Rosa's TurbineBenchmark

Percentage Accurate: 84.5% → 99.0%

Time: 14.7s

Alternatives: 10

Speedup: 1.7×

• 52.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (-
  (-
   (+ 3.0 (/ 2.0 (* r r)))
   (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v)))
  4.5))

C

double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    code = ((3.0d0 + (2.0d0 / (r * r))) - (((0.125d0 * (3.0d0 - (2.0d0 * v))) * (((w * w) * r) * r)) / (1.0d0 - v))) - 4.5d0
end function

Java

public static double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}

Python

def code(v, w, r):
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5

Julia

function code(v, w, r)
	return Float64(Float64(Float64(3.0 + Float64(2.0 / Float64(r * r))) - Float64(Float64(Float64(0.125 * Float64(3.0 - Float64(2.0 * v))) * Float64(Float64(Float64(w * w) * r) * r)) / Float64(1.0 - v))) - 4.5)
end

MATLAB

function tmp = code(v, w, r)
	tmp = ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
end

Wolfram

code[v_, w_, r_] := N[(N[(N[(3.0 + N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(0.125 * N[(3.0 - N[(2.0 * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(w * w), $MachinePrecision] * r), $MachinePrecision] * r), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 4.5), $MachinePrecision]

Initial Program: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (-
  (-
   (+ 3.0 (/ 2.0 (* r r)))
   (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v)))
  4.5))

C

double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    code = ((3.0d0 + (2.0d0 / (r * r))) - (((0.125d0 * (3.0d0 - (2.0d0 * v))) * (((w * w) * r) * r)) / (1.0d0 - v))) - 4.5d0
end function

Java

public static double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}

Python

def code(v, w, r):
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5

Julia

function code(v, w, r)
	return Float64(Float64(Float64(3.0 + Float64(2.0 / Float64(r * r))) - Float64(Float64(Float64(0.125 * Float64(3.0 - Float64(2.0 * v))) * Float64(Float64(Float64(w * w) * r) * r)) / Float64(1.0 - v))) - 4.5)
end

MATLAB

function tmp = code(v, w, r)
	tmp = ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
end

Wolfram

code[v_, w_, r_] := N[(N[(N[(3.0 + N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(0.125 * N[(3.0 - N[(2.0 * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(w * w), $MachinePrecision] * r), $MachinePrecision] * r), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 4.5), $MachinePrecision]

Alternative 1: 99.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{2}{r}}{r}\\ \mathbf{if}\;v \leq -7.5 \cdot 10^{+24}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot 0.25\right)\\ \mathbf{elif}\;v \leq 7.6 \cdot 10^{-40}:\\ \;\;\;\;-1.5 + \left(\frac{2}{r \cdot r} + \frac{r \cdot \left(w \cdot -0.375\right)}{\frac{\frac{1}{w}}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{0.25}{\frac{\frac{1}{r \cdot w}}{r \cdot w}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (/ (/ 2.0 r) r)))
   (if (<= v -7.5e+24)
     (+ t_0 (- -1.5 (* (* (* r w) (* r w)) 0.25)))
     (if (<= v 7.6e-40)
       (+ -1.5 (+ (/ 2.0 (* r r)) (/ (* r (* w -0.375)) (/ (/ 1.0 w) r))))
       (+ t_0 (- -1.5 (/ 0.25 (/ (/ 1.0 (* r w)) (* r w)))))))))

C

double code(double v, double w, double r) {
	double t_0 = (2.0 / r) / r;
	double tmp;
	if (v <= -7.5e+24) {
		tmp = t_0 + (-1.5 - (((r * w) * (r * w)) * 0.25));
	} else if (v <= 7.6e-40) {
		tmp = -1.5 + ((2.0 / (r * r)) + ((r * (w * -0.375)) / ((1.0 / w) / r)));
	} else {
		tmp = t_0 + (-1.5 - (0.25 / ((1.0 / (r * w)) / (r * w))));
	}
	return tmp;
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (2.0d0 / r) / r
    if (v <= (-7.5d+24)) then
        tmp = t_0 + ((-1.5d0) - (((r * w) * (r * w)) * 0.25d0))
    else if (v <= 7.6d-40) then
        tmp = (-1.5d0) + ((2.0d0 / (r * r)) + ((r * (w * (-0.375d0))) / ((1.0d0 / w) / r)))
    else
        tmp = t_0 + ((-1.5d0) - (0.25d0 / ((1.0d0 / (r * w)) / (r * w))))
    end if
    code = tmp
end function

