ABCF->ab-angle a

Percentage Accurate: 18.1% → 18.1%

Time: 6.3s

Alternatives: 4

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {B}^{2} - \left(4 \cdot A\right) \cdot C\\ \frac{-\sqrt{\left(2 \cdot \left(t\_0 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{t\_0} \end{array} \end{array} \]

FPCore

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (- (pow B 2.0) (* (* 4.0 A) C))))
   (/
    (-
     (sqrt
      (*
       (* 2.0 (* t_0 F))
       (+ (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
    t_0)))

C

double code(double A, double B, double C, double F) {
	double t_0 = pow(B, 2.0) - ((4.0 * A) * C);
	return -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / t_0;
}

Fortran

real(8) function code(a, b, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: t_0
    t_0 = (b ** 2.0d0) - ((4.0d0 * a) * c)
    code = -sqrt(((2.0d0 * (t_0 * f)) * ((a + c) + sqrt((((a - c) ** 2.0d0) + (b ** 2.0d0)))))) / t_0
end function

Java

public static double code(double A, double B, double C, double F) {
	double t_0 = Math.pow(B, 2.0) - ((4.0 * A) * C);
	return -Math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / t_0;
}

Python

def code(A, B, C, F):
	t_0 = math.pow(B, 2.0) - ((4.0 * A) * C)
	return -math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / t_0

Julia

function code(A, B, C, F)
	t_0 = Float64((B ^ 2.0) - Float64(Float64(4.0 * A) * C))
	return Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_0 * F)) * Float64(Float64(A + C) + sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0))))))) / t_0)
end

MATLAB

function tmp = code(A, B, C, F)
	t_0 = (B ^ 2.0) - ((4.0 * A) * C);
	tmp = -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / t_0;
end

Wolfram

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$0 * F), $MachinePrecision]), $MachinePrecision] * N[(N[(A + C), $MachinePrecision] + N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision]]

Initial Program: 18.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {B}^{2} - \left(4 \cdot A\right) \cdot C\\ \frac{-\sqrt{\left(2 \cdot \left(t\_0 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{t\_0} \end{array} \end{array} \]

FPCore

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (- (pow B 2.0) (* (* 4.0 A) C))))
   (/
    (-
     (sqrt
      (*
       (* 2.0 (* t_0 F))
       (+ (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
    t_0)))

C

double code(double A, double B, double C, double F) {
	double t_0 = pow(B, 2.0) - ((4.0 * A) * C);
	return -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / t_0;
}

Fortran

real(8) function code(a, b, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: t_0
    t_0 = (b ** 2.0d0) - ((4.0d0 * a) * c)
    code = -sqrt(((2.0d0 * (t_0 * f)) * ((a + c) + sqrt((((a - c) ** 2.0d0) + (b ** 2.0d0)))))) / t_0
end function

Java

public static double code(double A, double B, double C, double F) {
	double t_0 = Math.pow(B, 2.0) - ((4.0 * A) * C);
	return -Math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / t_0;
}

Python

def code(A, B, C, F):
	t_0 = math.pow(B, 2.0) - ((4.0 * A) * C)
	return -math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / t_0

Julia

function code(A, B, C, F)
	t_0 = Float64((B ^ 2.0) - Float64(Float64(4.0 * A) * C))
	return Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_0 * F)) * Float64(Float64(A + C) + sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0))))))) / t_0)
end

MATLAB

function tmp = code(A, B, C, F)
	t_0 = (B ^ 2.0) - ((4.0 * A) * C);
	tmp = -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / t_0;
end

Wolfram

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$0 * F), $MachinePrecision]), $MachinePrecision] * N[(N[(A + C), $MachinePrecision] + N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision]]

Alternative 1: 18.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {B}^{2} - \left(4 \cdot A\right) \cdot C\\ \frac{-\sqrt{\left(2 \cdot \left(t\_0 \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{t\_0} \end{array} \end{array} \]

FPCore

(FPCore (A B C F)
 :precision binary64
 (let* ((t_0 (- (pow B 2.0) (* (* 4.0 A) C))))
   (/
    (-
     (sqrt
      (*
       (* 2.0 (* t_0 F))
       (+ (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
    t_0)))

C

double code(double A, double B, double C, double F) {
	double t_0 = pow(B, 2.0) - ((4.0 * A) * C);
	return -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / t_0;
}

