Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D

Percentage Accurate: 99.8% → 99.8%

Time: 5.3s

Alternatives: 7

Speedup: 1.2×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(x \cdot 9\right) + x \cdot -12\right) + 3 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ (+ (* x (* x 9.0)) (* x -12.0)) 3.0))

C

double code(double x) {
	return ((x * (x * 9.0)) + (x * -12.0)) + 3.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((x * (x * 9.0d0)) + (x * (-12.0d0))) + 3.0d0
end function

Java

public static double code(double x) {
	return ((x * (x * 9.0)) + (x * -12.0)) + 3.0;
}

Python

def code(x):
	return ((x * (x * 9.0)) + (x * -12.0)) + 3.0

Julia

function code(x)
	return Float64(Float64(Float64(x * Float64(x * 9.0)) + Float64(x * -12.0)) + 3.0)
end

MATLAB

function tmp = code(x)
	tmp = ((x * (x * 9.0)) + (x * -12.0)) + 3.0;
end

Wolfram

code[x_] := N[(N[(N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] + N[(x * -12.0), $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
2. Step-by-step derivation

   1. distribute-rgt-in 99.8%

      \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

   2. *-commutative 99.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

   3. distribute-lft-out-- 99.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

   4. associate-*l* 99.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

   5. metadata-eval 99.8%

      \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

   6. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

   7. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

   8. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

   9. distribute-lft-in 99.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

   10. *-commutative 99.8%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

   11. associate-*l* 99.9%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

   12. fma-def 99.9%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

   13. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

   14. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

   15. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]
4. Step-by-step derivation

   1. fma-udef 99.9%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(x, 9, -12\right) + 3} \]

5. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(x, 9, -12\right) + 3} \]
6. Step-by-step derivation

   1. fma-udef 99.9%

      \[\leadsto x \cdot \color{blue}{\left(x \cdot 9 + -12\right)} + 3 \]

   2. distribute-lft-in 99.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 9\right) + x \cdot -12\right)} + 3 \]

7. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 9\right) + x \cdot -12\right)} + 3 \]

8. Final simplification 99.9%

   \[\leadsto \left(x \cdot \left(x \cdot 9\right) + x \cdot -12\right) + 3 \]

Alternative 2: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.56 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;9 \cdot \left(x \cdot x\right) + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;3 + x \cdot -12\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -0.56) (not (<= x 0.58)))
   (+ (* 9.0 (* x x)) (* x -12.0))
   (+ 3.0 (* x -12.0))))

C

double code(double x) {
	double tmp;
	if ((x <= -0.56) || !(x <= 0.58)) {
		tmp = (9.0 * (x * x)) + (x * -12.0);
	} else {
		tmp = 3.0 + (x * -12.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-0.56d0)) .or. (.not. (x <= 0.58d0))) then
        tmp = (9.0d0 * (x * x)) + (x * (-12.0d0))
    else
        tmp = 3.0d0 + (x * (-12.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -0.56) || !(x <= 0.58)) {
		tmp = (9.0 * (x * x)) + (x * -12.0);
	} else {
		tmp = 3.0 + (x * -12.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -0.56) or not (x <= 0.58):
		tmp = (9.0 * (x * x)) + (x * -12.0)
	else:
		tmp = 3.0 + (x * -12.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -0.56) || !(x <= 0.58))
		tmp = Float64(Float64(9.0 * Float64(x * x)) + Float64(x * -12.0));
	else
		tmp = Float64(3.0 + Float64(x * -12.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -0.56) || ~((x <= 0.58)))
		tmp = (9.0 * (x * x)) + (x * -12.0);
	else
		tmp = 3.0 + (x * -12.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -0.56], N[Not[LessEqual[x, 0.58]], $MachinePrecision]], N[(N[(9.0 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * -12.0), $MachinePrecision]), $MachinePrecision], N[(3.0 + N[(x * -12.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.56000000000000005 or 0.57999999999999996 < x

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. associate-*r* 99.6%

         \[\leadsto 3 \cdot \left(\left(\color{blue}{x \cdot \left(3 \cdot x\right)} - x \cdot 4\right) + 1\right) \]

      2. associate--r- 99.6%

         \[\leadsto 3 \cdot \color{blue}{\left(x \cdot \left(3 \cdot x\right) - \left(x \cdot 4 - 1\right)\right)} \]