Java

public static double code(double v, double w, double r) {
	double t_0 = (2.0 / r) / r;
	double tmp;
	if (v <= -7.5e+24) {
		tmp = t_0 + (-1.5 - (((r * w) * (r * w)) * 0.25));
	} else if (v <= 7.6e-40) {
		tmp = -1.5 + ((2.0 / (r * r)) + ((r * (w * -0.375)) / ((1.0 / w) / r)));
	} else {
		tmp = t_0 + (-1.5 - (0.25 / ((1.0 / (r * w)) / (r * w))));
	}
	return tmp;
}

Python

def code(v, w, r):
	t_0 = (2.0 / r) / r
	tmp = 0
	if v <= -7.5e+24:
		tmp = t_0 + (-1.5 - (((r * w) * (r * w)) * 0.25))
	elif v <= 7.6e-40:
		tmp = -1.5 + ((2.0 / (r * r)) + ((r * (w * -0.375)) / ((1.0 / w) / r)))
	else:
		tmp = t_0 + (-1.5 - (0.25 / ((1.0 / (r * w)) / (r * w))))
	return tmp

Julia

function code(v, w, r)
	t_0 = Float64(Float64(2.0 / r) / r)
	tmp = 0.0
	if (v <= -7.5e+24)
		tmp = Float64(t_0 + Float64(-1.5 - Float64(Float64(Float64(r * w) * Float64(r * w)) * 0.25)));
	elseif (v <= 7.6e-40)
		tmp = Float64(-1.5 + Float64(Float64(2.0 / Float64(r * r)) + Float64(Float64(r * Float64(w * -0.375)) / Float64(Float64(1.0 / w) / r))));
	else
		tmp = Float64(t_0 + Float64(-1.5 - Float64(0.25 / Float64(Float64(1.0 / Float64(r * w)) / Float64(r * w)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(v, w, r)
	t_0 = (2.0 / r) / r;
	tmp = 0.0;
	if (v <= -7.5e+24)
		tmp = t_0 + (-1.5 - (((r * w) * (r * w)) * 0.25));
	elseif (v <= 7.6e-40)
		tmp = -1.5 + ((2.0 / (r * r)) + ((r * (w * -0.375)) / ((1.0 / w) / r)));
	else
		tmp = t_0 + (-1.5 - (0.25 / ((1.0 / (r * w)) / (r * w))));
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := Block[{t$95$0 = N[(N[(2.0 / r), $MachinePrecision] / r), $MachinePrecision]}, If[LessEqual[v, -7.5e+24], N[(t$95$0 + N[(-1.5 - N[(N[(N[(r * w), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[v, 7.6e-40], N[(-1.5 + N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] + N[(N[(r * N[(w * -0.375), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 / w), $MachinePrecision] / r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(-1.5 - N[(0.25 / N[(N[(1.0 / N[(r * w), $MachinePrecision]), $MachinePrecision] / N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 99.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \left(3 + \left(\frac{2}{r \cdot r} - \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v}\right)\right)\right) + -4.5 \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (+
  (+
   3.0
   (-
    (/ 2.0 (* r r))
    (* (* r w) (* (* r w) (/ (fma v -0.25 0.375) (- 1.0 v))))))
  -4.5))

C

double code(double v, double w, double r) {
	return (3.0 + ((2.0 / (r * r)) - ((r * w) * ((r * w) * (fma(v, -0.25, 0.375) / (1.0 - v)))))) + -4.5;
}

