ab-angle->ABCF D

Percentage Accurate: 82.7% → 99.6%

Time: 3.9s

Alternatives: 3

Speedup: 1.0×

• 28.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ -\left(\left(a \cdot a\right) \cdot b\right) \cdot b \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (- (* (* (* a a) b) b)))

C

double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -(((a * a) * b) * b)
end function

Java

public static double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Python

def code(a, b):
	return -(((a * a) * b) * b)

Julia

function code(a, b)
	return Float64(-Float64(Float64(Float64(a * a) * b) * b))
end

MATLAB

function tmp = code(a, b)
	tmp = -(((a * a) * b) * b);
end

Wolfram

code[a_, b_] := (-N[(N[(N[(a * a), $MachinePrecision] * b), $MachinePrecision] * b), $MachinePrecision])

Initial Program: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ -\left(\left(a \cdot a\right) \cdot b\right) \cdot b \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (- (* (* (* a a) b) b)))

C

double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -(((a * a) * b) * b)
end function

Java

public static double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Python

def code(a, b):
	return -(((a * a) * b) * b)

Julia

function code(a, b)
	return Float64(-Float64(Float64(Float64(a * a) * b) * b))
end

MATLAB

function tmp = code(a, b)
	tmp = -(((a * a) * b) * b);
end

Wolfram

code[a_, b_] := (-N[(N[(N[(a * a), $MachinePrecision] * b), $MachinePrecision] * b), $MachinePrecision])

Alternative 1: 99.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} a = |a|\\ b = |b|\\ \\ {\left(a \cdot b\right)}^{1.25} \cdot \left(-{\left(a \cdot b\right)}^{0.75}\right) \end{array} \]

FPCore

NOTE: a should be positive before calling this function
NOTE: b should be positive before calling this function
(FPCore (a b)
 :precision binary64
 (* (pow (* a b) 1.25) (- (pow (* a b) 0.75))))

C

a = abs(a);
b = abs(b);
double code(double a, double b) {
	return pow((a * b), 1.25) * -pow((a * b), 0.75);
}

Fortran

NOTE: a should be positive before calling this function
NOTE: b should be positive before calling this function
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((a * b) ** 1.25d0) * -((a * b) ** 0.75d0)
end function

Java

a = Math.abs(a);
b = Math.abs(b);
public static double code(double a, double b) {
	return Math.pow((a * b), 1.25) * -Math.pow((a * b), 0.75);
}

Python

a = abs(a)
b = abs(b)
def code(a, b):
	return math.pow((a * b), 1.25) * -math.pow((a * b), 0.75)

Julia

a = abs(a)
b = abs(b)
function code(a, b)
	return Float64((Float64(a * b) ^ 1.25) * Float64(-(Float64(a * b) ^ 0.75)))
end

MATLAB

a = abs(a)
b = abs(b)
function tmp = code(a, b)
	tmp = ((a * b) ^ 1.25) * -((a * b) ^ 0.75);
end

Wolfram

NOTE: a should be positive before calling this function
NOTE: b should be positive before calling this function
code[a_, b_] := N[(N[Power[N[(a * b), $MachinePrecision], 1.25], $MachinePrecision] * (-N[Power[N[(a * b), $MachinePrecision], 0.75], $MachinePrecision])), $MachinePrecision]

Derivation

1. Initial program 79.2%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Step-by-step derivation

   1. associate-*l* 74.5%

      \[\leadsto -\color{blue}{\left(a \cdot a\right) \cdot \left(b \cdot b\right)} \]

3. Simplified 74.5%

   \[\leadsto \color{blue}{-\left(a \cdot a\right) \cdot \left(b \cdot b\right)} \]
4. Step-by-step derivation

   1. add-cbrt-cube 63.2%

      \[\leadsto -\color{blue}{\sqrt[3]{\left(\left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right) \cdot \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right) \cdot \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)}} \]

   2. pow3 63.2%

      \[\leadsto -\sqrt[3]{\color{blue}{{\left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)}^{3}}} \]

   3. add-sqr-sqrt 63.1%

      \[\leadsto -\sqrt[3]{{\color{blue}{\left(\sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)} \cdot \sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right)}}^{3}} \]

   4. pow2 63.1%

      \[\leadsto -\sqrt[3]{{\color{blue}{\left({\left(\sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right)}^{2}\right)}}^{3}} \]

   5. metadata-eval 63.1%

      \[\leadsto -\sqrt[3]{{\left({\left(\sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right)}^{2}\right)}^{\color{blue}{\left(2 + 1\right)}}} \]