Fortran

real(8) function code(a, b, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    real(8) :: t_0
    t_0 = (b ** 2.0d0) - ((4.0d0 * a) * c)
    code = -sqrt(((2.0d0 * (t_0 * f)) * ((a + c) + sqrt((((a - c) ** 2.0d0) + (b ** 2.0d0)))))) / t_0
end function

Java

public static double code(double A, double B, double C, double F) {
	double t_0 = Math.pow(B, 2.0) - ((4.0 * A) * C);
	return -Math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / t_0;
}

Python

def code(A, B, C, F):
	t_0 = math.pow(B, 2.0) - ((4.0 * A) * C)
	return -math.sqrt(((2.0 * (t_0 * F)) * ((A + C) + math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / t_0

Julia

function code(A, B, C, F)
	t_0 = Float64((B ^ 2.0) - Float64(Float64(4.0 * A) * C))
	return Float64(Float64(-sqrt(Float64(Float64(2.0 * Float64(t_0 * F)) * Float64(Float64(A + C) + sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0))))))) / t_0)
end

MATLAB

function tmp = code(A, B, C, F)
	t_0 = (B ^ 2.0) - ((4.0 * A) * C);
	tmp = -sqrt(((2.0 * (t_0 * F)) * ((A + C) + sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / t_0;
end

Wolfram

code[A_, B_, C_, F_] := Block[{t$95$0 = N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision]}, N[((-N[Sqrt[N[(N[(2.0 * N[(t$95$0 * F), $MachinePrecision]), $MachinePrecision] * N[(N[(A + C), $MachinePrecision] + N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t$95$0), $MachinePrecision]]

Derivation

1. Initial program 20.8%

   \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 3.7% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ -\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F \end{array} \]

FPCore

(FPCore (A B C F)
 :precision binary64
 (- (* (- (pow B 2.0) (* (* 4.0 A) C)) F)))

C

double code(double A, double B, double C, double F) {
	return -((pow(B, 2.0) - ((4.0 * A) * C)) * F);
}

Fortran

real(8) function code(a, b, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    code = -(((b ** 2.0d0) - ((4.0d0 * a) * c)) * f)
end function

Java

public static double code(double A, double B, double C, double F) {
	return -((Math.pow(B, 2.0) - ((4.0 * A) * C)) * F);
}

Python

def code(A, B, C, F):
	return -((math.pow(B, 2.0) - ((4.0 * A) * C)) * F)

Julia

function code(A, B, C, F)
	return Float64(-Float64(Float64((B ^ 2.0) - Float64(Float64(4.0 * A) * C)) * F))
end

MATLAB

function tmp = code(A, B, C, F)
	tmp = -(((B ^ 2.0) - ((4.0 * A) * C)) * F);
end

Wolfram

code[A_, B_, C_, F_] := (-N[(N[(N[Power[B, 2.0], $MachinePrecision] - N[(N[(4.0 * A), $MachinePrecision] * C), $MachinePrecision]), $MachinePrecision] * F), $MachinePrecision])

Derivation

1. Initial program 20.8%

   \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
2. Add Preprocessing

3. Taylor expanded in A around 0

   \[\leadsto \color{blue}{-1 \cdot \left(\frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right) + \frac{-1}{2} \cdot \left(\left(A \cdot \left(B \cdot \left(\sqrt{2} \cdot \left(\frac{F \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)}{{B}^{2}} - -4 \cdot \frac{C \cdot \left(F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)}{{B}^{4}}\right)\right)\right)\right) \cdot \sqrt{\frac{1}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}}\right)} \]

5. Applied rewrites 2.8%

   \[\leadsto \color{blue}{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}} \]

6. Taylor expanded in A around 0

   \[\leadsto -\sqrt{2 \cdot \left(A \cdot \left(F \cdot \left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right)\right)\right) + 2 \cdot \left({B}^{2} \cdot \left(F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)} \]

8. Applied rewrites 3.3%

   \[\leadsto -\sqrt{2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)} \]

9. Taylor expanded in A around 0

   \[\leadsto -\left(A \cdot \left(\frac{1}{2} \cdot \left(\frac{A \cdot \left(\sqrt{2} \cdot \left(F \cdot \left(-4 \cdot \left(C \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right) + \frac{1}{2} \cdot \left(\left({B}^{2} \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)\right) \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right) - \frac{1}{4} \cdot \frac{F \cdot {\left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right)}^{2}}{{B}^{2} \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right)\right)}{B} \cdot \sqrt{\frac{1}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}}\right) + \frac{1}{2} \cdot \left(\frac{\sqrt{2} \cdot \left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right)}{B} \cdot \sqrt{\frac{F}{C + \sqrt{{B}^{2} + {C}^{2}}}}\right)\right) + \left(B \cdot \sqrt{2}\right) \cdot \sqrt{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right) \]