Julia

function code(v, w, r)
	return Float64(Float64(3.0 + Float64(Float64(2.0 / Float64(r * r)) - Float64(Float64(r * w) * Float64(Float64(r * w) * Float64(fma(v, -0.25, 0.375) / Float64(1.0 - v)))))) + -4.5)
end

Wolfram

code[v_, w_, r_] := N[(N[(3.0 + N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] - N[(N[(r * w), $MachinePrecision] * N[(N[(r * w), $MachinePrecision] * N[(N[(v * -0.25 + 0.375), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 99.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{r}}{r} + \left(-1.5 - \left(\left(r \cdot w\right) \cdot \left(w \cdot \frac{r}{1 - v}\right)\right) \cdot \mathsf{fma}\left(v, -0.25, 0.375\right)\right) \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (+
  (/ (/ 2.0 r) r)
  (- -1.5 (* (* (* r w) (* w (/ r (- 1.0 v)))) (fma v -0.25 0.375)))))

C

double code(double v, double w, double r) {
	return ((2.0 / r) / r) + (-1.5 - (((r * w) * (w * (r / (1.0 - v)))) * fma(v, -0.25, 0.375)));
}

Julia

function code(v, w, r)
	return Float64(Float64(Float64(2.0 / r) / r) + Float64(-1.5 - Float64(Float64(Float64(r * w) * Float64(w * Float64(r / Float64(1.0 - v)))) * fma(v, -0.25, 0.375))))
end

Wolfram

code[v_, w_, r_] := N[(N[(N[(2.0 / r), $MachinePrecision] / r), $MachinePrecision] + N[(-1.5 - N[(N[(N[(r * w), $MachinePrecision] * N[(w * N[(r / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(v * -0.25 + 0.375), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{r}}{r} + \left(-1.5 - \mathsf{fma}\left(v, -0.25, 0.375\right) \cdot \frac{r \cdot w}{\frac{1 - v}{r \cdot w}}\right) \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (+
  (/ (/ 2.0 r) r)
  (- -1.5 (* (fma v -0.25 0.375) (/ (* r w) (/ (- 1.0 v) (* r w)))))))

C

double code(double v, double w, double r) {
	return ((2.0 / r) / r) + (-1.5 - (fma(v, -0.25, 0.375) * ((r * w) / ((1.0 - v) / (r * w)))));
}

Julia

function code(v, w, r)
	return Float64(Float64(Float64(2.0 / r) / r) + Float64(-1.5 - Float64(fma(v, -0.25, 0.375) * Float64(Float64(r * w) / Float64(Float64(1.0 - v) / Float64(r * w))))))
end

Wolfram

code[v_, w_, r_] := N[(N[(N[(2.0 / r), $MachinePrecision] / r), $MachinePrecision] + N[(-1.5 - N[(N[(v * -0.25 + 0.375), $MachinePrecision] * N[(N[(r * w), $MachinePrecision] / N[(N[(1.0 - v), $MachinePrecision] / N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{r}}{r} + \left(-1.5 - \mathsf{fma}\left(v, -0.25, 0.375\right) \cdot \left(\left(r \cdot w\right) \cdot \frac{r \cdot w}{1 - v}\right)\right) \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (+
  (/ (/ 2.0 r) r)
  (- -1.5 (* (fma v -0.25 0.375) (* (* r w) (/ (* r w) (- 1.0 v)))))))

C

double code(double v, double w, double r) {
	return ((2.0 / r) / r) + (-1.5 - (fma(v, -0.25, 0.375) * ((r * w) * ((r * w) / (1.0 - v)))));
}

Julia

function code(v, w, r)
	return Float64(Float64(Float64(2.0 / r) / r) + Float64(-1.5 - Float64(fma(v, -0.25, 0.375) * Float64(Float64(r * w) * Float64(Float64(r * w) / Float64(1.0 - v))))))
end

