Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B

Percentage Accurate: 99.9% → 99.9%

Time: 10.4s

Alternatives: 13

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + \cos y\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + cos(y)) - (z * sin(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \cos y\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + cos(y)) - (z * sin(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \cos y\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + cos(y)) - (z * sin(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := \left(x + \cos y\right) - t\_0\\ t_2 := \left(x + 1\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.996:\\ \;\;\;\;\cos y - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y)))
        (t_1 (- (+ x (cos y)) t_0))
        (t_2 (- (+ x 1.0) t_0)))
   (if (<= t_1 -1000000.0) t_2 (if (<= t_1 0.996) (- (cos y) t_0) t_2))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double t_1 = (x + cos(y)) - t_0;
	double t_2 = (x + 1.0) - t_0;
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.996) {
		tmp = cos(y) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = z * sin(y)
    t_1 = (x + cos(y)) - t_0
    t_2 = (x + 1.0d0) - t_0
    if (t_1 <= (-1000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.996d0) then
        tmp = cos(y) - t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double t_1 = (x + Math.cos(y)) - t_0;
	double t_2 = (x + 1.0) - t_0;
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.996) {
		tmp = Math.cos(y) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	t_1 = (x + math.cos(y)) - t_0
	t_2 = (x + 1.0) - t_0
	tmp = 0
	if t_1 <= -1000000.0:
		tmp = t_2
	elif t_1 <= 0.996:
		tmp = math.cos(y) - t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	t_1 = Float64(Float64(x + cos(y)) - t_0)
	t_2 = Float64(Float64(x + 1.0) - t_0)
	tmp = 0.0
	if (t_1 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.996)
		tmp = Float64(cos(y) - t_0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	t_1 = (x + cos(y)) - t_0;
	t_2 = (x + 1.0) - t_0;
	tmp = 0.0;
	if (t_1 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.996)
		tmp = cos(y) - t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000.0], t$95$2, If[LessEqual[t$95$1, 0.996], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -1e6 or 0.996 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(1 + x\right)} - z \cdot \sin y \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 99.4

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

   5. Simplified 99.4%

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

   if -1e6 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.996

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

      2. lower-cos.f64 N/A

         \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]

      3. lower-*.f64 N/A

         \[\leadsto \cos y - \color{blue}{z \cdot \sin y} \]

      4. lower-sin.f64 99.8

         \[\leadsto \cos y - z \cdot \color{blue}{\sin y} \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \cos y\right) - z \cdot \sin y\\ \mathbf{if}\;t\_0 \leq -1000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;t\_0 \leq 0.996:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x (cos y)) (* z (sin y)))))
   (if (<= t_0 -1000000.0) (+ x 1.0) (if (<= t_0 0.996) (cos y) (+ x 1.0)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (z * sin(y));
	double tmp;
	if (t_0 <= -1000000.0) {
		tmp = x + 1.0;
	} else if (t_0 <= 0.996) {
		tmp = cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + cos(y)) - (z * sin(y))
    if (t_0 <= (-1000000.0d0)) then
        tmp = x + 1.0d0
    else if (t_0 <= 0.996d0) then
        tmp = cos(y)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.cos(y)) - (z * Math.sin(y));
	double tmp;
	if (t_0 <= -1000000.0) {
		tmp = x + 1.0;
	} else if (t_0 <= 0.996) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.cos(y)) - (z * math.sin(y))
	tmp = 0
	if t_0 <= -1000000.0:
		tmp = x + 1.0
	elif t_0 <= 0.996:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
	tmp = 0.0
	if (t_0 <= -1000000.0)
		tmp = Float64(x + 1.0);
	elseif (t_0 <= 0.996)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + cos(y)) - (z * sin(y));
	tmp = 0.0;
	if (t_0 <= -1000000.0)
		tmp = x + 1.0;
	elseif (t_0 <= 0.996)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1000000.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[t$95$0, 0.996], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -1e6 or 0.996 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 69.8

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

   5. Simplified 69.8%

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

   if -1e6 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.996

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \cos y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. lower-cos.f64 92.4

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 92.4%

      \[\leadsto \color{blue}{\cos y + x} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y} \]
   7. Step-by-step derivation