11. Applied rewrites 3.8%

    \[\leadsto -\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F \]
12. Add Preprocessing

Alternative 3: 3.1% accurate, 81.8× speedup

Math

\[\begin{array}{l} \\ -\left(A + C\right) \end{array} \]

FPCore

(FPCore (A B C F) :precision binary64 (- (+ A C)))

C

double code(double A, double B, double C, double F) {
	return -(A + C);
}

Fortran

real(8) function code(a, b, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    code = -(a + c)
end function

Java

public static double code(double A, double B, double C, double F) {
	return -(A + C);
}

Python

def code(A, B, C, F):
	return -(A + C)

Julia

function code(A, B, C, F)
	return Float64(-Float64(A + C))
end

MATLAB

function tmp = code(A, B, C, F)
	tmp = -(A + C);
end

Wolfram

code[A_, B_, C_, F_] := (-N[(A + C), $MachinePrecision])

Derivation

1. Initial program 20.8%

   \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
2. Add Preprocessing

3. Taylor expanded in A around 0

   \[\leadsto \color{blue}{-1 \cdot \left(\frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right) + \frac{-1}{2} \cdot \left(\left(A \cdot \left(B \cdot \left(\sqrt{2} \cdot \left(\frac{F \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)}{{B}^{2}} - -4 \cdot \frac{C \cdot \left(F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)}{{B}^{4}}\right)\right)\right)\right) \cdot \sqrt{\frac{1}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}}\right)} \]

5. Applied rewrites 2.8%

   \[\leadsto \color{blue}{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}} \]

6. Taylor expanded in A around 0

   \[\leadsto -\left(A \cdot \left(\frac{1}{2} \cdot \left(\frac{\sqrt{2} \cdot \left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right)}{B} \cdot \sqrt{\frac{F}{C + \sqrt{{B}^{2} + {C}^{2}}}}\right) + A \cdot \left(\frac{1}{2} \cdot \left(\frac{A \cdot \left(\sqrt{2} \cdot \left(F \cdot \left(-2 \cdot \left(\left(C \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)\right) \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right) + \frac{1}{2} \cdot \left(\left({B}^{2} \cdot \left(C \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)\right)\right) \cdot \sqrt{\frac{1}{{\left({B}^{2} + {C}^{2}\right)}^{3}}}\right)\right) - \frac{1}{2} \cdot \frac{\left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right) \cdot \left(F \cdot \left(-4 \cdot \left(C \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right) + \frac{1}{2} \cdot \left(\left({B}^{2} \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)\right) \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right) - \frac{1}{4} \cdot \frac{F \cdot {\left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right)}^{2}}{{B}^{2} \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right)}{{B}^{2} \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right)\right)}{B} \cdot \sqrt{\frac{1}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}}\right) + \frac{1}{2} \cdot \left(\frac{\sqrt{2} \cdot \left(F \cdot \left(-4 \cdot \left(C \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right) + \frac{1}{2} \cdot \left(\left({B}^{2} \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)\right) \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right) - \frac{1}{4} \cdot \frac{F \cdot {\left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right)}^{2}}{{B}^{2} \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right)}{B} \cdot \sqrt{\frac{1}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}}\right)\right)\right) + \left(B \cdot \sqrt{2}\right) \cdot \sqrt{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right) \]

8. Applied rewrites 3.3%

   \[\leadsto -\left(A + C\right) \]
9. Add Preprocessing

Alternative 4: 3.1% accurate, 122.8× speedup

Math

\[\begin{array}{l} \\ A + C \end{array} \]

FPCore

(FPCore (A B C F) :precision binary64 (+ A C))

C

double code(double A, double B, double C, double F) {
	return A + C;
}

Fortran

real(8) function code(a, b, c, f)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: f
    code = a + c
end function

Java

public static double code(double A, double B, double C, double F) {
	return A + C;
}

Python

def code(A, B, C, F):
	return A + C

Julia

function code(A, B, C, F)
	return Float64(A + C)
end

MATLAB

function tmp = code(A, B, C, F)
	tmp = A + C;
end

Wolfram

code[A_, B_, C_, F_] := N[(A + C), $MachinePrecision]