      3. sub-neg 99.6%

         \[\leadsto 3 \cdot \color{blue}{\left(x \cdot \left(3 \cdot x\right) + \left(-\left(x \cdot 4 - 1\right)\right)\right)} \]

      4. associate-*r* 99.6%

         \[\leadsto 3 \cdot \left(\color{blue}{\left(x \cdot 3\right) \cdot x} + \left(-\left(x \cdot 4 - 1\right)\right)\right) \]

      5. distribute-rgt-in 99.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x\right) \cdot 3 + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3} \]

      6. *-commutative 99.6%

         \[\leadsto \left(\color{blue}{\left(3 \cdot x\right)} \cdot x\right) \cdot 3 + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      7. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(3 \cdot x\right) \cdot \left(x \cdot 3\right)} + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      8. *-commutative 99.6%

         \[\leadsto \left(3 \cdot x\right) \cdot \color{blue}{\left(3 \cdot x\right)} + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      9. swap-sqr 99.7%

         \[\leadsto \color{blue}{\left(3 \cdot 3\right) \cdot \left(x \cdot x\right)} + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      10. metadata-eval 99.7%

          \[\leadsto \color{blue}{9} \cdot \left(x \cdot x\right) + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      11. sub-neg 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(-\color{blue}{\left(x \cdot 4 + \left(-1\right)\right)}\right) \cdot 3 \]

      12. distribute-neg-in 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \color{blue}{\left(\left(-x \cdot 4\right) + \left(-\left(-1\right)\right)\right)} \cdot 3 \]

      13. distribute-rgt-neg-in 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(\color{blue}{x \cdot \left(-4\right)} + \left(-\left(-1\right)\right)\right) \cdot 3 \]

      14. metadata-eval 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(x \cdot \color{blue}{-4} + \left(-\left(-1\right)\right)\right) \cdot 3 \]

      15. metadata-eval 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(x \cdot -4 + \left(-\color{blue}{-1}\right)\right) \cdot 3 \]

      16. metadata-eval 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(x \cdot -4 + \color{blue}{1}\right) \cdot 3 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot x\right) + \left(x \cdot -4 + 1\right) \cdot 3} \]

   4. Taylor expanded in x around inf 99.5%

      \[\leadsto 9 \cdot \left(x \cdot x\right) + \color{blue}{-12 \cdot x} \]

   if -0.56000000000000005 < x < 0.57999999999999996

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 100.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 100.0%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around 0 97.8%

      \[\leadsto \color{blue}{3 + -12 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.56 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;9 \cdot \left(x \cdot x\right) + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;3 + x \cdot -12\\ \end{array} \]

Alternative 3: 98.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.56 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;x \cdot \left(-12 + x \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;3 + x \cdot -12\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -0.56) (not (<= x 0.58)))
   (* x (+ -12.0 (* x 9.0)))
   (+ 3.0 (* x -12.0))))

C

double code(double x) {
	double tmp;
	if ((x <= -0.56) || !(x <= 0.58)) {
		tmp = x * (-12.0 + (x * 9.0));
	} else {
		tmp = 3.0 + (x * -12.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-0.56d0)) .or. (.not. (x <= 0.58d0))) then
        tmp = x * ((-12.0d0) + (x * 9.0d0))
    else
        tmp = 3.0d0 + (x * (-12.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -0.56) || !(x <= 0.58)) {
		tmp = x * (-12.0 + (x * 9.0));
	} else {
		tmp = 3.0 + (x * -12.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -0.56) or not (x <= 0.58):
		tmp = x * (-12.0 + (x * 9.0))
	else:
		tmp = 3.0 + (x * -12.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -0.56) || !(x <= 0.58))
		tmp = Float64(x * Float64(-12.0 + Float64(x * 9.0)));
	else
		tmp = Float64(3.0 + Float64(x * -12.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -0.56) || ~((x <= 0.58)))
		tmp = x * (-12.0 + (x * 9.0));
	else
		tmp = 3.0 + (x * -12.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -0.56], N[Not[LessEqual[x, 0.58]], $MachinePrecision]], N[(x * N[(-12.0 + N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.0 + N[(x * -12.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.56000000000000005 or 0.57999999999999996 < x

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. associate-*r* 99.6%

         \[\leadsto 3 \cdot \left(\left(\color{blue}{x \cdot \left(3 \cdot x\right)} - x \cdot 4\right) + 1\right) \]

