ab-angle->ABCF B

Average Accuracy: 33.7% → 44.6%

Time: 41.5s

Precision: binary64

Cost: 13568

Math

\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

↓

\[\left(\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \left(b + a\right)\right) \cdot \left(b - a\right) \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (*
  (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0))))
  (cos (* PI (/ angle 180.0)))))

↓

(FPCore (a b angle)
 :precision binary64
 (* (* (sin (* angle (* PI 0.011111111111111112))) (+ b a)) (- b a)))

C

double code(double a, double b, double angle) {
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin((((double) M_PI) * (angle / 180.0)))) * cos((((double) M_PI) * (angle / 180.0)));
}

↓

double code(double a, double b, double angle) {
	return (sin((angle * (((double) M_PI) * 0.011111111111111112))) * (b + a)) * (b - a);
}

Java

public static double code(double a, double b, double angle) {
	return ((2.0 * (Math.pow(b, 2.0) - Math.pow(a, 2.0))) * Math.sin((Math.PI * (angle / 180.0)))) * Math.cos((Math.PI * (angle / 180.0)));
}

↓

public static double code(double a, double b, double angle) {
	return (Math.sin((angle * (Math.PI * 0.011111111111111112))) * (b + a)) * (b - a);
}

Python

def code(a, b, angle):
	return ((2.0 * (math.pow(b, 2.0) - math.pow(a, 2.0))) * math.sin((math.pi * (angle / 180.0)))) * math.cos((math.pi * (angle / 180.0)))

↓

def code(a, b, angle):
	return (math.sin((angle * (math.pi * 0.011111111111111112))) * (b + a)) * (b - a)

Julia

function code(a, b, angle)
	return Float64(Float64(Float64(2.0 * Float64((b ^ 2.0) - (a ^ 2.0))) * sin(Float64(pi * Float64(angle / 180.0)))) * cos(Float64(pi * Float64(angle / 180.0))))
end

↓

function code(a, b, angle)
	return Float64(Float64(sin(Float64(angle * Float64(pi * 0.011111111111111112))) * Float64(b + a)) * Float64(b - a))
end

MATLAB

function tmp = code(a, b, angle)
	tmp = ((2.0 * ((b ^ 2.0) - (a ^ 2.0))) * sin((pi * (angle / 180.0)))) * cos((pi * (angle / 180.0)));
end

↓

function tmp = code(a, b, angle)
	tmp = (sin((angle * (pi * 0.011111111111111112))) * (b + a)) * (b - a);
end

Wolfram

code[a_, b_, angle_] := N[(N[(N[(2.0 * N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[a_, b_, angle_] := N[(N[(N[Sin[N[(angle * N[(Pi * 0.011111111111111112), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision] * N[(b - a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 35.9%

   \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

2. Simplified 35.9%

   \[\leadsto \color{blue}{\left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
   Step-by-step derivation

   [Start] 35.9	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [=>] 35.9	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
   unpow2 [=>] 35.9	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   unpow2 [=>] 35.9	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

3. Applied egg-rr 35.7%

   \[\leadsto \color{blue}{\frac{\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right) \cdot \left(0 + \sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}{2}} \]
   Step-by-step derivation

   [Start] 35.9	\[ \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
   sin-cos-mult [=>] 35.9	\[ \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \color{blue}{\frac{\sin \left(\pi \cdot \frac{angle}{180} - \pi \cdot \frac{angle}{180}\right) + \sin \left(\pi \cdot \frac{angle}{180} + \pi \cdot \frac{angle}{180}\right)}{2}} \]
   associate-*r/ [=>] 35.9	\[ \color{blue}{\frac{\left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180} - \pi \cdot \frac{angle}{180}\right) + \sin \left(\pi \cdot \frac{angle}{180} + \pi \cdot \frac{angle}{180}\right)\right)}{2}} \]

4. Simplified 36.2%

   \[\leadsto \color{blue}{\frac{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}{\frac{1}{b \cdot b - a \cdot a}}} \]
   Step-by-step derivation

   [Start] 35.7	\[ \frac{\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right) \cdot \left(0 + \sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}{2} \]
   +-lft-identity [=>] 35.7	\[ \frac{\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right) \cdot \color{blue}{\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}}{2} \]
   *-commutative [=>] 35.7	\[ \frac{\color{blue}{\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}}{2} \]
   associate-/l* [=>] 35.7	\[ \color{blue}{\frac{\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}{\frac{2}{2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)}}} \]
   *-commutative [=>] 35.7	\[ \frac{\sin \color{blue}{\left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)}}{\frac{2}{2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)}} \]
   associate-*r* [=>] 36.2	\[ \frac{\sin \left(\color{blue}{\left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)} \cdot 2\right)}{\frac{2}{2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)}} \]
   *-commutative [<=] 36.2	\[ \frac{\sin \left(\left(\color{blue}{\left(angle \cdot \pi\right)} \cdot 0.005555555555555556\right) \cdot 2\right)}{\frac{2}{2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)}} \]
   associate-*l* [=>] 36.2	\[ \frac{\sin \color{blue}{\left(\left(angle \cdot \pi\right) \cdot \left(0.005555555555555556 \cdot 2\right)\right)}}{\frac{2}{2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)}} \]
   metadata-eval [=>] 36.2	\[ \frac{\sin \left(\left(angle \cdot \pi\right) \cdot \color{blue}{0.011111111111111112}\right)}{\frac{2}{2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)}} \]
   associate-/r* [=>] 36.2	\[ \frac{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}{\color{blue}{\frac{\frac{2}{2}}{\mathsf{fma}\left(b, b, -a \cdot a\right)}}} \]
   metadata-eval [=>] 36.2	\[ \frac{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}{\frac{\color{blue}{1}}{\mathsf{fma}\left(b, b, -a \cdot a\right)}} \]
   fma-neg [<=] 36.2	\[ \frac{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}{\frac{1}{\color{blue}{b \cdot b - a \cdot a}}} \]

