Rosa's TurbineBenchmark

Percentage Accurate: 85.9% → 99.8%

Time: 11.5s

Alternatives: 9

Speedup: 1.7×

• 53.9% 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: 85.9% 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: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double v, double w, double r) {
	return ((2.0 / (r * r)) + (((-0.375 + (v * 0.25)) / (1.0 - v)) * ((r * w) / ((1.0 / r) / w)))) + -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)) + ((((-0.375d0) + (v * 0.25d0)) / (1.0d0 - v)) * ((r * w) / ((1.0d0 / r) / w)))) + (-1.5d0)
end function

Java

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

Python

def code(v, w, r):
	return ((2.0 / (r * r)) + (((-0.375 + (v * 0.25)) / (1.0 - v)) * ((r * w) / ((1.0 / r) / w)))) + -1.5

Julia

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

MATLAB

function tmp = code(v, w, r)
	tmp = ((2.0 / (r * r)) + (((-0.375 + (v * 0.25)) / (1.0 - v)) * ((r * w) / ((1.0 / r) / w)))) + -1.5;
end

Wolfram

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

Derivation

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

Alternative 2: 98.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(r \cdot w\right) \cdot \left(r \cdot w\right)\\ t_1 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -27000 \lor \neg \left(v \leq 1.75 \cdot 10^{-68}\right):\\ \;\;\;\;-1.5 + \left(t_1 + t_0 \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + \left(t_1 + t_0 \cdot \left(v \cdot -0.125 - 0.375\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (* (* r w) (* r w))) (t_1 (/ 2.0 (* r r))))
   (if (or (<= v -27000.0) (not (<= v 1.75e-68)))
     (+ -1.5 (+ t_1 (* t_0 -0.25)))
     (+ -1.5 (+ t_1 (* t_0 (- (* v -0.125) 0.375)))))))

C

double code(double v, double w, double r) {
	double t_0 = (r * w) * (r * w);
	double t_1 = 2.0 / (r * r);
	double tmp;
	if ((v <= -27000.0) || !(v <= 1.75e-68)) {
		tmp = -1.5 + (t_1 + (t_0 * -0.25));
	} else {
		tmp = -1.5 + (t_1 + (t_0 * ((v * -0.125) - 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) :: t_1
    real(8) :: tmp
    t_0 = (r * w) * (r * w)
    t_1 = 2.0d0 / (r * r)
    if ((v <= (-27000.0d0)) .or. (.not. (v <= 1.75d-68))) then
        tmp = (-1.5d0) + (t_1 + (t_0 * (-0.25d0)))
    else
        tmp = (-1.5d0) + (t_1 + (t_0 * ((v * (-0.125d0)) - 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 t_1 = 2.0 / (r * r);
	double tmp;
	if ((v <= -27000.0) || !(v <= 1.75e-68)) {
		tmp = -1.5 + (t_1 + (t_0 * -0.25));
	} else {
		tmp = -1.5 + (t_1 + (t_0 * ((v * -0.125) - 0.375)));
	}
	return tmp;
}

Python

def code(v, w, r):
	t_0 = (r * w) * (r * w)
	t_1 = 2.0 / (r * r)
	tmp = 0
	if (v <= -27000.0) or not (v <= 1.75e-68):
		tmp = -1.5 + (t_1 + (t_0 * -0.25))
	else:
		tmp = -1.5 + (t_1 + (t_0 * ((v * -0.125) - 0.375)))
	return tmp