      2. associate--r- 99.6%

         \[\leadsto 3 \cdot \color{blue}{\left(x \cdot \left(3 \cdot x\right) - \left(x \cdot 4 - 1\right)\right)} \]

      3. sub-neg 99.6%

         \[\leadsto 3 \cdot \color{blue}{\left(x \cdot \left(3 \cdot x\right) + \left(-\left(x \cdot 4 - 1\right)\right)\right)} \]

      4. associate-*r* 99.6%

         \[\leadsto 3 \cdot \left(\color{blue}{\left(x \cdot 3\right) \cdot x} + \left(-\left(x \cdot 4 - 1\right)\right)\right) \]

      5. distribute-rgt-in 99.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x\right) \cdot 3 + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3} \]

      6. *-commutative 99.6%

         \[\leadsto \left(\color{blue}{\left(3 \cdot x\right)} \cdot x\right) \cdot 3 + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      7. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(3 \cdot x\right) \cdot \left(x \cdot 3\right)} + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      8. *-commutative 99.6%

         \[\leadsto \left(3 \cdot x\right) \cdot \color{blue}{\left(3 \cdot x\right)} + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      9. swap-sqr 99.7%

         \[\leadsto \color{blue}{\left(3 \cdot 3\right) \cdot \left(x \cdot x\right)} + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      10. metadata-eval 99.7%

          \[\leadsto \color{blue}{9} \cdot \left(x \cdot x\right) + \left(-\left(x \cdot 4 - 1\right)\right) \cdot 3 \]

      11. sub-neg 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(-\color{blue}{\left(x \cdot 4 + \left(-1\right)\right)}\right) \cdot 3 \]

      12. distribute-neg-in 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \color{blue}{\left(\left(-x \cdot 4\right) + \left(-\left(-1\right)\right)\right)} \cdot 3 \]

      13. distribute-rgt-neg-in 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(\color{blue}{x \cdot \left(-4\right)} + \left(-\left(-1\right)\right)\right) \cdot 3 \]

      14. metadata-eval 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(x \cdot \color{blue}{-4} + \left(-\left(-1\right)\right)\right) \cdot 3 \]

      15. metadata-eval 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(x \cdot -4 + \left(-\color{blue}{-1}\right)\right) \cdot 3 \]

      16. metadata-eval 99.7%

          \[\leadsto 9 \cdot \left(x \cdot x\right) + \left(x \cdot -4 + \color{blue}{1}\right) \cdot 3 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot x\right) + \left(x \cdot -4 + 1\right) \cdot 3} \]

   4. Taylor expanded in x around inf 99.5%

      \[\leadsto 9 \cdot \left(x \cdot x\right) + \color{blue}{-12 \cdot x} \]
   5. Step-by-step derivation

      1. associate-*r* 99.5%

         \[\leadsto \color{blue}{\left(9 \cdot x\right) \cdot x} + -12 \cdot x \]

      2. distribute-rgt-out 99.5%

         \[\leadsto \color{blue}{x \cdot \left(9 \cdot x + -12\right)} \]

   6. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{x \cdot \left(9 \cdot x + -12\right)} \]

   if -0.56000000000000005 < x < 0.57999999999999996

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 100.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 100.0%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around 0 97.8%

      \[\leadsto \color{blue}{3 + -12 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.56 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;x \cdot \left(-12 + x \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;3 + x \cdot -12\\ \end{array} \]

Alternative 4: 97.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.56 \lor \neg \left(x \leq 0.2\right):\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;3\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -0.56) (not (<= x 0.2))) (* 9.0 (* x x)) 3.0))

C

double code(double x) {
	double tmp;
	if ((x <= -0.56) || !(x <= 0.2)) {
		tmp = 9.0 * (x * x);
	} else {
		tmp = 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-0.56d0)) .or. (.not. (x <= 0.2d0))) then
        tmp = 9.0d0 * (x * x)
    else
        tmp = 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -0.56) || !(x <= 0.2)) {
		tmp = 9.0 * (x * x);
	} else {
		tmp = 3.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -0.56) or not (x <= 0.2):
		tmp = 9.0 * (x * x)
	else:
		tmp = 3.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -0.56) || !(x <= 0.2))
		tmp = Float64(9.0 * Float64(x * x));
	else
		tmp = 3.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -0.56) || ~((x <= 0.2)))
		tmp = 9.0 * (x * x);
	else
		tmp = 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -0.56], N[Not[LessEqual[x, 0.2]], $MachinePrecision]], N[(9.0 * N[(x * x), $MachinePrecision]), $MachinePrecision], 3.0]

