Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E

Percentage Accurate: 99.9% → 99.9%

Time: 6.0s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (- 1.0 x) (* y (sqrt x))))

C

double code(double x, double y) {
	return (1.0 - x) + (y * sqrt(x));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (1.0 - x) + (y * Math.sqrt(x));
}

Python

def code(x, y):
	return (1.0 - x) + (y * math.sqrt(x))

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) + Float64(y * sqrt(x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) + (y * sqrt(x));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (- 1.0 x) (* y (sqrt x))))

C

double code(double x, double y) {
	return (1.0 - x) + (y * sqrt(x));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (1.0 - x) + (y * Math.sqrt(x));
}

Python

def code(x, y):
	return (1.0 - x) + (y * math.sqrt(x))

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) + Float64(y * sqrt(x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) + (y * sqrt(x));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, \sqrt{x}, 1 - x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y (sqrt x) (- 1.0 x)))

C

double code(double x, double y) {
	return fma(y, sqrt(x), (1.0 - x));
}

Julia

function code(x, y)
	return fma(y, sqrt(x), Float64(1.0 - x))
end

Wolfram

code[x_, y_] := N[(y * N[Sqrt[x], $MachinePrecision] + N[(1.0 - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(1 - x\right) + y \cdot \sqrt{x} \]
2. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \sqrt{x}, 1 - x\right)} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \sqrt{x}, 1 - x\right)} \]

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(y, \sqrt{x}, 1 - x\right) \]

Alternative 2: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+19} \lor \neg \left(y \leq 1.2 \cdot 10^{+17}\right):\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.5e+19) (not (<= y 1.2e+17)))
   (+ 1.0 (* y (sqrt x)))
   (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.5e+19) || !(y <= 1.2e+17)) {
		tmp = 1.0 + (y * sqrt(x));
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-8.5d+19)) .or. (.not. (y <= 1.2d+17))) then
        tmp = 1.0d0 + (y * sqrt(x))
    else
        tmp = 1.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8.5e+19) || !(y <= 1.2e+17)) {
		tmp = 1.0 + (y * Math.sqrt(x));
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.5e+19) or not (y <= 1.2e+17):
		tmp = 1.0 + (y * math.sqrt(x))
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.5e+19) || !(y <= 1.2e+17))
		tmp = Float64(1.0 + Float64(y * sqrt(x)));
	else
		tmp = Float64(1.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8.5e+19) || ~((y <= 1.2e+17)))
		tmp = 1.0 + (y * sqrt(x));
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.5e+19], N[Not[LessEqual[y, 1.2e+17]], $MachinePrecision]], N[(1.0 + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5e19 or 1.2e17 < y

   1. Initial program 99.8%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. add-sqr-sqrt 99.4%

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

      4. associate-*l* 99.4%

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

      5. fma-def 99.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\sqrt{x}}, \sqrt{\sqrt{x}} \cdot y, 1 - x\right)} \]

      6. pow1/2 99.4%

         \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{{x}^{0.5}}}, \sqrt{\sqrt{x}} \cdot y, 1 - x\right) \]

      7. sqrt-pow1 99.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{x}^{\left(\frac{0.5}{2}\right)}}, \sqrt{\sqrt{x}} \cdot y, 1 - x\right) \]

      8. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left({x}^{\color{blue}{0.25}}, \sqrt{\sqrt{x}} \cdot y, 1 - x\right) \]

      9. pow1/2 99.5%

         \[\leadsto \mathsf{fma}\left({x}^{0.25}, \sqrt{\color{blue}{{x}^{0.5}}} \cdot y, 1 - x\right) \]

      10. sqrt-pow1 99.5%

          \[\leadsto \mathsf{fma}\left({x}^{0.25}, \color{blue}{{x}^{\left(\frac{0.5}{2}\right)}} \cdot y, 1 - x\right) \]

      11. metadata-eval 99.5%

          \[\leadsto \mathsf{fma}\left({x}^{0.25}, {x}^{\color{blue}{0.25}} \cdot y, 1 - x\right) \]

   3. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left({x}^{0.25}, {x}^{0.25} \cdot y, 1 - x\right)} \]

   4. Taylor expanded in x around 0 90.6%

      \[\leadsto \color{blue}{y \cdot \sqrt{x} + 1} \]

   if -8.5e19 < y < 1.2e17

   1. Initial program 100.0%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]

   2. Taylor expanded in y around 0 99.1%

      \[\leadsto \color{blue}{1 - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+19} \lor \neg \left(y \leq 1.2 \cdot 10^{+17}\right):\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]