Julia

function code(v, w, r)
	t_0 = Float64(Float64(r * w) * Float64(r * w))
	t_1 = Float64(2.0 / Float64(r * r))
	tmp = 0.0
	if ((v <= -27000.0) || !(v <= 1.75e-68))
		tmp = Float64(-1.5 + Float64(t_1 + Float64(t_0 * -0.25)));
	else
		tmp = Float64(-1.5 + Float64(t_1 + Float64(t_0 * Float64(Float64(v * -0.125) - 0.375))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(v, w, r)
	t_0 = (r * w) * (r * w);
	t_1 = 2.0 / (r * r);
	tmp = 0.0;
	if ((v <= -27000.0) || ~((v <= 1.75e-68)))
		tmp = -1.5 + (t_1 + (t_0 * -0.25));
	else
		tmp = -1.5 + (t_1 + (t_0 * ((v * -0.125) - 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]}, Block[{t$95$1 = N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[v, -27000.0], N[Not[LessEqual[v, 1.75e-68]], $MachinePrecision]], N[(-1.5 + N[(t$95$1 + N[(t$95$0 * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.5 + N[(t$95$1 + N[(t$95$0 * N[(N[(v * -0.125), $MachinePrecision] - 0.375), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 3: 99.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double v, double w, double r) {
	return -1.5 + ((2.0 / (r * r)) + (((-0.375 + (v * 0.25)) / (1.0 - v)) * ((r * w) * (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 = (-1.5d0) + ((2.0d0 / (r * r)) + ((((-0.375d0) + (v * 0.25d0)) / (1.0d0 - v)) * ((r * w) * (r * w))))
end function

Java

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

Python

def code(v, w, r):
	return -1.5 + ((2.0 / (r * r)) + (((-0.375 + (v * 0.25)) / (1.0 - v)) * ((r * w) * (r * w))))

Julia

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

MATLAB

function tmp = code(v, w, r)
	tmp = -1.5 + ((2.0 / (r * r)) + (((-0.375 + (v * 0.25)) / (1.0 - v)) * ((r * w) * (r * w))));
end

Wolfram

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

Derivation

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

Alternative 4: 98.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -8.8 \cdot 10^{+24} \lor \neg \left(v \leq 1.75 \cdot 10^{-68}\right):\\ \;\;\;\;-1.5 + \left(t_0 + \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(3 + \left(t_0 - \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot 0.375\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (/ 2.0 (* r r))))
   (if (or (<= v -8.8e+24) (not (<= v 1.75e-68)))
     (+ -1.5 (+ t_0 (* (* (* r w) (* r w)) -0.25)))
     (+ -4.5 (+ 3.0 (- t_0 (* (* r w) (* (* r w) 0.375))))))))

C

double code(double v, double w, double r) {
	double t_0 = 2.0 / (r * r);
	double tmp;
	if ((v <= -8.8e+24) || !(v <= 1.75e-68)) {
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25));
	} else {
		tmp = -4.5 + (3.0 + (t_0 - ((r * w) * ((r * w) * 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 = 2.0d0 / (r * r)
    if ((v <= (-8.8d+24)) .or. (.not. (v <= 1.75d-68))) then
        tmp = (-1.5d0) + (t_0 + (((r * w) * (r * w)) * (-0.25d0)))
    else
        tmp = (-4.5d0) + (3.0d0 + (t_0 - ((r * w) * ((r * w) * 0.375d0))))
    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 <= -8.8e+24) || !(v <= 1.75e-68)) {
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25));
	} else {
		tmp = -4.5 + (3.0 + (t_0 - ((r * w) * ((r * w) * 0.375))));
	}
	return tmp;
}

Python

def code(v, w, r):
	t_0 = 2.0 / (r * r)
	tmp = 0
	if (v <= -8.8e+24) or not (v <= 1.75e-68):
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25))
	else:
		tmp = -4.5 + (3.0 + (t_0 - ((r * w) * ((r * w) * 0.375))))
	return tmp