Derivation

1. Initial program 20.8%

   \[\frac{-\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}}{{B}^{2} - \left(4 \cdot A\right) \cdot C} \]
2. Add Preprocessing

3. Taylor expanded in A around 0

   \[\leadsto \color{blue}{-1 \cdot \left(\frac{\sqrt{2}}{B} \cdot \sqrt{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right) + A \cdot \left(\frac{-1}{2} \cdot \left(\left(A \cdot \left(B \cdot \left(\sqrt{2} \cdot \left(\frac{1}{2} \cdot \left(\frac{F \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)}{{B}^{2}} \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right) - \left(-4 \cdot \frac{C \cdot \left(\frac{F \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)}{{B}^{2}} - -4 \cdot \frac{C \cdot \left(F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)}{{B}^{4}}\right)}{{B}^{2}} + \frac{1}{4} \cdot \frac{{B}^{2} \cdot {\left(\frac{F \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)}{{B}^{2}} - -4 \cdot \frac{C \cdot \left(F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)}{{B}^{4}}\right)}^{2}}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right)\right)\right)\right)\right) \cdot \sqrt{\frac{1}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}}\right) + \frac{-1}{2} \cdot \left(\left(B \cdot \left(\sqrt{2} \cdot \left(\frac{F \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)}{{B}^{2}} - -4 \cdot \frac{C \cdot \left(F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right)}{{B}^{4}}\right)\right)\right) \cdot \sqrt{\frac{1}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}}\right)\right)} \]

5. Applied rewrites 1.6%

   \[\leadsto \color{blue}{\sqrt{\left(2 \cdot \left(\left({B}^{2} - \left(4 \cdot A\right) \cdot C\right) \cdot F\right)\right) \cdot \left(\left(A + C\right) + \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}} \]

6. Taylor expanded in A around 0

   \[\leadsto A \cdot \left(\frac{1}{2} \cdot \left(\frac{\sqrt{2} \cdot \left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right)}{B} \cdot \sqrt{\frac{F}{C + \sqrt{{B}^{2} + {C}^{2}}}}\right) + A \cdot \left(\frac{1}{2} \cdot \left(\frac{A \cdot \left(\sqrt{2} \cdot \left(F \cdot \left(-2 \cdot \left(\left(C \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)\right) \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right) + \frac{1}{2} \cdot \left(\left({B}^{2} \cdot \left(C \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)\right)\right) \cdot \sqrt{\frac{1}{{\left({B}^{2} + {C}^{2}\right)}^{3}}}\right)\right) - \frac{1}{2} \cdot \frac{\left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right) \cdot \left(F \cdot \left(-4 \cdot \left(C \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right) + \frac{1}{2} \cdot \left(\left({B}^{2} \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)\right) \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right) - \frac{1}{4} \cdot \frac{F \cdot {\left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right)}^{2}}{{B}^{2} \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right)}{{B}^{2} \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right)\right)}{B} \cdot \sqrt{\frac{1}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}}\right) + \frac{1}{2} \cdot \left(\frac{\sqrt{2} \cdot \left(F \cdot \left(-4 \cdot \left(C \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right) + \frac{1}{2} \cdot \left(\left({B}^{2} \cdot \left(1 - \frac{{C}^{2}}{{B}^{2} + {C}^{2}}\right)\right) \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right) - \frac{1}{4} \cdot \frac{F \cdot {\left(-4 \cdot \left(C \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)\right) + {B}^{2} \cdot \left(1 + -1 \cdot \left(C \cdot \sqrt{\frac{1}{{B}^{2} + {C}^{2}}}\right)\right)\right)}^{2}}{{B}^{2} \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}\right)}{B} \cdot \sqrt{\frac{1}{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}}\right)\right)\right) + \color{blue}{\left(B \cdot \sqrt{2}\right) \cdot \sqrt{F \cdot \left(C + \sqrt{{B}^{2} + {C}^{2}}\right)}} \]

8. Applied rewrites 2.8%

   \[\leadsto A + \color{blue}{C} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (A B C F)
  :name "ABCF->ab-angle a"
  :precision binary64
  :pre (TRUE)
  (/ (- (sqrt (* (* 2.0 (* (- (pow B 2.0) (* (* 4.0 A) C)) F)) (+ (+ A C) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))) (- (pow B 2.0) (* (* 4.0 A) C))))