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

Average Error: 6.4 → 0.7

Time: 21.8s

Precision: binary64

Cost: 1736

Math

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

↓

\[\begin{array}{l} t_1 := a + b \cdot c\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;i \leq -1.45 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(t_2 - \left(t_1 \cdot c\right) \cdot i\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-192}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right) + c \cdot \left(a \cdot i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_2 - t_1 \cdot \left(i \cdot c\right)\right)\\ \end{array} \]

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 (+ a (* b c))) (t_2 (+ (* x y) (* z t))))
   (if (<= i -1.45e+52)
     (* 2.0 (- t_2 (* (* t_1 c) i)))
     (if (<= i 2e-192)
       (* 2.0 (+ (* x y) (- (* z t) (+ (* c (* b (* c i))) (* c (* a i))))))
       (* 2.0 (- t_2 (* t_1 (* i c))))))))

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 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (i <= -1.45e+52) {
		tmp = 2.0 * (t_2 - ((t_1 * c) * i));
	} else if (i <= 2e-192) {
		tmp = 2.0 * ((x * y) + ((z * t) - ((c * (b * (c * i))) + (c * (a * i)))));
	} else {
		tmp = 2.0 * (t_2 - (t_1 * (i * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

↓

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (b * c)
    t_2 = (x * y) + (z * t)
    if (i <= (-1.45d+52)) then
        tmp = 2.0d0 * (t_2 - ((t_1 * c) * i))
    else if (i <= 2d-192) then
        tmp = 2.0d0 * ((x * y) + ((z * t) - ((c * (b * (c * i))) + (c * (a * i)))))
    else
        tmp = 2.0d0 * (t_2 - (t_1 * (i * c)))
    end if
    code = tmp
end function

Java

public static 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));
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (i <= -1.45e+52) {
		tmp = 2.0 * (t_2 - ((t_1 * c) * i));
	} else if (i <= 2e-192) {
		tmp = 2.0 * ((x * y) + ((z * t) - ((c * (b * (c * i))) + (c * (a * i)))));
	} else {
		tmp = 2.0 * (t_2 - (t_1 * (i * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

↓

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if i <= -1.45e+52:
		tmp = 2.0 * (t_2 - ((t_1 * c) * i))
	elif i <= 2e-192:
		tmp = 2.0 * ((x * y) + ((z * t) - ((c * (b * (c * i))) + (c * (a * i)))))
	else:
		tmp = 2.0 * (t_2 - (t_1 * (i * c)))
	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(a + Float64(b * c))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (i <= -1.45e+52)
		tmp = Float64(2.0 * Float64(t_2 - Float64(Float64(t_1 * c) * i)));
	elseif (i <= 2e-192)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(Float64(c * Float64(b * Float64(c * i))) + Float64(c * Float64(a * i))))));
	else
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(i * c))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

↓

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if (i <= -1.45e+52)
		tmp = 2.0 * (t_2 - ((t_1 * c) * i));
	elseif (i <= 2e-192)
		tmp = 2.0 * ((x * y) + ((z * t) - ((c * (b * (c * i))) + (c * (a * i)))));
	else
		tmp = 2.0 * (t_2 - (t_1 * (i * c)));
	end
	tmp_2 = 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[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.45e+52], N[(2.0 * N[(t$95$2 - N[(N[(t$95$1 * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e-192], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	6.4
Target	1.9
Herbie	0.7

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

Derivation

1. Split input into 3 regimes

2. if i < -1.45e52

   1. Initial program 0.7

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

   if -1.45e52 < i < 2.0000000000000002e-192

   1. Initial program 10.2

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

   2. Simplified 2.3

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

      [Start] 10.2	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational_best_oopsla_all_46_json_45_simplify-89 [=>] 10.2	\[ \color{blue}{2 \cdot \left(\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \cdot \frac{2}{2}\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 10.2	\[ 2 \cdot \color{blue}{\left(\frac{2}{2} \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-35 [=>] 10.2	\[ 2 \cdot \left(\frac{2}{2} \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-107 [=>] 10.2	\[ 2 \cdot \left(\frac{2}{2} \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-37 [=>] 10.2	\[ 2 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \frac{2}{2} + \frac{2}{2} \cdot \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]
      metadata-eval [=>] 10.2	\[ 2 \cdot \left(\left(x \cdot y\right) \cdot \color{blue}{1} + \frac{2}{2} \cdot \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-52 [=>] 10.2	\[ 2 \cdot \left(\color{blue}{x \cdot y} + \frac{2}{2} \cdot \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 10.2	\[ 2 \cdot \left(x \cdot y + \color{blue}{\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \cdot \frac{2}{2}}\right) \]
      metadata-eval [=>] 10.2	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \cdot \color{blue}{1}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-52 [=>] 10.2	\[ 2 \cdot \left(x \cdot y + \color{blue}{\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 10.2	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 10.2	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - i \cdot \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)}\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 2.3	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 2.3	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right)\right) \]

   3. Applied egg-rr 0.4

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

   if 2.0000000000000002e-192 < i

   1. Initial program 4.0

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

   2. Simplified 1.0

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

      [Start] 4.0	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational_best_oopsla_all_46_json_45_simplify-89 [=>] 4.0	\[ \color{blue}{2 \cdot \left(\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \cdot \frac{2}{2}\right)} \]
      metadata-eval [=>] 4.0	\[ 2 \cdot \left(\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \cdot \color{blue}{1}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-52 [=>] 4.0	\[ 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 4.0	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 1.0	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(i \cdot c\right)}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.45 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-192}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right) + c \cdot \left(a \cdot i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(i \cdot c\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	2.5
Cost	2504

\[\begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+227}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - \left(b \cdot \left(\left(c \cdot i\right) \cdot c\right) + a \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 2
Error	10.0
Cost	2248

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	7.7
Cost	2248

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+238}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	5.3
Cost	2248

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := 2 \cdot \left(t_1 - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+114}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	21.2
Cost	1560

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.45 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.45 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(y \cdot x - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	21.2
Cost	1560

\[\begin{array}{l} t_1 := a + c \cdot b\\ t_2 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_3 := 2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -6.5 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(y \cdot x - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-t_1\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	21.3
Cost	1560

\[\begin{array}{l} t_1 := a + c \cdot b\\ t_2 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;c \leq -2.36 \cdot 10^{+104}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.45 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(y \cdot x - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{+27}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-t_1\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 \cdot \left(i \cdot \left(-c\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	20.8
Cost	1232

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-139}:\\ \;\;\;\;2 \cdot \left(y \cdot x - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	1.9
Cost	1216

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

Alternative 10
Error	38.1
Cost	1172

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := 2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -1.06 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-134}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	23.0
Cost	972

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{+102}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot a\right) \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	22.5
Cost	972

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(c \cdot \left(i \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 2.55 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot a\right) \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	37.7
Cost	848

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := 2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -1.06 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	23.1
Cost	840

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	36.4
Cost	716

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-133}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	42.7
Cost	320

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

Reproduce

herbie shell --seed 2023090 
(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))))