   6. pow-pow 63.2%

      \[\leadsto -\sqrt[3]{\color{blue}{{\left(\sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right)}^{\left(2 \cdot \left(2 + 1\right)\right)}}} \]

   7. unswap-sqr 74.6%

      \[\leadsto -\sqrt[3]{{\left(\sqrt{\color{blue}{\left(a \cdot b\right) \cdot \left(a \cdot b\right)}}\right)}^{\left(2 \cdot \left(2 + 1\right)\right)}} \]

   8. sqrt-prod 44.1%

      \[\leadsto -\sqrt[3]{{\color{blue}{\left(\sqrt{a \cdot b} \cdot \sqrt{a \cdot b}\right)}}^{\left(2 \cdot \left(2 + 1\right)\right)}} \]

   9. add-sqr-sqrt 74.6%

      \[\leadsto -\sqrt[3]{{\color{blue}{\left(a \cdot b\right)}}^{\left(2 \cdot \left(2 + 1\right)\right)}} \]

   10. metadata-eval 74.6%

       \[\leadsto -\sqrt[3]{{\left(a \cdot b\right)}^{\left(2 \cdot \color{blue}{3}\right)}} \]

   11. metadata-eval 74.6%

       \[\leadsto -\sqrt[3]{{\left(a \cdot b\right)}^{\color{blue}{6}}} \]

5. Applied egg-rr 74.6%

   \[\leadsto -\color{blue}{\sqrt[3]{{\left(a \cdot b\right)}^{6}}} \]
6. Step-by-step derivation

   1. pow1/3 73.5%

      \[\leadsto -\color{blue}{{\left({\left(a \cdot b\right)}^{6}\right)}^{0.3333333333333333}} \]

   2. pow-pow 99.7%

      \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{\left(6 \cdot 0.3333333333333333\right)}} \]

   3. metadata-eval 99.7%

      \[\leadsto -{\left(a \cdot b\right)}^{\color{blue}{2}} \]

   4. metadata-eval 99.7%

      \[\leadsto -{\left(a \cdot b\right)}^{\color{blue}{\left(0.3333333333333333 \cdot 6\right)}} \]

   5. pow-pow 59.6%

      \[\leadsto -\color{blue}{{\left({\left(a \cdot b\right)}^{0.3333333333333333}\right)}^{6}} \]

   6. pow1/3 98.6%

      \[\leadsto -{\color{blue}{\left(\sqrt[3]{a \cdot b}\right)}}^{6} \]

7. Applied egg-rr 98.6%

   \[\leadsto -\color{blue}{{\left(\sqrt[3]{a \cdot b}\right)}^{6}} \]
8. Step-by-step derivation

   1. pow1/3 59.6%

      \[\leadsto -{\color{blue}{\left({\left(a \cdot b\right)}^{0.3333333333333333}\right)}}^{6} \]

   2. pow-pow 99.7%

      \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{\left(0.3333333333333333 \cdot 6\right)}} \]

   3. metadata-eval 99.7%

      \[\leadsto -{\left(a \cdot b\right)}^{\color{blue}{2}} \]

   4. metadata-eval 99.7%

      \[\leadsto -{\left(a \cdot b\right)}^{\color{blue}{\left(1.5 + 0.5\right)}} \]

   5. pow-prod-up 61.6%

      \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{1.5} \cdot {\left(a \cdot b\right)}^{0.5}} \]

   6. pow1/2 55.3%

      \[\leadsto -{\left(a \cdot b\right)}^{1.5} \cdot \color{blue}{\sqrt{a \cdot b}} \]

   7. add-sqr-sqrt 55.3%

      \[\leadsto -\color{blue}{\left(\sqrt{{\left(a \cdot b\right)}^{1.5}} \cdot \sqrt{{\left(a \cdot b\right)}^{1.5}}\right)} \cdot \sqrt{a \cdot b} \]

   8. associate-*l* 55.3%

      \[\leadsto -\color{blue}{\sqrt{{\left(a \cdot b\right)}^{1.5}} \cdot \left(\sqrt{{\left(a \cdot b\right)}^{1.5}} \cdot \sqrt{a \cdot b}\right)} \]

   9. sqrt-pow1 55.3%

      \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{\left(\frac{1.5}{2}\right)}} \cdot \left(\sqrt{{\left(a \cdot b\right)}^{1.5}} \cdot \sqrt{a \cdot b}\right) \]

