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

Average Accuracy: 89.5% → 95.1%

Time: 25.0s

Precision: binary64

Cost: 2248

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a + b \cdot c\\ t_3 := c \cdot t_2\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(t_2 \cdot i\right)\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot t_3\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

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 (+ a (* b c))) (t_3 (* c t_2)))
   (if (<= t_3 (- INFINITY))
     (* 2.0 (- (* x y) (* c (* t_2 i))))
     (if (<= t_3 5e+258)
       (* 2.0 (- t_1 (* i t_3)))
       (* 2.0 (- t_1 (* c (* a 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 = (x * y) + (z * t);
	double t_2 = a + (b * c);
	double t_3 = c * t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) - (c * (t_2 * i)));
	} else if (t_3 <= 5e+258) {
		tmp = 2.0 * (t_1 - (i * t_3));
	} else {
		tmp = 2.0 * (t_1 - (c * (a * i)));
	}
	return tmp;
}

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 = (x * y) + (z * t);
	double t_2 = a + (b * c);
	double t_3 = c * t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) - (c * (t_2 * i)));
	} else if (t_3 <= 5e+258) {
		tmp = 2.0 * (t_1 - (i * t_3));
	} else {
		tmp = 2.0 * (t_1 - (c * (a * i)));
	}
	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 = (x * y) + (z * t)
	t_2 = a + (b * c)
	t_3 = c * t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = 2.0 * ((x * y) - (c * (t_2 * i)))
	elif t_3 <= 5e+258:
		tmp = 2.0 * (t_1 - (i * t_3))
	else:
		tmp = 2.0 * (t_1 - (c * (a * 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(Float64(x * y) + Float64(z * t))
	t_2 = Float64(a + Float64(b * c))
	t_3 = Float64(c * t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(t_2 * i))));
	elseif (t_3 <= 5e+258)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * t_3)));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(a * i))));
	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 = (x * y) + (z * t);
	t_2 = a + (b * c);
	t_3 = c * t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = 2.0 * ((x * y) - (c * (t_2 * i)));
	elseif (t_3 <= 5e+258)
		tmp = 2.0 * (t_1 - (i * t_3));
	else
		tmp = 2.0 * (t_1 - (c * (a * i)));
	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[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(t$95$2 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+258], N[(2.0 * N[(t$95$1 - N[(i * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	89.5%
Target	97.2%
Herbie	95.1%

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around 0 74.0%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 5e258

   1. Initial program 99.5%

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

   if 5e258 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 29.1%

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

   2. Simplified 91.5%

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

      [Start] 29.1	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      associate-*l* [=>] 91.5	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]
      fma-def [=>] 91.5	\[ 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Applied egg-rr 91.5%

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

      [Start] 91.5	\[ 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]
      fma-udef [=>] 91.5	\[ 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]
      +-commutative [=>] 91.5	\[ 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   4. Taylor expanded in b around 0 55.9%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{c \cdot \left(i \cdot a\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 5 \cdot 10^{+258}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	82.5%
Cost	2000

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := 2 \cdot \left(t_1 - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-180}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-5}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	62.5%
Cost	1499

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+21} \lor \neg \left(x \leq -3.8 \cdot 10^{-8} \lor \neg \left(x \leq -7.5 \cdot 10^{-216}\right) \land \left(x \leq -3.15 \cdot 10^{-245} \lor \neg \left(x \leq -7.2 \cdot 10^{-281}\right) \land x \leq 5.3 \cdot 10^{-238}\right)\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \end{array} \]

Alternative 3
Accuracy	72.9%
Cost	1490

\[\begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-47} \lor \neg \left(y \leq 2.5 \cdot 10^{-31}\right) \land \left(y \leq 3850000000 \lor \neg \left(y \leq 4.3 \cdot 10^{+38}\right)\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	68.6%
Cost	1488

\[\begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := 2 \cdot \left(z \cdot t - t_1\right)\\ t_3 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+120}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-13}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-269}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	84.0%
Cost	1480

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-49}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-152}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	86.6%
Cost	1224

\[\begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+65}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \]

Alternative 7
Accuracy	84.9%
Cost	1224

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -7 \cdot 10^{-127}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+66}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	97.2%
Cost	1216

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

Alternative 9
Accuracy	43.0%
Cost	1113

\[\begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-57}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+33} \lor \neg \left(y \leq 2.3 \cdot 10^{+67}\right) \land y \leq 6.5 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	43.7%
Cost	850

\[\begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-55} \lor \neg \left(y \leq 5 \cdot 10^{+34}\right) \land \left(y \leq 2.4 \cdot 10^{+72} \lor \neg \left(y \leq 7.5 \cdot 10^{+91}\right)\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 11
Accuracy	64.3%
Cost	712

\[\begin{array}{l} \mathbf{if}\;i \leq 3.8 \cdot 10^{+191}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{+265}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12
Accuracy	33.5%
Cost	320

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

Reproduce

herbie shell --seed 2023135 
(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))))