Alternative 3: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+84} \lor \neg \left(y \leq 4.2 \cdot 10^{+59}\right):\\ \;\;\;\;y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.5e+84) (not (<= y 4.2e+59))) (* y (sqrt x)) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e+84) || !(y <= 4.2e+59)) {
		tmp = y * sqrt(x);
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-4.5d+84)) .or. (.not. (y <= 4.2d+59))) then
        tmp = y * sqrt(x)
    else
        tmp = 1.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e+84) || !(y <= 4.2e+59)) {
		tmp = y * Math.sqrt(x);
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.5e+84) or not (y <= 4.2e+59):
		tmp = y * math.sqrt(x)
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.5e+84) || !(y <= 4.2e+59))
		tmp = Float64(y * sqrt(x));
	else
		tmp = Float64(1.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.5e+84) || ~((y <= 4.2e+59)))
		tmp = y * sqrt(x);
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.5e+84], N[Not[LessEqual[y, 4.2e+59]], $MachinePrecision]], N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999997e84 or 4.19999999999999968e59 < y

   1. Initial program 99.8%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]

   2. Taylor expanded in y around inf 90.6%

      \[\leadsto \color{blue}{y \cdot \sqrt{x}} \]

   if -4.4999999999999997e84 < y < 4.19999999999999968e59

   1. Initial program 100.0%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]

   2. Taylor expanded in y around 0 92.5%

      \[\leadsto \color{blue}{1 - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+84} \lor \neg \left(y \leq 4.2 \cdot 10^{+59}\right):\\ \;\;\;\;y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (- 1.0 x) (* y (sqrt x))))

C

double code(double x, double y) {
	return (1.0 - x) + (y * sqrt(x));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (1.0 - x) + (y * Math.sqrt(x));
}

Python

def code(x, y):
	return (1.0 - x) + (y * math.sqrt(x))

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) + Float64(y * sqrt(x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) + (y * sqrt(x));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(1 - x\right) + y \cdot \sqrt{x} \]

2. Final simplification 99.9%

   \[\leadsto \left(1 - x\right) + y \cdot \sqrt{x} \]

Alternative 5: 67.0% accurate, 21.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{+147}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 4e+147) (- 1.0 x) (* y y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4e+147) {
		tmp = 1.0 - x;
	} else {
		tmp = y * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 4d+147) then
        tmp = 1.0d0 - x
    else
        tmp = y * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4e+147) {
		tmp = 1.0 - x;
	} else {
		tmp = y * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4e+147:
		tmp = 1.0 - x
	else:
		tmp = y * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4e+147)
		tmp = Float64(1.0 - x);
	else
		tmp = Float64(y * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4e+147)
		tmp = 1.0 - x;
	else
		tmp = y * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4e+147], N[(1.0 - x), $MachinePrecision], N[(y * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.9999999999999999e147

   1. Initial program 99.9%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]

   2. Taylor expanded in y around 0 67.3%

      \[\leadsto \color{blue}{1 - x} \]

   if 3.9999999999999999e147 < y

   1. Initial program 99.7%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Step-by-step derivation

      1. flip-+ 29.5%

         \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \left(1 - x\right) - \left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)}{\left(1 - x\right) - y \cdot \sqrt{x}}} \]

      2. div-sub 29.5%

         \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \left(1 - x\right)}{\left(1 - x\right) - y \cdot \sqrt{x}} - \frac{\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)}{\left(1 - x\right) - y \cdot \sqrt{x}}} \]

      3. pow2 29.5%

         \[\leadsto \frac{\color{blue}{{\left(1 - x\right)}^{2}}}{\left(1 - x\right) - y \cdot \sqrt{x}} - \frac{\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

      4. *-commutative 29.5%

         \[\leadsto \frac{{\left(1 - x\right)}^{2}}{\left(1 - x\right) - y \cdot \sqrt{x}} - \frac{\color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot \left(y \cdot \sqrt{x}\right)}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

      5. *-commutative 29.5%

         \[\leadsto \frac{{\left(1 - x\right)}^{2}}{\left(1 - x\right) - y \cdot \sqrt{x}} - \frac{\left(\sqrt{x} \cdot y\right) \cdot \color{blue}{\left(\sqrt{x} \cdot y\right)}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

      6. swap-sqr 3.5%

         \[\leadsto \frac{{\left(1 - x\right)}^{2}}{\left(1 - x\right) - y \cdot \sqrt{x}} - \frac{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(y \cdot y\right)}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

      7. add-sqr-sqrt 3.5%

         \[\leadsto \frac{{\left(1 - x\right)}^{2}}{\left(1 - x\right) - y \cdot \sqrt{x}} - \frac{\color{blue}{x} \cdot \left(y \cdot y\right)}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

