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

Average Error: 6.3 → 1.8

Time: 49.8s

Precision: binary64

Cost: 22408

Math

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

↓

\[\begin{array}{l} t_1 := \left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) + x \cdot y\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+242}:\\ \;\;\;\;t_1 \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), c \cdot \left(-i\right), x \cdot y\right)\right)\\ \end{array} \]

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 (- (+ (* z t) (* x y)) (* (* c (+ a (* b c))) i))))
   (if (<= t_1 (- INFINITY))
     (* 2.0 (+ (- (* z t) (* c (* b (* c i)))) (* x y)))
     (if (<= t_1 2e+242)
       (* t_1 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 = ((z * t) + (x * y)) - ((c * (a + (b * c))) * i);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = 2.0 * (((z * t) - (c * (b * (c * i)))) + (x * y));
	} else if (t_1 <= 2e+242) {
		tmp = t_1 * 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(Float64(z * t) + Float64(x * y)) - Float64(Float64(c * Float64(a + Float64(b * c))) * i))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i)))) + Float64(x * y)));
	elseif (t_1 <= 2e+242)
		tmp = Float64(t_1 * 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[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+242], N[(t$95$1 * 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	6.3
Target	2.1
Herbie	1.8

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

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. Applied egg-rr 58.5

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

   3. Applied egg-rr 64.0

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{c \cdot \left(a \cdot a - {\left(b \cdot c\right)}^{2}\right)}{1} \cdot \frac{i}{a - b \cdot c}}\right) \]

   4. Taylor expanded in c around inf 39.0

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

   5. Simplified 20.7

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]
      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))): 57 points increase in error, 25 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

   6. Applied egg-rr 16.1

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

   if -inf.0 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < 2.0000000000000001e242

   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 2.0000000000000001e242 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 23.4

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

   2. Simplified 5.5

      \[\leadsto \color{blue}{2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), i \cdot \left(-c\right), x \cdot y\right)\right)} \]
      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)))): 39 points increase in error, 16 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))))): 2 points increase in error, 1 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 1.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) + x \cdot y\right)\\ \mathbf{elif}\;\left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+242}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), c \cdot \left(-i\right), x \cdot y\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.5
Cost	8004

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

Alternative 2
Error	1.8
Cost	2248

\[\begin{array}{l} t_1 := 2 \cdot \left(\left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) + x \cdot y\right)\\ t_2 := c \cdot \left(a + b \cdot c\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - t_2 \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	22.0
Cost	1496

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \leq -6.182775484365983 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.4525818274980723 \cdot 10^{+21}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;x \leq -2.4700470201173367 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.910250013515232 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.634591360892117 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.076986484897491 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	21.7
Cost	1496

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \leq -3.1256848889312855 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.4525818274980723 \cdot 10^{+21}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \mathbf{elif}\;x \leq -2.4700470201173367 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.910250013515232 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.634591360892117 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.076986484897491 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	8.4
Cost	1484

\[\begin{array}{l} t_1 := 2 \cdot \left(\left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) + x \cdot y\right)\\ \mathbf{if}\;c \leq -6200000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	8.6
Cost	1484

\[\begin{array}{l} t_1 := z \cdot t + x \cdot y\\ \mathbf{if}\;c \leq -6200000:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) + x \cdot y\right)\\ \end{array} \]

Alternative 7
Error	17.8
Cost	1356

\[\begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ t_2 := \left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{if}\;t \leq -3.017286432512051 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.643974802983974 \cdot 10^{+31}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;t \leq 10^{+188}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \]

Alternative 8
Error	38.4
Cost	1244

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := i \cdot \left(\left(a \cdot c\right) \cdot -2\right)\\ \mathbf{if}\;t \leq -7.697268119563488 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.905218937568645 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6703335760582365 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.096766794723694 \cdot 10^{-257}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.239000897412339 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.451983810892383 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	38.3
Cost	1244

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -7.697268119563488 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.905218937568645 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6703335760582365 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.096766794723694 \cdot 10^{-257}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;t \leq 5.239000897412339 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.451983810892383 \cdot 10^{-35}:\\ \;\;\;\;i \cdot \left(\left(a \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	16.5
Cost	1224

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -1060000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.513979011664591 \cdot 10^{-75}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	9.0
Cost	1224

\[\begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{if}\;c \leq -1060000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \]

Alternative 12
Error	24.2
Cost	1104

\[\begin{array}{l} t_1 := \left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{if}\;b \leq -5.4868945868749014 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.401628551492398 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(\left(a \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+246}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	22.5
Cost	972

\[\begin{array}{l} t_1 := \left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1060000000000:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	22.6
Cost	972

\[\begin{array}{l} t_1 := \left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1060000000000:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	37.3
Cost	584

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.119743268266134 \cdot 10^{-151}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	42.8
Cost	320

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

Reproduce

herbie shell --seed 2022306 
(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))))