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

Average Error: 6.1 → 1.7

Time: 34.2s

Precision: binary64

Cost: 22408

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := t_1 - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+263}:\\ \;\;\;\;t_2 \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), c \cdot \left(-i\right), x \cdot y\right)\right)\\ \end{array} \]

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 (+ (* x y) (* z t))) (t_2 (- t_1 (* (* c (+ a (* b c))) i))))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- t_1 (* c (* c (* b i)))))
     (if (<= t_2 4e+263)
       (* t_2 2.0)
       (* 2.0 (fma z t (fma (fma b c a) (* c (- i)) (* x y))))))))

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 = (x * y) + (z * t);
	double t_2 = t_1 - ((c * (a + (b * c))) * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	} else if (t_2 <= 4e+263) {
		tmp = t_2 * 2.0;
	} else {
		tmp = 2.0 * fma(z, t, fma(fma(b, c, a), (c * -i), (x * y)));
	}
	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(x * y) + Float64(z * t))
	t_2 = Float64(t_1 - Float64(Float64(c * Float64(a + Float64(b * c))) * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(c * Float64(b * i)))));
	elseif (t_2 <= 4e+263)
		tmp = Float64(t_2 * 2.0);
	else
		tmp = Float64(2.0 * fma(z, t, fma(fma(b, c, a), Float64(c * Float64(-i)), Float64(x * y))));
	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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(t$95$1 - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+263], N[(t$95$2 * 2.0), $MachinePrecision], N[(2.0 * N[(z * t + N[(N[(b * c + a), $MachinePrecision] * N[(c * (-i)), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	6.1
Target	1.9
Herbie	1.7

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

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.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 a around 0 39.1

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

   3. Simplified 18.6

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]
      Proof
      (*.f64 c (*.f64 c (*.f64 i b))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 c c) (*.f64 i b))): 45 points increase in error, 23 points decrease in error
      (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 c 2)) (*.f64 i b)): 0 points increase in error, 0 points decrease in error

   if -inf.0 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < 4.00000000000000006e263

   1. Initial program 0.4

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

   if 4.00000000000000006e263 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 28.5

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

   2. Simplified 5.6

      \[\leadsto \color{blue}{2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), i \cdot \left(-c\right), x \cdot y\right)\right)} \]
      Proof
      (*.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (*.f64 i (neg.f64 c)) (*.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (fma.f64 z t (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 b c) a)) (*.f64 i (neg.f64 c)) (*.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (fma.f64 z t (fma.f64 (Rewrite<= +-commutative_binary64 (+.f64 a (*.f64 b c))) (*.f64 i (neg.f64 c)) (*.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (fma.f64 z t (fma.f64 (+.f64 a (*.f64 b c)) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 i c))) (*.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (fma.f64 z t (fma.f64 (+.f64 a (*.f64 b c)) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 c i))) (*.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (fma.f64 z t (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 a (*.f64 b c)) (neg.f64 (*.f64 c i))) (*.f64 x y))))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (fma.f64 z t (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (+.f64 a (*.f64 b c)) (*.f64 c i)))) (*.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (fma.f64 z t (+.f64 (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))) (*.f64 x y)))): 25 points increase in error, 12 points decrease in error
      (*.f64 2 (fma.f64 z t (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))) (*.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (fma.f64 z t (Rewrite=> associate-+l-_binary64 (-.f64 0 (-.f64 (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) (*.f64 x y)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (fma.f64 z t (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) (*.f64 x y)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 z t) (-.f64 (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) (*.f64 x y))))): 1 points increase in error, 0 points decrease in error
      (*.f64 2 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (*.f64 z t) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) (*.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x y) (-.f64 (*.f64 z t) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 4 \cdot 10^{+263}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), c \cdot \left(-i\right), x \cdot y\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	2.4
Cost	7876

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - \mathsf{fma}\left(c, b, a\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+289}:\\ \;\;\;\;\left(t_1 - t_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 2
Error	7.8
Cost	3664

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a + b \cdot c\\ t_3 := \left(c \cdot t_2\right) \cdot i\\ t_4 := 2 \cdot \left(x \cdot y - t_3\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot t_2\right)\right)\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{+77}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+203}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;t_3 \leq 10^{+289}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 3
Error	8.3
Cost	3536

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a + b \cdot c\\ t_3 := \left(c \cdot t_2\right) \cdot i\\ t_4 := 2 \cdot \left(x \cdot y - t_3\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot t_2\right)\right)\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{+77}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+203}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;t_3 \leq 10^{+299}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

Alternative 4
Error	2.7
Cost	2504

\[\begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ t_3 := x \cdot y + z \cdot t\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot t_1\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+289}:\\ \;\;\;\;\left(t_3 - t_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_3 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 5
Error	23.3
Cost	1892

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - \left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ t_3 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{if}\;i \leq -6 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -6.7 \cdot 10^{+25}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;i \leq -9.927924936437255 \cdot 10^{-53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -9.87201383555949 \cdot 10^{-94}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;i \leq -7.070929070278678 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+86}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.92 \cdot 10^{+127}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	25.7
Cost	1764

\[\begin{array}{l} t_1 := a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ t_2 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.65 \cdot 10^{+239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.554661835876736 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.0049071778337858 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.065827332268066 \cdot 10^{-201}:\\ \;\;\;\;\left(c \cdot \left(b \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;a \leq 1697990147775141400:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.819709894847415 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+220}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	26.4
Cost	1760

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ t_2 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_3 := 2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+105}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.28166229731793 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7906374844620517 \cdot 10^{-202}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	23.6
Cost	1232

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ t_2 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.7561818919710307 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	22.6
Cost	1232

\[\begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := 2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{if}\;a \leq -4613969795.600826:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.0049071778337858 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.065827332268066 \cdot 10^{-201}:\\ \;\;\;\;\left(c \cdot \left(b \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;a \leq 1697990147775141400:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	21.8
Cost	1232

\[\begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := -2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.7 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	10.9
Cost	1224

\[\begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+121}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	37.0
Cost	848

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -7.59638539695203 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.6815645232716406 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4166239457881337 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;t \leq 6.924138406732553 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	36.8
Cost	584

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -7.59638539695203 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.924138406732553 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	42.4
Cost	320

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

Reproduce

herbie shell --seed 2022294 
(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))))