   3. Applied egg-rr 3.5%

      \[\leadsto \color{blue}{\frac{{\left(1 - x\right)}^{2}}{\left(1 - x\right) - y \cdot \sqrt{x}} - \frac{x \cdot \left(y \cdot y\right)}{\left(1 - x\right) - y \cdot \sqrt{x}}} \]
   4. Step-by-step derivation

      1. div-sub 3.5%

         \[\leadsto \color{blue}{\frac{{\left(1 - x\right)}^{2} - x \cdot \left(y \cdot y\right)}{\left(1 - x\right) - y \cdot \sqrt{x}}} \]

   5. Simplified 3.5%

      \[\leadsto \color{blue}{\frac{{\left(1 - x\right)}^{2} - x \cdot \left(y \cdot y\right)}{\left(1 - x\right) - y \cdot \sqrt{x}}} \]

   6. Taylor expanded in x around 0 4.4%

      \[\leadsto \frac{\color{blue}{1 + -1 \cdot \left(x \cdot \left(2 + {y}^{2}\right)\right)}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]
   7. Step-by-step derivation

      1. associate-*r* 4.4%

         \[\leadsto \frac{1 + \color{blue}{\left(-1 \cdot x\right) \cdot \left(2 + {y}^{2}\right)}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

      2. neg-mul-1 4.4%

         \[\leadsto \frac{1 + \color{blue}{\left(-x\right)} \cdot \left(2 + {y}^{2}\right)}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

      3. unpow2 4.4%

         \[\leadsto \frac{1 + \left(-x\right) \cdot \left(2 + \color{blue}{y \cdot y}\right)}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

   8. Simplified 4.4%

      \[\leadsto \frac{\color{blue}{1 + \left(-x\right) \cdot \left(2 + y \cdot y\right)}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

   9. Taylor expanded in y around inf 4.4%

      \[\leadsto \frac{1 + \color{blue}{-1 \cdot \left({y}^{2} \cdot x\right)}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]
   10. Step-by-step derivation

       1. *-commutative 4.4%

          \[\leadsto \frac{1 + -1 \cdot \color{blue}{\left(x \cdot {y}^{2}\right)}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

       2. associate-*r* 4.4%

          \[\leadsto \frac{1 + \color{blue}{\left(-1 \cdot x\right) \cdot {y}^{2}}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

       3. mul-1-neg 4.4%

          \[\leadsto \frac{1 + \color{blue}{\left(-x\right)} \cdot {y}^{2}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

       4. unpow2 4.4%

          \[\leadsto \frac{1 + \left(-x\right) \cdot \color{blue}{\left(y \cdot y\right)}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

       5. associate-*r* 30.2%

          \[\leadsto \frac{1 + \color{blue}{\left(\left(-x\right) \cdot y\right) \cdot y}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

   11. Simplified 30.2%

       \[\leadsto \frac{1 + \color{blue}{\left(\left(-x\right) \cdot y\right) \cdot y}}{\left(1 - x\right) - y \cdot \sqrt{x}} \]

   12. Taylor expanded in x around inf 28.6%

       \[\leadsto \color{blue}{{y}^{2}} \]
   13. Step-by-step derivation

       1. unpow2 28.6%

          \[\leadsto \color{blue}{y \cdot y} \]

   14. Simplified 28.6%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{+147}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 6: 62.4% accurate, 26.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7400:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 7400.0) 1.0 (- x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 7400.0) {
		tmp = 1.0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 7400.0d0) then
        tmp = 1.0d0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 7400.0) {
		tmp = 1.0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 7400.0:
		tmp = 1.0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 7400.0)
		tmp = 1.0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 7400.0)
		tmp = 1.0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 7400.0], 1.0, (-x)]

Derivation

1. Split input into 2 regimes

2. if x < 7400

   1. Initial program 99.9%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]

   2. Taylor expanded in x around 0 53.4%

      \[\leadsto \color{blue}{1} \]

   if 7400 < x

   1. Initial program 99.9%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]

   2. Taylor expanded in x around inf 61.2%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. neg-mul-1 61.2%

         \[\leadsto \color{blue}{-x} \]

   4. Simplified 61.2%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7400:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 7: 31.9% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 99.9%

   \[\left(1 - x\right) + y \cdot \sqrt{x} \]

2. Taylor expanded in x around 0 28.1%

   \[\leadsto \color{blue}{1} \]

3. Final simplification 28.1%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E"
  :precision binary64
  (+ (- 1.0 x) (* y (sqrt x))))