rsin A (should all be same)

Average Error: 15.0 → 15.0

Time: 25.4s

Precision: binary64

Cost: 13248

Math

\[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]

↓

\[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]

FPCore

(FPCore (r a b) :precision binary64 (/ (* r (sin b)) (cos (+ a b))))

↓

(FPCore (r a b) :precision binary64 (/ (* r (sin b)) (cos (+ a b))))

C

double code(double r, double a, double b) {
	return (r * sin(b)) / cos((a + b));
}

↓

double code(double r, double a, double b) {
	return (r * sin(b)) / cos((a + b));
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (r * sin(b)) / cos((a + b))
end function

↓

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (r * sin(b)) / cos((a + b))
end function

Java

public static double code(double r, double a, double b) {
	return (r * Math.sin(b)) / Math.cos((a + b));
}

↓

public static double code(double r, double a, double b) {
	return (r * Math.sin(b)) / Math.cos((a + b));
}

Python

def code(r, a, b):
	return (r * math.sin(b)) / math.cos((a + b))

↓

def code(r, a, b):
	return (r * math.sin(b)) / math.cos((a + b))

Julia

function code(r, a, b)
	return Float64(Float64(r * sin(b)) / cos(Float64(a + b)))
end

↓

function code(r, a, b)
	return Float64(Float64(r * sin(b)) / cos(Float64(a + b)))
end

MATLAB

function tmp = code(r, a, b)
	tmp = (r * sin(b)) / cos((a + b));
end

↓

function tmp = code(r, a, b)
	tmp = (r * sin(b)) / cos((a + b));
end

Wolfram

code[r_, a_, b_] := N[(N[(r * N[Sin[b], $MachinePrecision]), $MachinePrecision] / N[Cos[N[(a + b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[r_, a_, b_] := N[(N[(r * N[Sin[b], $MachinePrecision]), $MachinePrecision] / N[Cos[N[(a + b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.0

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]

2. Final simplification 15.0

   \[\leadsto \frac{r \cdot \sin b}{\cos \left(a + b\right)} \]

Alternatives

Alternative 1
Error	15.2
Cost	13384

\[\begin{array}{l} t_0 := r \cdot \frac{\sin b}{\cos b}\\ \mathbf{if}\;b \leq -1.05:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 0.00017:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	15.2
Cost	13384

\[\begin{array}{l} \mathbf{if}\;b \leq -1.05:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\sin b \cdot \frac{r}{\cos b}\\ \end{array} \]

Alternative 3
Error	15.2
Cost	13384

\[\begin{array}{l} t_0 := \frac{\sin b \cdot r}{\cos b}\\ \mathbf{if}\;b \leq -1.05:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 0.0003:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	15.0
Cost	13248

\[r \cdot \frac{\sin b}{\cos \left(b + a\right)} \]

Alternative 5
Error	15.0
Cost	13248

\[\sin b \cdot \frac{r}{\cos \left(b + a\right)} \]

Alternative 6
Error	28.7
Cost	13120

\[r \cdot \frac{\sin b}{\cos a} \]

Alternative 7
Error	28.6
Cost	6984

\[\begin{array}{l} t_0 := r \cdot \frac{\sin b}{1}\\ \mathbf{if}\;b \leq -10500000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 1.45:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	31.4
Cost	6720

\[b \cdot \frac{r}{\cos a} \]

Alternative 9
Error	42.1
Cost	192

\[r \cdot b \]

Reproduce

herbie shell --seed 2023068 
(FPCore (r a b)
  :name "rsin A (should all be same)"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))