Wolfram

code[v_, w_, r_] := N[(N[(N[(2.0 / r), $MachinePrecision] / r), $MachinePrecision] + N[(-1.5 - N[(N[(v * -0.25 + 0.375), $MachinePrecision] * N[(N[(r * w), $MachinePrecision] * N[(N[(r * w), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ -4.5 + \left(3 + \left(\frac{2}{r \cdot r} - \frac{0.125 \cdot \left(3 + v \cdot -2\right)}{\frac{1 - v}{r \cdot w} \cdot \frac{1}{r \cdot w}}\right)\right) \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (+
  -4.5
  (+
   3.0
   (-
    (/ 2.0 (* r r))
    (/
     (* 0.125 (+ 3.0 (* v -2.0)))
     (* (/ (- 1.0 v) (* r w)) (/ 1.0 (* r w))))))))

C

double code(double v, double w, double r) {
	return -4.5 + (3.0 + ((2.0 / (r * r)) - ((0.125 * (3.0 + (v * -2.0))) / (((1.0 - v) / (r * w)) * (1.0 / (r * w))))));
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    code = (-4.5d0) + (3.0d0 + ((2.0d0 / (r * r)) - ((0.125d0 * (3.0d0 + (v * (-2.0d0)))) / (((1.0d0 - v) / (r * w)) * (1.0d0 / (r * w))))))
end function

Java

public static double code(double v, double w, double r) {
	return -4.5 + (3.0 + ((2.0 / (r * r)) - ((0.125 * (3.0 + (v * -2.0))) / (((1.0 - v) / (r * w)) * (1.0 / (r * w))))));
}

Python

def code(v, w, r):
	return -4.5 + (3.0 + ((2.0 / (r * r)) - ((0.125 * (3.0 + (v * -2.0))) / (((1.0 - v) / (r * w)) * (1.0 / (r * w))))))

Julia

function code(v, w, r)
	return Float64(-4.5 + Float64(3.0 + Float64(Float64(2.0 / Float64(r * r)) - Float64(Float64(0.125 * Float64(3.0 + Float64(v * -2.0))) / Float64(Float64(Float64(1.0 - v) / Float64(r * w)) * Float64(1.0 / Float64(r * w)))))))
end

MATLAB

function tmp = code(v, w, r)
	tmp = -4.5 + (3.0 + ((2.0 / (r * r)) - ((0.125 * (3.0 + (v * -2.0))) / (((1.0 - v) / (r * w)) * (1.0 / (r * w))))));
end

Wolfram

code[v_, w_, r_] := N[(-4.5 + N[(3.0 + N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] - N[(N[(0.125 * N[(3.0 + N[(v * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(1.0 - v), $MachinePrecision] / N[(r * w), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 99.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;v \leq -2 \cdot 10^{+25} \lor \neg \left(v \leq 7.6 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{\frac{2}{r}}{r} + \left(-1.5 - \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + \left(\frac{2}{r \cdot r} + \frac{r \cdot \left(w \cdot -0.375\right)}{\frac{\frac{1}{w}}{r}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (if (or (<= v -2e+25) (not (<= v 7.6e-40)))
   (+ (/ (/ 2.0 r) r) (- -1.5 (* (* (* r w) (* r w)) 0.25)))
   (+ -1.5 (+ (/ 2.0 (* r r)) (/ (* r (* w -0.375)) (/ (/ 1.0 w) r))))))

C

double code(double v, double w, double r) {
	double tmp;
	if ((v <= -2e+25) || !(v <= 7.6e-40)) {
		tmp = ((2.0 / r) / r) + (-1.5 - (((r * w) * (r * w)) * 0.25));
	} else {
		tmp = -1.5 + ((2.0 / (r * r)) + ((r * (w * -0.375)) / ((1.0 / w) / r)));
	}
	return tmp;
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    real(8) :: tmp
    if ((v <= (-2d+25)) .or. (.not. (v <= 7.6d-40))) then
        tmp = ((2.0d0 / r) / r) + ((-1.5d0) - (((r * w) * (r * w)) * 0.25d0))
    else
        tmp = (-1.5d0) + ((2.0d0 / (r * r)) + ((r * (w * (-0.375d0))) / ((1.0d0 / w) / r)))
    end if
    code = tmp
end function

