cost	448

\[-4.5 \cdot \left(t \cdot \frac{z}{a}\right) \]

Reproduce

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

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))