Julia

function code(v, w, r)
	t_0 = Float64(2.0 / Float64(r * r))
	tmp = 0.0
	if ((v <= -8.8e+24) || !(v <= 1.75e-68))
		tmp = Float64(-1.5 + Float64(t_0 + Float64(Float64(Float64(r * w) * Float64(r * w)) * -0.25)));
	else
		tmp = Float64(-4.5 + Float64(3.0 + Float64(t_0 - Float64(Float64(r * w) * Float64(Float64(r * w) * 0.375)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(v, w, r)
	t_0 = 2.0 / (r * r);
	tmp = 0.0;
	if ((v <= -8.8e+24) || ~((v <= 1.75e-68)))
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25));
	else
		tmp = -4.5 + (3.0 + (t_0 - ((r * w) * ((r * w) * 0.375))));
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := Block[{t$95$0 = N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[v, -8.8e+24], N[Not[LessEqual[v, 1.75e-68]], $MachinePrecision]], N[(-1.5 + N[(t$95$0 + N[(N[(N[(r * w), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 + N[(3.0 + N[(t$95$0 - N[(N[(r * w), $MachinePrecision] * N[(N[(r * w), $MachinePrecision] * 0.375), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 5: 98.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -8.8 \cdot 10^{+24} \lor \neg \left(v \leq 1.75 \cdot 10^{-68}\right):\\ \;\;\;\;-1.5 + \left(t_0 + \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;\left(3 + \left(t_0 - \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot 0.375\right)\right)\right)\right) + -4.5\\ \end{array} \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (/ 2.0 (* r r))))
   (if (or (<= v -8.8e+24) (not (<= v 1.75e-68)))
     (+ -1.5 (+ t_0 (* (* (* r w) (* r w)) -0.25)))
     (+ (+ 3.0 (- t_0 (* (* r w) (* r (* w 0.375))))) -4.5))))

C

double code(double v, double w, double r) {
	double t_0 = 2.0 / (r * r);
	double tmp;
	if ((v <= -8.8e+24) || !(v <= 1.75e-68)) {
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25));
	} else {
		tmp = (3.0 + (t_0 - ((r * w) * (r * (w * 0.375))))) + -4.5;
	}
	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 <= (-8.8d+24)) .or. (.not. (v <= 1.75d-68))) then
        tmp = (-1.5d0) + (t_0 + (((r * w) * (r * w)) * (-0.25d0)))
    else
        tmp = (3.0d0 + (t_0 - ((r * w) * (r * (w * 0.375d0))))) + (-4.5d0)
    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 <= -8.8e+24) || !(v <= 1.75e-68)) {
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25));
	} else {
		tmp = (3.0 + (t_0 - ((r * w) * (r * (w * 0.375))))) + -4.5;
	}
	return tmp;
}

Python

def code(v, w, r):
	t_0 = 2.0 / (r * r)
	tmp = 0
	if (v <= -8.8e+24) or not (v <= 1.75e-68):
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25))
	else:
		tmp = (3.0 + (t_0 - ((r * w) * (r * (w * 0.375))))) + -4.5
	return tmp

Julia

function code(v, w, r)
	t_0 = Float64(2.0 / Float64(r * r))
	tmp = 0.0
	if ((v <= -8.8e+24) || !(v <= 1.75e-68))
		tmp = Float64(-1.5 + Float64(t_0 + Float64(Float64(Float64(r * w) * Float64(r * w)) * -0.25)));
	else
		tmp = Float64(Float64(3.0 + Float64(t_0 - Float64(Float64(r * w) * Float64(r * Float64(w * 0.375))))) + -4.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(v, w, r)
	t_0 = 2.0 / (r * r);
	tmp = 0.0;
	if ((v <= -8.8e+24) || ~((v <= 1.75e-68)))
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25));
	else
		tmp = (3.0 + (t_0 - ((r * w) * (r * (w * 0.375))))) + -4.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := Block[{t$95$0 = N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[v, -8.8e+24], N[Not[LessEqual[v, 1.75e-68]], $MachinePrecision]], N[(-1.5 + N[(t$95$0 + N[(N[(N[(r * w), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(3.0 + N[(t$95$0 - N[(N[(r * w), $MachinePrecision] * N[(r * N[(w * 0.375), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision]]]

Derivation

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

Alternative 6: 98.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -8.8 \cdot 10^{+24} \lor \neg \left(v \leq 1.6 \cdot 10^{-68}\right):\\ \;\;\;\;-1.5 + \left(t_0 + \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + \left(t_0 + -0.375 \cdot \frac{r \cdot w}{\frac{\frac{1}{r}}{w}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (/ 2.0 (* r r))))
   (if (or (<= v -8.8e+24) (not (<= v 1.6e-68)))
     (+ -1.5 (+ t_0 (* (* (* r w) (* r w)) -0.25)))
     (+ -1.5 (+ t_0 (* -0.375 (/ (* r w) (/ (/ 1.0 r) w))))))))