Derivation

1. Split input into 2 regimes

2. if x < -0.56000000000000005 or 0.20000000000000001 < x

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 99.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 99.6%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 99.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 99.6%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 99.6%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 99.6%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 99.7%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 99.7%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around inf 98.5%

      \[\leadsto \color{blue}{9 \cdot {x}^{2}} \]
   5. Step-by-step derivation

      1. unpow2 98.5%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot x\right)} \]

   6. Simplified 98.5%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot x\right)} \]

   if -0.56000000000000005 < x < 0.20000000000000001

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 100.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 100.0%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around 0 96.6%

      \[\leadsto \color{blue}{3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.56 \lor \neg \left(x \leq 0.2\right):\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;3\\ \end{array} \]

Alternative 5: 97.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.56:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq 0.2:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.56) (* 9.0 (* x x)) (if (<= x 0.2) 3.0 (* x (* x 9.0)))))

C

double code(double x) {
	double tmp;
	if (x <= -0.56) {
		tmp = 9.0 * (x * x);
	} else if (x <= 0.2) {
		tmp = 3.0;
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.56d0)) then
        tmp = 9.0d0 * (x * x)
    else if (x <= 0.2d0) then
        tmp = 3.0d0
    else
        tmp = x * (x * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.56) {
		tmp = 9.0 * (x * x);
	} else if (x <= 0.2) {
		tmp = 3.0;
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.56:
		tmp = 9.0 * (x * x)
	elif x <= 0.2:
		tmp = 3.0
	else:
		tmp = x * (x * 9.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.56)
		tmp = Float64(9.0 * Float64(x * x));
	elseif (x <= 0.2)
		tmp = 3.0;
	else
		tmp = Float64(x * Float64(x * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.56)
		tmp = 9.0 * (x * x);
	elseif (x <= 0.2)
		tmp = 3.0;
	else
		tmp = x * (x * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.56], N[(9.0 * N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.2], 3.0, N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.56000000000000005

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 99.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 99.6%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 99.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 99.6%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 99.6%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 99.6%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 99.7%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 99.7%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around inf 98.6%

      \[\leadsto \color{blue}{9 \cdot {x}^{2}} \]
   5. Step-by-step derivation

      1. unpow2 98.6%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot x\right)} \]

   6. Simplified 98.6%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot x\right)} \]

   if -0.56000000000000005 < x < 0.20000000000000001

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 100.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 100.0%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around 0 96.6%

      \[\leadsto \color{blue}{3} \]

   if 0.20000000000000001 < x

   1. Initial program 99.5%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 99.5%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 99.5%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 99.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 99.6%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 99.6%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 99.6%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 99.7%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{9 \cdot {x}^{2}} \]
   5. Step-by-step derivation

      1. unpow2 98.3%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot x\right)} \]

      2. *-commutative 98.3%

         \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot 9} \]

      3. associate-*l* 98.3%

         \[\leadsto \color{blue}{x \cdot \left(x \cdot 9\right)} \]

   6. Simplified 98.3%

      \[\leadsto \color{blue}{x \cdot \left(x \cdot 9\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.56:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq 0.2:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \end{array} \]

Alternative 6: 98.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.55)
   (* 9.0 (* x x))
   (if (<= x 1.0) (+ 3.0 (* x -12.0)) (* x (* x 9.0)))))

C

double code(double x) {
	double tmp;
	if (x <= -1.55) {
		tmp = 9.0 * (x * x);
	} else if (x <= 1.0) {
		tmp = 3.0 + (x * -12.0);
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.55d0)) then
        tmp = 9.0d0 * (x * x)
    else if (x <= 1.0d0) then
        tmp = 3.0d0 + (x * (-12.0d0))
    else
        tmp = x * (x * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.55) {
		tmp = 9.0 * (x * x);
	} else if (x <= 1.0) {
		tmp = 3.0 + (x * -12.0);
	} else {
		tmp = x * (x * 9.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.55:
		tmp = 9.0 * (x * x)
	elif x <= 1.0:
		tmp = 3.0 + (x * -12.0)
	else:
		tmp = x * (x * 9.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.55)
		tmp = Float64(9.0 * Float64(x * x));
	elseif (x <= 1.0)
		tmp = Float64(3.0 + Float64(x * -12.0));
	else
		tmp = Float64(x * Float64(x * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.55)
		tmp = 9.0 * (x * x);
	elseif (x <= 1.0)
		tmp = 3.0 + (x * -12.0);
	else
		tmp = x * (x * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.55], N[(9.0 * N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(3.0 + N[(x * -12.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55000000000000004

