Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Average Error: 5.8 → 1.4

Time: 51.6s

Precision: binary64

Cost: 8648

Math

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

↓

\[\begin{array}{l} t_1 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ t_2 := c \cdot \mathsf{fma}\left(c \cdot i, b, a \cdot i\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;2 \cdot \left(t \cdot z - t_2\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+276}:\\ \;\;\;\;2 \cdot \left(\left(t \cdot z + x \cdot y\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_2\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))

↓

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (+ a (* b c))) i)) (t_2 (* c (fma (* c i) b (* a i)))))
   (if (<= t_1 (- INFINITY))
     (* 2.0 (- (* t z) t_2))
     (if (<= t_1 5e+276)
       (* 2.0 (- (+ (* t z) (* x y)) t_1))
       (* 2.0 (- (* x y) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * (a + (b * c))) * i;
	double t_2 = c * fma((c * i), b, (a * i));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = 2.0 * ((t * z) - t_2);
	} else if (t_1 <= 5e+276) {
		tmp = 2.0 * (((t * z) + (x * y)) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - t_2);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

↓

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	t_2 = Float64(c * fma(Float64(c * i), b, Float64(a * i)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(t * z) - t_2));
	elseif (t_1 <= 5e+276)
		tmp = Float64(2.0 * Float64(Float64(Float64(t * z) + Float64(x * y)) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(c * i), $MachinePrecision] * b + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(2.0 * N[(N[(t * z), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+276], N[(2.0 * N[(N[(N[(t * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	5.8
Target	1.7
Herbie	1.4

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0

   1. Initial program 64.0

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around 0 17.7

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   3. Applied egg-rr 6.7

      \[\leadsto 2 \cdot \left(t \cdot z - c \cdot \color{blue}{\mathsf{fma}\left(c \cdot i, b, i \cdot a\right)}\right) \]

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.00000000000000001e276

   1. Initial program 0.3

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   if 5.00000000000000001e276 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 46.7

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 17.6

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   3. Applied egg-rr 13.6

      \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\mathsf{fma}\left(c \cdot i, b, i \cdot a\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 1.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \mathsf{fma}\left(c \cdot i, b, a \cdot i\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+276}:\\ \;\;\;\;2 \cdot \left(\left(t \cdot z + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \mathsf{fma}\left(c \cdot i, b, a \cdot i\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.9
Cost	8648

\[\begin{array}{l} t_1 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right) + a \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+276}:\\ \;\;\;\;2 \cdot \left(\left(t \cdot z + x \cdot y\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \mathsf{fma}\left(c \cdot i, b, a \cdot i\right)\right)\\ \end{array} \]

Alternative 2
Error	15.1
Cost	2520

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z + x \cdot y\right)\\ t_2 := 2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{if}\;t \cdot z \leq -1 \cdot 10^{+84}:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;t \cdot z \leq -2 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \cdot z \leq -2 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \cdot z \leq 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \cdot z \leq 5 \cdot 10^{-123}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;t \cdot z \leq 4 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	15.4
Cost	2520

\[\begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ t_2 := 2 \cdot \left(x \cdot y - t_1\right)\\ t_3 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ t_4 := 2 \cdot \left(t \cdot z - t_1\right)\\ \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \cdot z \leq -50000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \cdot z \leq -5 \cdot 10^{-40}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \cdot z \leq 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \cdot z \leq 5 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \cdot z \leq 4 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z + x \cdot y\right)\\ \end{array} \]

Alternative 4
Error	1.9
Cost	2504

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

Alternative 5
Error	27.2
Cost	1892

\[\begin{array}{l} t_1 := \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ t_2 := i \cdot \left(a \cdot c\right)\\ t_3 := 2 \cdot \left(t \cdot z + x \cdot y\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+230}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+150}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_2\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+115}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.107492661228812 \cdot 10^{+28}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.4822028255731206 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.154066635379002 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3844309023797015 \cdot 10^{-178}:\\ \;\;\;\;2 \cdot \left(t \cdot z - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.6075096035303107 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.931937965679693 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(t \cdot z - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

Alternative 6
Error	25.6
Cost	1760

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ t_2 := 2 \cdot \left(t \cdot z + x \cdot y\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.4822028255731206 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.2833394740944131 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.41555354135507 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.04201547142122 \cdot 10^{-220}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right) \cdot -2\\ \mathbf{elif}\;x \leq 5.058560714379455 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.626279025830369 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	24.0
Cost	1760

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z + x \cdot y\right)\\ t_2 := 2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{if}\;c \leq -3.45 \cdot 10^{+102}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.4943338063243916 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.1751916629481212 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 5.2199458871262985 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.1428427497378974 \cdot 10^{-99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3800:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right) \cdot -2\\ \end{array} \]

Alternative 8
Error	22.3
Cost	1756

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z + x \cdot y\right)\\ t_2 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -3.45 \cdot 10^{+102}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.4943338063243916 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.1751916629481212 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.2199458871262985 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.1428427497378974 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	23.1
Cost	1756

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ t_2 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{if}\;c \leq -3.45 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.4943338063243916 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.1751916629481212 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.2199458871262985 \cdot 10^{-139}:\\ \;\;\;\;2 \cdot \left(t \cdot z + x \cdot y\right)\\ \mathbf{elif}\;c \leq 7.190946674944164 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 0.44:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	8.8
Cost	1612

\[\begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ t_2 := 2 \cdot \left(\left(t \cdot z + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(t \cdot z - t_1\right)\\ \mathbf{elif}\;c \leq 1.9773004827293404 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.28 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right) + a \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 3800:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \]

Alternative 11
Error	38.2
Cost	1508

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ t_3 := \left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{if}\;x \leq -9 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.3643973738765885 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.5682490716156495 \cdot 10^{-126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.3844309023797015 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.0118969056333048 \cdot 10^{-237}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.058560714379455 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.626279025830369 \cdot 10^{-64}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;x \leq 1.931937965679693 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	37.5
Cost	1244

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ t_3 := \left(a \cdot c\right) \cdot \left(i \cdot -2\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.3643973738765885 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.2833394740944131 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.058560714379455 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.626279025830369 \cdot 10^{-64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.931937965679693 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	37.7
Cost	1244

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.611680142910716 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.5682490716156495 \cdot 10^{-126}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{elif}\;x \leq 5.058560714379455 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.626279025830369 \cdot 10^{-64}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;x \leq 1.931937965679693 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	8.8
Cost	1224

\[\begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(t \cdot z - t_1\right)\\ \mathbf{elif}\;c \leq 3800:\\ \;\;\;\;2 \cdot \left(\left(t \cdot z + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \]

Alternative 15
Error	24.8
Cost	972

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z + x \cdot y\right)\\ \mathbf{if}\;a \leq -2.7568198486349694 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.0301497960856297 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{elif}\;a \leq 3.4491559386026935 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]

Alternative 16
Error	37.4
Cost	584

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -9.002802749271966 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9391426660653465 \cdot 10^{-160}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	43.0
Cost	320

\[2 \cdot \left(x \cdot y\right) \]

Reproduce

herbie shell --seed 2022297 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))