Java

public static double code(double v, double w, double r) {
	double tmp;
	if ((v <= -2e+25) || !(v <= 7.6e-40)) {
		tmp = ((2.0 / r) / r) + (-1.5 - (((r * w) * (r * w)) * 0.25));
	} else {
		tmp = -1.5 + ((2.0 / (r * r)) + ((r * (w * -0.375)) / ((1.0 / w) / r)));
	}
	return tmp;
}

Python

def code(v, w, r):
	tmp = 0
	if (v <= -2e+25) or not (v <= 7.6e-40):
		tmp = ((2.0 / r) / r) + (-1.5 - (((r * w) * (r * w)) * 0.25))
	else:
		tmp = -1.5 + ((2.0 / (r * r)) + ((r * (w * -0.375)) / ((1.0 / w) / r)))
	return tmp

Julia

function code(v, w, r)
	tmp = 0.0
	if ((v <= -2e+25) || !(v <= 7.6e-40))
		tmp = Float64(Float64(Float64(2.0 / r) / r) + Float64(-1.5 - Float64(Float64(Float64(r * w) * Float64(r * w)) * 0.25)));
	else
		tmp = Float64(-1.5 + Float64(Float64(2.0 / Float64(r * r)) + Float64(Float64(r * Float64(w * -0.375)) / Float64(Float64(1.0 / w) / r))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(v, w, r)
	tmp = 0.0;
	if ((v <= -2e+25) || ~((v <= 7.6e-40)))
		tmp = ((2.0 / r) / r) + (-1.5 - (((r * w) * (r * w)) * 0.25));
	else
		tmp = -1.5 + ((2.0 / (r * r)) + ((r * (w * -0.375)) / ((1.0 / w) / r)));
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := If[Or[LessEqual[v, -2e+25], N[Not[LessEqual[v, 7.6e-40]], $MachinePrecision]], N[(N[(N[(2.0 / r), $MachinePrecision] / r), $MachinePrecision] + N[(-1.5 - N[(N[(N[(r * w), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.5 + N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] + N[(N[(r * N[(w * -0.375), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 / w), $MachinePrecision] / r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 99.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(r \cdot w\right) \cdot \left(r \cdot w\right)\\ \mathbf{if}\;v \leq -7.5 \cdot 10^{+24} \lor \neg \left(v \leq 7.6 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{\frac{2}{r}}{r} + \left(-1.5 - t_0 \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + \left(\frac{2}{r \cdot r} + t_0 \cdot -0.375\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (* (* r w) (* r w))))
   (if (or (<= v -7.5e+24) (not (<= v 7.6e-40)))
     (+ (/ (/ 2.0 r) r) (- -1.5 (* t_0 0.25)))
     (+ -1.5 (+ (/ 2.0 (* r r)) (* t_0 -0.375))))))

C

double code(double v, double w, double r) {
	double t_0 = (r * w) * (r * w);
	double tmp;
	if ((v <= -7.5e+24) || !(v <= 7.6e-40)) {
		tmp = ((2.0 / r) / r) + (-1.5 - (t_0 * 0.25));
	} else {
		tmp = -1.5 + ((2.0 / (r * r)) + (t_0 * -0.375));
	}
	return tmp;
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (r * w) * (r * w)
    if ((v <= (-7.5d+24)) .or. (.not. (v <= 7.6d-40))) then
        tmp = ((2.0d0 / r) / r) + ((-1.5d0) - (t_0 * 0.25d0))
    else
        tmp = (-1.5d0) + ((2.0d0 / (r * r)) + (t_0 * (-0.375d0)))
    end if
    code = tmp
end function

Java

public static double code(double v, double w, double r) {
	double t_0 = (r * w) * (r * w);
	double tmp;
	if ((v <= -7.5e+24) || !(v <= 7.6e-40)) {
		tmp = ((2.0 / r) / r) + (-1.5 - (t_0 * 0.25));
	} else {
		tmp = -1.5 + ((2.0 / (r * r)) + (t_0 * -0.375));
	}
	return tmp;
}