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 99.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 99.6%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 99.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 99.6%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 99.6%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 99.6%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 99.7%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 99.7%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around inf 98.6%

      \[\leadsto \color{blue}{9 \cdot {x}^{2}} \]
   5. Step-by-step derivation

      1. unpow2 98.6%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot x\right)} \]

   6. Simplified 98.6%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot x\right)} \]

   if -1.55000000000000004 < x < 1

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 100.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 100.0%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around 0 97.8%

      \[\leadsto \color{blue}{3 + -12 \cdot x} \]

   if 1 < x

   1. Initial program 99.5%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-in 99.5%

         \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

      2. *-commutative 99.5%

         \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

      3. distribute-lft-out-- 99.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

      4. associate-*l* 99.6%

         \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

      5. metadata-eval 99.6%

         \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

      6. fma-def 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

      7. *-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

      8. sub-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

      9. distribute-lft-in 99.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

      10. *-commutative 99.6%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

      11. associate-*l* 99.7%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

      12. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

      13. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

      14. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

      15. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

   4. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{9 \cdot {x}^{2}} \]
   5. Step-by-step derivation

      1. unpow2 98.3%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot x\right)} \]

      2. *-commutative 98.3%

         \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot 9} \]

      3. associate-*l* 98.3%

         \[\leadsto \color{blue}{x \cdot \left(x \cdot 9\right)} \]

   6. Simplified 98.3%

      \[\leadsto \color{blue}{x \cdot \left(x \cdot 9\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 9\right)\\ \end{array} \]

Alternative 7: 51.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 3 \end{array} \]

FPCore

(FPCore (x) :precision binary64 3.0)

C

double code(double x) {
	return 3.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0
end function

Java

public static double code(double x) {
	return 3.0;
}

Python

def code(x):
	return 3.0

Julia

function code(x)
	return 3.0
end

MATLAB

function tmp = code(x)
	tmp = 3.0;
end

Wolfram

code[x_] := 3.0

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
2. Step-by-step derivation

   1. distribute-rgt-in 99.8%

      \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

   2. *-commutative 99.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 1 \cdot 3 \]

   3. distribute-lft-out-- 99.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 1 \cdot 3 \]

   4. associate-*l* 99.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 1 \cdot 3 \]

   5. metadata-eval 99.8%

      \[\leadsto x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right) + \color{blue}{3} \]

   6. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

   7. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

   8. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

   9. distribute-lft-in 99.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3\right) + 3 \cdot \left(-4\right)}, 3\right) \]

   10. *-commutative 99.8%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(x \cdot 3\right) \cdot 3} + 3 \cdot \left(-4\right), 3\right) \]

   11. associate-*l* 99.9%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{x \cdot \left(3 \cdot 3\right)} + 3 \cdot \left(-4\right), 3\right) \]

   12. fma-def 99.9%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 3 \cdot 3, 3 \cdot \left(-4\right)\right)}, 3\right) \]

   13. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{9}, 3 \cdot \left(-4\right)\right), 3\right) \]

   14. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, 3 \cdot \color{blue}{-4}\right), 3\right) \]

   15. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, \color{blue}{-12}\right), 3\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 9, -12\right), 3\right)} \]

4. Taylor expanded in x around 0 51.1%

   \[\leadsto \color{blue}{3} \]

5. Final simplification 51.1%

   \[\leadsto 3 \]

Developer target: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x))))

C

double code(double x) {
	return 3.0 + (((9.0 * x) * x) - (12.0 * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 + (((9.0d0 * x) * x) - (12.0d0 * x))
end function

Java

public static double code(double x) {
	return 3.0 + (((9.0 * x) * x) - (12.0 * x));
}

Python

def code(x):
	return 3.0 + (((9.0 * x) * x) - (12.0 * x))

Julia

function code(x)
	return Float64(3.0 + Float64(Float64(Float64(9.0 * x) * x) - Float64(12.0 * x)))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 + (((9.0 * x) * x) - (12.0 * x));
end

Wolfram

code[x_] := N[(3.0 + N[(N[(N[(9.0 * x), $MachinePrecision] * x), $MachinePrecision] - N[(12.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023290 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))