      1. lower-cos.f64 92.3

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

   8. Simplified 92.3%

      \[\leadsto \color{blue}{\cos y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \cos y\right) - z \cdot \sin y\\ \mathbf{if}\;t\_0 \leq -0.1:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x (cos y)) (* z (sin y)))))
   (if (<= t_0 -0.1) x (if (<= t_0 2.0) 1.0 x))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (z * sin(y));
	double tmp;
	if (t_0 <= -0.1) {
		tmp = x;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + cos(y)) - (z * sin(y))
    if (t_0 <= (-0.1d0)) then
        tmp = x
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.cos(y)) - (z * Math.sin(y));
	double tmp;
	if (t_0 <= -0.1) {
		tmp = x;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.cos(y)) - (z * math.sin(y))
	tmp = 0
	if t_0 <= -0.1:
		tmp = x
	elif t_0 <= 2.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
	tmp = 0.0
	if (t_0 <= -0.1)
		tmp = x;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + cos(y)) - (z * sin(y));
	tmp = 0.0;
	if (t_0 <= -0.1)
		tmp = x;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.1], x, If[LessEqual[t$95$0, 2.0], 1.0, x]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -0.10000000000000001 or 2 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(x + \color{blue}{\cos y}\right) - z \cdot \sin y \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \cos y\right)} - z \cdot \sin y \]

      3. lift-sin.f64 N/A

         \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\sin y} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(x + \cos y\right) - \color{blue}{z \cdot \sin y} \]

      5. flip-- N/A

         \[\leadsto \color{blue}{\frac{\left(x + \cos y\right) \cdot \left(x + \cos y\right) - \left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right)}{\left(x + \cos y\right) + z \cdot \sin y}} \]

      6. clear-num N/A

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

      7. lower-/.f64 N/A

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

      8. clear-num N/A

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

      9. flip-- N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 99.6

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

      12. lift--.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate--l+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 53.1

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

   7. Simplified 53.1%

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

      1. remove-double-div 53.2

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

   9. Applied egg-rr 53.2%

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

   if -0.10000000000000001 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 2

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 76.8

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

   5. Simplified 76.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Simplified 76.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 99.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + 1\right) - z \cdot \sin y\\ \mathbf{if}\;z \leq -0.85:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.88:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x 1.0) (* z (sin y)))))
   (if (<= z -0.85) t_0 (if (<= z 0.88) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + 1.0) - (z * sin(y));
	double tmp;
	if (z <= -0.85) {
		tmp = t_0;
	} else if (z <= 0.88) {
		tmp = x + cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + 1.0d0) - (z * sin(y))
    if (z <= (-0.85d0)) then
        tmp = t_0
    else if (z <= 0.88d0) then
        tmp = x + cos(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + 1.0) - (z * Math.sin(y));
	double tmp;
	if (z <= -0.85) {
		tmp = t_0;
	} else if (z <= 0.88) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + 1.0) - (z * math.sin(y))
	tmp = 0
	if z <= -0.85:
		tmp = t_0
	elif z <= 0.88:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + 1.0) - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -0.85)
		tmp = t_0;
	elseif (z <= 0.88)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + 1.0) - (z * sin(y));
	tmp = 0.0;
	if (z <= -0.85)
		tmp = t_0;
	elseif (z <= 0.88)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.85], t$95$0, If[LessEqual[z, 0.88], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.849999999999999978 or 0.880000000000000004 < z

   1. Initial program 99.8%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(1 + x\right)} - z \cdot \sin y \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 99.3

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

   5. Simplified 99.3%

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

   if -0.849999999999999978 < z < 0.880000000000000004

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \cos y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. lower-cos.f64 98.7

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 98.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.85:\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{elif}\;z \leq 0.88:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+204}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+128}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+204)
   (* (sin y) (- z))
   (if (<= z 1.4e+128) (+ x (cos y)) (- 1.0 (* z (sin y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+204) {
		tmp = sin(y) * -z;
	} else if (z <= 1.4e+128) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 - (z * sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.1d+204)) then
        tmp = sin(y) * -z
    else if (z <= 1.4d+128) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 - (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+204) {
		tmp = Math.sin(y) * -z;
	} else if (z <= 1.4e+128) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+204:
		tmp = math.sin(y) * -z
	elif z <= 1.4e+128:
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 - (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+204)
		tmp = Float64(sin(y) * Float64(-z));
	elseif (z <= 1.4e+128)
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 - Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+204)
		tmp = sin(y) * -z;
	elseif (z <= 1.4e+128)
		tmp = x + cos(y);
	else
		tmp = 1.0 - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+204], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[z, 1.4e+128], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000006e204

   1. Initial program 99.8%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \sin y\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\sin y \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      5. lower-sin.f64 N/A

         \[\leadsto \color{blue}{\sin y} \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      6. lower-neg.f64 75.7

         \[\leadsto \sin y \cdot \color{blue}{\left(-z\right)} \]

   5. Simplified 75.7%

      \[\leadsto \color{blue}{\sin y \cdot \left(-z\right)} \]

   if -1.10000000000000006e204 < z < 1.39999999999999991e128

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \cos y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. lower-cos.f64 87.4