C

double code(double v, double w, double r) {
	double t_0 = 2.0 / (r * r);
	double tmp;
	if ((v <= -8.8e+24) || !(v <= 1.6e-68)) {
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25));
	} else {
		tmp = -1.5 + (t_0 + (-0.375 * ((r * w) / ((1.0 / 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 <= (-8.8d+24)) .or. (.not. (v <= 1.6d-68))) then
        tmp = (-1.5d0) + (t_0 + (((r * w) * (r * w)) * (-0.25d0)))
    else
        tmp = (-1.5d0) + (t_0 + ((-0.375d0) * ((r * w) / ((1.0d0 / 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 <= -8.8e+24) || !(v <= 1.6e-68)) {
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25));
	} else {
		tmp = -1.5 + (t_0 + (-0.375 * ((r * w) / ((1.0 / r) / w))));
	}
	return tmp;
}

Python

def code(v, w, r):
	t_0 = 2.0 / (r * r)
	tmp = 0
	if (v <= -8.8e+24) or not (v <= 1.6e-68):
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25))
	else:
		tmp = -1.5 + (t_0 + (-0.375 * ((r * w) / ((1.0 / r) / w))))
	return tmp

Julia

function code(v, w, r)
	t_0 = Float64(2.0 / Float64(r * r))
	tmp = 0.0
	if ((v <= -8.8e+24) || !(v <= 1.6e-68))
		tmp = Float64(-1.5 + Float64(t_0 + Float64(Float64(Float64(r * w) * Float64(r * w)) * -0.25)));
	else
		tmp = Float64(-1.5 + Float64(t_0 + Float64(-0.375 * Float64(Float64(r * w) / Float64(Float64(1.0 / 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 <= -8.8e+24) || ~((v <= 1.6e-68)))
		tmp = -1.5 + (t_0 + (((r * w) * (r * w)) * -0.25));
	else
		tmp = -1.5 + (t_0 + (-0.375 * ((r * w) / ((1.0 / r) / w))));
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := Block[{t$95$0 = N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[v, -8.8e+24], N[Not[LessEqual[v, 1.6e-68]], $MachinePrecision]], N[(-1.5 + N[(t$95$0 + N[(N[(N[(r * w), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.5 + N[(t$95$0 + N[(-0.375 * N[(N[(r * w), $MachinePrecision] / N[(N[(1.0 / r), $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 7: 98.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(r \cdot w\right) \cdot \left(r \cdot w\right)\\ t_1 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -4 \cdot 10^{+25} \lor \neg \left(v \leq 1.75 \cdot 10^{-68}\right):\\ \;\;\;\;-1.5 + \left(t_1 + t_0 \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + \left(t_1 + -0.375 \cdot t_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (* (* r w) (* r w))) (t_1 (/ 2.0 (* r r))))
   (if (or (<= v -4e+25) (not (<= v 1.75e-68)))
     (+ -1.5 (+ t_1 (* t_0 -0.25)))
     (+ -1.5 (+ t_1 (* -0.375 t_0))))))

C

double code(double v, double w, double r) {
	double t_0 = (r * w) * (r * w);
	double t_1 = 2.0 / (r * r);
	double tmp;
	if ((v <= -4e+25) || !(v <= 1.75e-68)) {
		tmp = -1.5 + (t_1 + (t_0 * -0.25));
	} else {
		tmp = -1.5 + (t_1 + (-0.375 * t_0));
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (r * w) * (r * w)
    t_1 = 2.0d0 / (r * r)
    if ((v <= (-4d+25)) .or. (.not. (v <= 1.75d-68))) then
        tmp = (-1.5d0) + (t_1 + (t_0 * (-0.25d0)))
    else
        tmp = (-1.5d0) + (t_1 + ((-0.375d0) * t_0))
    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 t_1 = 2.0 / (r * r);
	double tmp;
	if ((v <= -4e+25) || !(v <= 1.75e-68)) {
		tmp = -1.5 + (t_1 + (t_0 * -0.25));
	} else {
		tmp = -1.5 + (t_1 + (-0.375 * t_0));
	}
	return tmp;
}