Python

def code(v, w, r):
	t_0 = (r * w) * (r * w)
	tmp = 0
	if (v <= -7.5e+24) or not (v <= 7.6e-40):
		tmp = ((2.0 / r) / r) + (-1.5 - (t_0 * 0.25))
	else:
		tmp = -1.5 + ((2.0 / (r * r)) + (t_0 * -0.375))
	return tmp

Julia

function code(v, w, r)
	t_0 = Float64(Float64(r * w) * Float64(r * w))
	tmp = 0.0
	if ((v <= -7.5e+24) || !(v <= 7.6e-40))
		tmp = Float64(Float64(Float64(2.0 / r) / r) + Float64(-1.5 - Float64(t_0 * 0.25)));
	else
		tmp = Float64(-1.5 + Float64(Float64(2.0 / Float64(r * r)) + Float64(t_0 * -0.375)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(v, w, r)
	t_0 = (r * w) * (r * w);
	tmp = 0.0;
	if ((v <= -7.5e+24) || ~((v <= 7.6e-40)))
		tmp = ((2.0 / r) / r) + (-1.5 - (t_0 * 0.25));
	else
		tmp = -1.5 + ((2.0 / (r * r)) + (t_0 * -0.375));
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := Block[{t$95$0 = N[(N[(r * w), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[v, -7.5e+24], N[Not[LessEqual[v, 7.6e-40]], $MachinePrecision]], N[(N[(N[(2.0 / r), $MachinePrecision] / r), $MachinePrecision] + N[(-1.5 - N[(t$95$0 * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.5 + N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * -0.375), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 93.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ -1.5 + \left(\frac{2}{r \cdot r} + \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot -0.375\right) \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (+ -1.5 (+ (/ 2.0 (* r r)) (* (* (* r w) (* r w)) -0.375))))

C

double code(double v, double w, double r) {
	return -1.5 + ((2.0 / (r * r)) + (((r * w) * (r * w)) * -0.375));
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    code = (-1.5d0) + ((2.0d0 / (r * r)) + (((r * w) * (r * w)) * (-0.375d0)))
end function

Java

public static double code(double v, double w, double r) {
	return -1.5 + ((2.0 / (r * r)) + (((r * w) * (r * w)) * -0.375));
}

Python

def code(v, w, r):
	return -1.5 + ((2.0 / (r * r)) + (((r * w) * (r * w)) * -0.375))

Julia

function code(v, w, r)
	return Float64(-1.5 + Float64(Float64(2.0 / Float64(r * r)) + Float64(Float64(Float64(r * w) * Float64(r * w)) * -0.375)))
end

MATLAB

function tmp = code(v, w, r)
	tmp = -1.5 + ((2.0 / (r * r)) + (((r * w) * (r * w)) * -0.375));
end

Wolfram

code[v_, w_, r_] := N[(-1.5 + N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(r * w), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision] * -0.375), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 57.0% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{r}}{r} + -1.5 \end{array} \]

FPCore

(FPCore (v w r) :precision binary64 (+ (/ (/ 2.0 r) r) -1.5))

C

double code(double v, double w, double r) {
	return ((2.0 / r) / r) + -1.5;
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    code = ((2.0d0 / r) / r) + (-1.5d0)
end function

Java

public static double code(double v, double w, double r) {
	return ((2.0 / r) / r) + -1.5;
}

Python

def code(v, w, r):
	return ((2.0 / r) / r) + -1.5

Julia

function code(v, w, r)
	return Float64(Float64(Float64(2.0 / r) / r) + -1.5)
end

MATLAB

function tmp = code(v, w, r)
	tmp = ((2.0 / r) / r) + -1.5;
end

Wolfram

code[v_, w_, r_] := N[(N[(N[(2.0 / r), $MachinePrecision] / r), $MachinePrecision] + -1.5), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023343 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))