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

Average Error: 6.1 → 3.2

Time: 34.6s

Precision: binary64

Cost: 7876

Math

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

↓

\[\begin{array}{l} t_1 := i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+167}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \mathsf{fma}\left(c, b, a\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+277}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

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 (* i (* c (+ a (* b c))))))
   (if (<= t_1 -1e+167)
     (* 2.0 (- (* x y) (* (fma c b a) (* c i))))
     (if (<= t_1 5e+277)
       (* 2.0 (- (+ (* x y) (* z t)) t_1))
       (* 2.0 (- (* z t) (* c (* b (* c i)))))))))

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 = i * (c * (a + (b * c)));
	double tmp;
	if (t_1 <= -1e+167) {
		tmp = 2.0 * ((x * y) - (fma(c, b, a) * (c * i)));
	} else if (t_1 <= 5e+277) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	}
	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(i * Float64(c * Float64(a + Float64(b * c))))
	tmp = 0.0
	if (t_1 <= -1e+167)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(fma(c, b, a) * Float64(c * i))));
	elseif (t_1 <= 5e+277)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i)))));
	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[(i * N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+167], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(N[(c * b + a), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+277], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	6.1
Target	1.8
Herbie	3.2

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1e167

   1. Initial program 25.1

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

   2. Taylor expanded in z around 0 20.5

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

   3. Simplified 11.1

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - \mathsf{fma}\left(c, b, a\right) \cdot \left(c \cdot i\right)\right)} \]
      Proof
      (-.f64 (*.f64 y x) (*.f64 (fma.f64 c b a) (*.f64 c i))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (*.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 c b) a)) (*.f64 c i))): 1 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 c i) (+.f64 (*.f64 c b) a)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (Rewrite<= associate-*r*_binary64 (*.f64 c (*.f64 i (+.f64 (*.f64 c b) a))))): 31 points increase in error, 19 points decrease in error
      (-.f64 (*.f64 y x) (*.f64 c (Rewrite=> distribute-rgt-in_binary64 (+.f64 (*.f64 (*.f64 c b) i) (*.f64 a i))))): 2 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (Rewrite=> distribute-lft-in_binary64 (+.f64 (*.f64 c (*.f64 (*.f64 c b) i)) (*.f64 c (*.f64 a i))))): 1 points increase in error, 2 points decrease in error
      (-.f64 (*.f64 y x) (+.f64 (*.f64 c (Rewrite=> associate-*l*_binary64 (*.f64 c (*.f64 b i)))) (*.f64 c (*.f64 a i)))): 18 points increase in error, 13 points decrease in error
      (-.f64 (*.f64 y x) (+.f64 (*.f64 c (*.f64 c (Rewrite<= *-commutative_binary64 (*.f64 i b)))) (*.f64 c (*.f64 a i)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 c c) (*.f64 i b))) (*.f64 c (*.f64 a i)))): 26 points increase in error, 4 points decrease in error
      (-.f64 (*.f64 y x) (+.f64 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 c 2)) (*.f64 i b)) (*.f64 c (*.f64 a i)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (Rewrite<= cancel-sign-sub_binary64 (-.f64 (*.f64 (pow.f64 c 2) (*.f64 i b)) (*.f64 (neg.f64 c) (*.f64 a i))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (-.f64 (*.f64 (pow.f64 c 2) (*.f64 i b)) (Rewrite=> distribute-lft-neg-out_binary64 (neg.f64 (*.f64 c (*.f64 a i)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (-.f64 (*.f64 (pow.f64 c 2) (*.f64 i b)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 c (*.f64 a i)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (-.f64 (*.f64 (pow.f64 c 2) (*.f64 i b)) (Rewrite=> mul-1-neg_binary64 (neg.f64 (*.f64 c (*.f64 a i)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (-.f64 (*.f64 (pow.f64 c 2) (*.f64 i b)) (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 c) (*.f64 a i))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (Rewrite=> cancel-sign-sub_binary64 (+.f64 (*.f64 (pow.f64 c 2) (*.f64 i b)) (*.f64 c (*.f64 a i))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (+.f64 (*.f64 (Rewrite=> unpow2_binary64 (*.f64 c c)) (*.f64 i b)) (*.f64 c (*.f64 a i)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (+.f64 (Rewrite=> associate-*l*_binary64 (*.f64 c (*.f64 c (*.f64 i b)))) (*.f64 c (*.f64 a i)))): 4 points increase in error, 26 points decrease in error
      (-.f64 (*.f64 y x) (+.f64 (*.f64 c (*.f64 c (Rewrite=> *-commutative_binary64 (*.f64 b i)))) (*.f64 c (*.f64 a i)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 y x) (+.f64 (*.f64 c (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 c b) i))) (*.f64 c (*.f64 a i)))): 13 points increase in error, 18 points decrease in error
      (-.f64 (*.f64 y x) (Rewrite<= distribute-lft-in_binary64 (*.f64 c (+.f64 (*.f64 (*.f64 c b) i) (*.f64 a i))))): 2 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 y x) (*.f64 c (Rewrite<= distribute-rgt-in_binary64 (*.f64 i (+.f64 (*.f64 c b) a))))): 0 points increase in error, 2 points decrease in error