Python

def code(v, w, r):
	t_0 = (r * w) * (r * w)
	t_1 = 2.0 / (r * r)
	tmp = 0
	if (v <= -4e+25) or not (v <= 1.75e-68):
		tmp = -1.5 + (t_1 + (t_0 * -0.25))
	else:
		tmp = -1.5 + (t_1 + (-0.375 * t_0))
	return tmp

Julia

function code(v, w, r)
	t_0 = Float64(Float64(r * w) * Float64(r * w))
	t_1 = Float64(2.0 / Float64(r * r))
	tmp = 0.0
	if ((v <= -4e+25) || !(v <= 1.75e-68))
		tmp = Float64(-1.5 + Float64(t_1 + Float64(t_0 * -0.25)));
	else
		tmp = Float64(-1.5 + Float64(t_1 + Float64(-0.375 * t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(v, w, r)
	t_0 = (r * w) * (r * w);
	t_1 = 2.0 / (r * r);
	tmp = 0.0;
	if ((v <= -4e+25) || ~((v <= 1.75e-68)))
		tmp = -1.5 + (t_1 + (t_0 * -0.25));
	else
		tmp = -1.5 + (t_1 + (-0.375 * t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := Block[{t$95$0 = N[(N[(r * w), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[v, -4e+25], N[Not[LessEqual[v, 1.75e-68]], $MachinePrecision]], N[(-1.5 + N[(t$95$1 + N[(t$95$0 * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.5 + N[(t$95$1 + N[(-0.375 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 8: 96.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1 \cdot 10^{+25}:\\ \;\;\;\;-1.5 + \left(t_0 + -0.25 \cdot \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + \left(t_0 + -0.375 \cdot \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (/ 2.0 (* r r))))
   (if (<= v -1e+25)
     (+ -1.5 (+ t_0 (* -0.25 (* r (* w (* r w))))))
     (+ -1.5 (+ t_0 (* -0.375 (* (* r w) (* r w))))))))

C

double code(double v, double w, double r) {
	double t_0 = 2.0 / (r * r);
	double tmp;
	if (v <= -1e+25) {
		tmp = -1.5 + (t_0 + (-0.25 * (r * (w * (r * w)))));
	} else {
		tmp = -1.5 + (t_0 + (-0.375 * ((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 <= (-1d+25)) then
        tmp = (-1.5d0) + (t_0 + ((-0.25d0) * (r * (w * (r * w)))))
    else
        tmp = (-1.5d0) + (t_0 + ((-0.375d0) * ((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 <= -1e+25) {
		tmp = -1.5 + (t_0 + (-0.25 * (r * (w * (r * w)))));
	} else {
		tmp = -1.5 + (t_0 + (-0.375 * ((r * w) * (r * w))));
	}
	return tmp;
}

Python

def code(v, w, r):
	t_0 = 2.0 / (r * r)
	tmp = 0
	if v <= -1e+25:
		tmp = -1.5 + (t_0 + (-0.25 * (r * (w * (r * w)))))
	else:
		tmp = -1.5 + (t_0 + (-0.375 * ((r * w) * (r * w))))
	return tmp

Julia

function code(v, w, r)
	t_0 = Float64(2.0 / Float64(r * r))
	tmp = 0.0
	if (v <= -1e+25)
		tmp = Float64(-1.5 + Float64(t_0 + Float64(-0.25 * Float64(r * Float64(w * Float64(r * w))))));
	else
		tmp = Float64(-1.5 + Float64(t_0 + Float64(-0.375 * Float64(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 <= -1e+25)
		tmp = -1.5 + (t_0 + (-0.25 * (r * (w * (r * w)))));
	else
		tmp = -1.5 + (t_0 + (-0.375 * ((r * w) * (r * w))));
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := Block[{t$95$0 = N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[v, -1e+25], N[(-1.5 + N[(t$95$0 + N[(-0.25 * N[(r * N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.5 + N[(t$95$0 + N[(-0.375 * N[(N[(r * w), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 9: 93.8% accurate, 1.7× speedup

Math

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

FPCore

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

C

double code(double v, double w, double r) {
	return -1.5 + ((2.0 / (r * r)) + (-0.375 * ((r * w) * (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 = (-1.5d0) + ((2.0d0 / (r * r)) + ((-0.375d0) * ((r * w) * (r * w))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2023347 
(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))