5. Applied egg-rr 43.9%

   \[\leadsto \color{blue}{\left(\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \left(b + a\right)\right) \cdot \left(b - a\right)} \]
   Step-by-step derivation

   [Start] 36.2	\[ \frac{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}{\frac{1}{b \cdot b - a \cdot a}} \]
   associate-/r/ [=>] 36.2	\[ \color{blue}{\frac{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}{1} \cdot \left(b \cdot b - a \cdot a\right)} \]
   /-rgt-identity [=>] 36.2	\[ \color{blue}{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)} \cdot \left(b \cdot b - a \cdot a\right) \]
   difference-of-squares [=>] 36.2	\[ \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)} \]
   associate-*r* [=>] 44.0	\[ \color{blue}{\left(\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot \left(b + a\right)\right) \cdot \left(b - a\right)} \]
   associate-*l* [=>] 43.9	\[ \left(\sin \color{blue}{\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)} \cdot \left(b + a\right)\right) \cdot \left(b - a\right) \]

6. Final simplification 43.9%

   \[\leadsto \left(\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \left(b + a\right)\right) \cdot \left(b - a\right) \]

Alternatives

Alternative 1
Accuracy	43.3%
Cost	13704

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.00012:\\ \;\;\;\;\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \left(a \cdot \left(-a\right)\right)\\ \mathbf{elif}\;angle \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(b - a\right) \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot \left(b \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	43.3%
Cost	13704

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.000125:\\ \;\;\;\;\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \left(a \cdot \left(-a\right)\right)\\ \mathbf{elif}\;angle \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(b - a\right) \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot \left(b \cdot \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	43.1%
Cost	13577

\[\begin{array}{l} \mathbf{if}\;angle \leq -1.02 \cdot 10^{+31} \lor \neg \left(angle \leq 7.5 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	43.1%
Cost	13576

\[\begin{array}{l} t_0 := \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{if}\;angle \leq -1.05 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(b \cdot t_0\right)\\ \mathbf{elif}\;angle \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(b - a\right) \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(b \cdot b\right)\\ \end{array} \]

Alternative 5
Accuracy	42.9%
Cost	13576

\[\begin{array}{l} t_0 := \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{if}\;angle \leq -6 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \left(\left(-a\right) \cdot t_0\right)\\ \mathbf{elif}\;angle \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(b - a\right) \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(b \cdot b\right)\\ \end{array} \]

Alternative 6
Accuracy	43.3%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.000125:\\ \;\;\;\;\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \left(a \cdot \left(-a\right)\right)\\ \mathbf{elif}\;angle \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(b - a\right) \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(b \cdot b\right)\\ \end{array} \]

Alternative 7
Accuracy	34.7%
Cost	7433

\[\begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-43} \lor \neg \left(a \leq 3.8 \cdot 10^{+149}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \left(-\pi\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(angle \cdot \pi\right) \cdot \left(b \cdot b - a \cdot a\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	33.6%
Cost	7241

\[\begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-56} \lor \neg \left(a \leq 5.3 \cdot 10^{-67}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(a \cdot \left(-\pi\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	32.3%
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-70}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+26}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(\pi \cdot a\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	32.3%
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-70}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+26}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(\pi \cdot a\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(angle \cdot \pi\right) \cdot \left(0.011111111111111112 \cdot b\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	39.6%
Cost	7168

\[0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \]

Alternative 12
Accuracy	39.7%
Cost	7168

\[\left(b - a\right) \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right) \]

Alternative 13
Accuracy	21.1%
Cost	6912

\[0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(\pi \cdot b\right)\right)\right) \]

Alternative 14
Accuracy	25.0%
Cost	6912

\[0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right) \]

Alternative 15
Accuracy	25.0%
Cost	6912

\[0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right) \]

Alternative 16
Accuracy	13.0%
Cost	320

\[0.011111111111111112 \cdot \left(angle \cdot 0\right) \]

Reproduce

herbie shell --seed 2023157 
(FPCore (a b angle)
  :name "ab-angle->ABCF B"
  :precision binary64
  (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0)))) (cos (* PI (/ angle 180.0)))))