   10. metadata-eval 55.3%

       \[\leadsto -{\left(a \cdot b\right)}^{\color{blue}{0.75}} \cdot \left(\sqrt{{\left(a \cdot b\right)}^{1.5}} \cdot \sqrt{a \cdot b}\right) \]

   11. sqrt-pow1 55.3%

       \[\leadsto -{\left(a \cdot b\right)}^{0.75} \cdot \left(\color{blue}{{\left(a \cdot b\right)}^{\left(\frac{1.5}{2}\right)}} \cdot \sqrt{a \cdot b}\right) \]

   12. pow1/2 61.5%

       \[\leadsto -{\left(a \cdot b\right)}^{0.75} \cdot \left({\left(a \cdot b\right)}^{\left(\frac{1.5}{2}\right)} \cdot \color{blue}{{\left(a \cdot b\right)}^{0.5}}\right) \]

   13. pow-prod-up 61.6%

       \[\leadsto -{\left(a \cdot b\right)}^{0.75} \cdot \color{blue}{{\left(a \cdot b\right)}^{\left(\frac{1.5}{2} + 0.5\right)}} \]

   14. metadata-eval 61.6%

       \[\leadsto -{\left(a \cdot b\right)}^{0.75} \cdot {\left(a \cdot b\right)}^{\left(\color{blue}{0.75} + 0.5\right)} \]

   15. metadata-eval 61.6%

       \[\leadsto -{\left(a \cdot b\right)}^{0.75} \cdot {\left(a \cdot b\right)}^{\color{blue}{1.25}} \]

9. Applied egg-rr 61.6%

   \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{0.75} \cdot {\left(a \cdot b\right)}^{1.25}} \]
10. Step-by-step derivation

    1. *-commutative 61.6%

       \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{1.25} \cdot {\left(a \cdot b\right)}^{0.75}} \]

11. Simplified 61.6%

    \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{1.25} \cdot {\left(a \cdot b\right)}^{0.75}} \]

12. Final simplification 61.6%

    \[\leadsto {\left(a \cdot b\right)}^{1.25} \cdot \left(-{\left(a \cdot b\right)}^{0.75}\right) \]

Alternative 2: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} a = |a|\\ b = |b|\\ \\ \left(b \cdot b\right) \cdot \left(a \cdot \left(-a\right)\right) \end{array} \]

FPCore

NOTE: a should be positive before calling this function
NOTE: b should be positive before calling this function
(FPCore (a b) :precision binary64 (* (* b b) (* a (- a))))

C

a = abs(a);
b = abs(b);
double code(double a, double b) {
	return (b * b) * (a * -a);
}

Fortran

NOTE: a should be positive before calling this function
NOTE: b should be positive before calling this function
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (b * b) * (a * -a)
end function

Java

a = Math.abs(a);
b = Math.abs(b);
public static double code(double a, double b) {
	return (b * b) * (a * -a);
}

Python

a = abs(a)
b = abs(b)
def code(a, b):
	return (b * b) * (a * -a)

Julia

a = abs(a)
b = abs(b)
function code(a, b)
	return Float64(Float64(b * b) * Float64(a * Float64(-a)))
end

MATLAB

a = abs(a)
b = abs(b)
function tmp = code(a, b)
	tmp = (b * b) * (a * -a);
end

Wolfram

NOTE: a should be positive before calling this function
NOTE: b should be positive before calling this function
code[a_, b_] := N[(N[(b * b), $MachinePrecision] * N[(a * (-a)), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.2%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Step-by-step derivation

   1. associate-*l* 74.5%

      \[\leadsto -\color{blue}{\left(a \cdot a\right) \cdot \left(b \cdot b\right)} \]

3. Simplified 74.5%

   \[\leadsto \color{blue}{-\left(a \cdot a\right) \cdot \left(b \cdot b\right)} \]

4. Final simplification 74.5%

   \[\leadsto \left(b \cdot b\right) \cdot \left(a \cdot \left(-a\right)\right) \]

Alternative 3: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} a = |a|\\ b = |b|\\ \\ \left(a \cdot b\right) \cdot \left(a \cdot \left(-b\right)\right) \end{array} \]

FPCore

NOTE: a should be positive before calling this function
NOTE: b should be positive before calling this function
(FPCore (a b) :precision binary64 (* (* a b) (* a (- b))))

C

a = abs(a);
b = abs(b);
double code(double a, double b) {
	return (a * b) * (a * -b);
}