   if -1e167 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999982e277

   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 4.99999999999999982e277 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 48.5

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

   2. Taylor expanded in x around 0 20.8

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

   3. Taylor expanded in c around inf 35.4

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

   4. Taylor expanded in i around 0 30.4

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

   5. Simplified 27.6

      \[\leadsto 2 \cdot \left(t \cdot z - c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right) \]
      Proof
      (*.f64 b (*.f64 c i)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 c i) b)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 c (*.f64 i b))): 50 points increase in error, 43 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 3.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq -1 \cdot 10^{+167}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \mathsf{fma}\left(c, b, a\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 5 \cdot 10^{+277}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.8
Cost	20096

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

Alternative 2
Error	1.9
Cost	3528

\[\begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot t_1\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+308}:\\ \;\;\;\;2 \cdot t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot t_1\right)\right)\\ \end{array} \]

Alternative 3
Error	19.0
Cost	2148

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ t_2 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;y \leq -5.464629613500086 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.20615124162754 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+89}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+129}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+138}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	21.0
Cost	1492

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;c \leq -2.55 \cdot 10^{+26}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -3.278228003854966 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.3049039246418873 \cdot 10^{-169}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 8.904395668895877 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 5
Error	10.6
Cost	1480

\[\begin{array}{l} t_1 := 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{if}\;x \cdot y \leq -70000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-81}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	10.1
Cost	1480

\[\begin{array}{l} t_1 := 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{if}\;z \cdot t \leq -6 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 10^{-84}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	23.4
Cost	1364

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;c \leq -4.4 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.278228003854966 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.3049039246418873 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.904395668895877 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	23.6
Cost	1364

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;c \leq -4.4 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.278228003854966 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.3049039246418873 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.904395668895877 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+146}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 9
Error	21.3
Cost	1364

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -2.55 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.278228003854966 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.3049039246418873 \cdot 10^{-169}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 8.904395668895877 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	9.4
Cost	1356

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -2.55 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.4714024412207523 \cdot 10^{-87}:\\ \;\;\;\;2 \cdot \left(t_2 - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.87746920313087 \cdot 10^{-36}:\\ \;\;\;\;2 \cdot \left(t_2 - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	37.9
Cost	848

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -4.03419317300362 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9148503450033737 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5379807336701835 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;t \leq 1.0109624942244328 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	22.8
Cost	708

\[\begin{array}{l} \mathbf{if}\;c \leq 6.5 \cdot 10^{+146}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(c \cdot \left(\left(b \cdot i\right) \cdot -2\right)\right)\\ \end{array} \]

Alternative 13
Error	22.6
Cost	708

\[\begin{array}{l} \mathbf{if}\;c \leq 6.5 \cdot 10^{+146}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	37.4
Cost	584

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -4.03419317300362 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.0109624942244328 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	42.6
Cost	320

\[2 \cdot \left(z \cdot t\right) \]

Alternative 16
Error	62.2
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2022316 
(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))))