Fortran

NOTE: a should be positive before calling this function
NOTE: b should be positive before calling this function
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (a * b) * (a * -b)
end function

Java

a = Math.abs(a);
b = Math.abs(b);
public static double code(double a, double b) {
	return (a * b) * (a * -b);
}

Python

a = abs(a)
b = abs(b)
def code(a, b):
	return (a * b) * (a * -b)

Julia

a = abs(a)
b = abs(b)
function code(a, b)
	return Float64(Float64(a * b) * Float64(a * Float64(-b)))
end

MATLAB

a = abs(a)
b = abs(b)
function tmp = code(a, b)
	tmp = (a * b) * (a * -b);
end

Wolfram

NOTE: a should be positive before calling this function
NOTE: b should be positive before calling this function
code[a_, b_] := N[(N[(a * b), $MachinePrecision] * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.2%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Step-by-step derivation

   1. associate-*l* 74.5%

      \[\leadsto -\color{blue}{\left(a \cdot a\right) \cdot \left(b \cdot b\right)} \]

3. Simplified 74.5%

   \[\leadsto \color{blue}{-\left(a \cdot a\right) \cdot \left(b \cdot b\right)} \]
4. Step-by-step derivation

   1. add-cbrt-cube 63.2%

      \[\leadsto -\color{blue}{\sqrt[3]{\left(\left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right) \cdot \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right) \cdot \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)}} \]

   2. pow3 63.2%

      \[\leadsto -\sqrt[3]{\color{blue}{{\left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)}^{3}}} \]

   3. add-sqr-sqrt 63.1%

      \[\leadsto -\sqrt[3]{{\color{blue}{\left(\sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)} \cdot \sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right)}}^{3}} \]

   4. pow2 63.1%

      \[\leadsto -\sqrt[3]{{\color{blue}{\left({\left(\sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right)}^{2}\right)}}^{3}} \]

   5. metadata-eval 63.1%

      \[\leadsto -\sqrt[3]{{\left({\left(\sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right)}^{2}\right)}^{\color{blue}{\left(2 + 1\right)}}} \]

   6. pow-pow 63.2%

      \[\leadsto -\sqrt[3]{\color{blue}{{\left(\sqrt{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right)}^{\left(2 \cdot \left(2 + 1\right)\right)}}} \]

   7. unswap-sqr 74.6%

      \[\leadsto -\sqrt[3]{{\left(\sqrt{\color{blue}{\left(a \cdot b\right) \cdot \left(a \cdot b\right)}}\right)}^{\left(2 \cdot \left(2 + 1\right)\right)}} \]

   8. sqrt-prod 44.1%

      \[\leadsto -\sqrt[3]{{\color{blue}{\left(\sqrt{a \cdot b} \cdot \sqrt{a \cdot b}\right)}}^{\left(2 \cdot \left(2 + 1\right)\right)}} \]

   9. add-sqr-sqrt 74.6%

      \[\leadsto -\sqrt[3]{{\color{blue}{\left(a \cdot b\right)}}^{\left(2 \cdot \left(2 + 1\right)\right)}} \]

   10. metadata-eval 74.6%

       \[\leadsto -\sqrt[3]{{\left(a \cdot b\right)}^{\left(2 \cdot \color{blue}{3}\right)}} \]

   11. metadata-eval 74.6%

       \[\leadsto -\sqrt[3]{{\left(a \cdot b\right)}^{\color{blue}{6}}} \]

5. Applied egg-rr 74.6%

   \[\leadsto -\color{blue}{\sqrt[3]{{\left(a \cdot b\right)}^{6}}} \]
6. Step-by-step derivation

   1. pow1/3 73.5%

      \[\leadsto -\color{blue}{{\left({\left(a \cdot b\right)}^{6}\right)}^{0.3333333333333333}} \]

   2. pow-pow 99.7%

      \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{\left(6 \cdot 0.3333333333333333\right)}} \]

   3. metadata-eval 99.7%

      \[\leadsto -{\left(a \cdot b\right)}^{\color{blue}{2}} \]

   4. unpow2 99.7%

      \[\leadsto -\color{blue}{\left(a \cdot b\right) \cdot \left(a \cdot b\right)} \]

7. Applied egg-rr 99.7%

   \[\leadsto -\color{blue}{\left(a \cdot b\right) \cdot \left(a \cdot b\right)} \]

8. Final simplification 99.7%

   \[\leadsto \left(a \cdot b\right) \cdot \left(a \cdot \left(-b\right)\right) \]

Reproduce

herbie shell --seed 2023311 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))