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 87.4%

      \[\leadsto \color{blue}{\cos y + x} \]

   if 1.39999999999999991e128 < z

   1. Initial program 99.6%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(1 + x\right)} - z \cdot \sin y \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 99.6

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} - z \cdot \sin y \]
   7. Step-by-step derivation

   8. Simplified 81.4%

      \[\leadsto \color{blue}{1} - z \cdot \sin y \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+204}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+128}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+204}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+217}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -1.1e+204) t_0 (if (<= z 8e+217) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -1.1e+204) {
		tmp = t_0;
	} else if (z <= 8e+217) {
		tmp = x + cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(y) * -z
    if (z <= (-1.1d+204)) then
        tmp = t_0
    else if (z <= 8d+217) then
        tmp = x + cos(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double tmp;
	if (z <= -1.1e+204) {
		tmp = t_0;
	} else if (z <= 8e+217) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -1.1e+204:
		tmp = t_0
	elif z <= 8e+217:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -1.1e+204)
		tmp = t_0;
	elseif (z <= 8e+217)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -1.1e+204)
		tmp = t_0;
	elseif (z <= 8e+217)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.1e+204], t$95$0, If[LessEqual[z, 8e+217], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000006e204 or 7.99999999999999968e217 < z

   1. Initial program 99.7%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \sin y\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\sin y \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      5. lower-sin.f64 N/A

         \[\leadsto \color{blue}{\sin y} \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      6. lower-neg.f64 83.3

         \[\leadsto \sin y \cdot \color{blue}{\left(-z\right)} \]

   5. Simplified 83.3%

      \[\leadsto \color{blue}{\sin y \cdot \left(-z\right)} \]

   if -1.10000000000000006e204 < z < 7.99999999999999968e217

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \cos y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. lower-cos.f64 84.7

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 84.7%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+204}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+217}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -0.88:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.18:\\ \;\;\;\;\mathsf{fma}\left(y, \left(y \cdot y\right) \cdot \left(z \cdot \mathsf{fma}\left(y \cdot y, -0.008333333333333333, 0.16666666666666666\right)\right) - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (<= y -0.88)
     t_0
     (if (<= y 0.18)
       (fma
        y
        (-
         (*
          (* y y)
          (* z (fma (* y y) -0.008333333333333333 0.16666666666666666)))
         z)
        (+ x 1.0))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if (y <= -0.88) {
		tmp = t_0;
	} else if (y <= 0.18) {
		tmp = fma(y, (((y * y) * (z * fma((y * y), -0.008333333333333333, 0.16666666666666666))) - z), (x + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if (y <= -0.88)
		tmp = t_0;
	elseif (y <= 0.18)
		tmp = fma(y, Float64(Float64(Float64(y * y) * Float64(z * fma(Float64(y * y), -0.008333333333333333, 0.16666666666666666))) - z), Float64(x + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.88], t$95$0, If[LessEqual[y, 0.18], N[(y * N[(N[(N[(y * y), $MachinePrecision] * N[(z * N[(N[(y * y), $MachinePrecision] * -0.008333333333333333 + 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.880000000000000004 or 0.17999999999999999 < y

   1. Initial program 99.8%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \cos y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. lower-cos.f64 63.4

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 63.4%

      \[\leadsto \color{blue}{\cos y + x} \]

   if -0.880000000000000004 < y < 0.17999999999999999

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(1 + x\right)} - z \cdot \sin y \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left({y}^{2} \cdot \left(\frac{-1}{120} \cdot \left({y}^{2} \cdot z\right) - \frac{-1}{6} \cdot z\right) - z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(1 + x\right) + y \cdot \left({y}^{2} \cdot \left(\frac{-1}{120} \cdot \left({y}^{2} \cdot z\right) - \frac{-1}{6} \cdot z\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left({y}^{2} \cdot \left(\frac{-1}{120} \cdot \left({y}^{2} \cdot z\right) - \frac{-1}{6} \cdot z\right) - z\right) + \left(1 + x\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, {y}^{2} \cdot \left(\frac{-1}{120} \cdot \left({y}^{2} \cdot z\right) - \frac{-1}{6} \cdot z\right) - z, 1 + x\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(y \cdot y\right) \cdot \left(z \cdot \mathsf{fma}\left(y \cdot y, -0.008333333333333333, 0.16666666666666666\right)\right) - z, x + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.88:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq 0.18:\\ \;\;\;\;\mathsf{fma}\left(y, \left(y \cdot y\right) \cdot \left(z \cdot \mathsf{fma}\left(y \cdot y, -0.008333333333333333, 0.16666666666666666\right)\right) - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.8% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -35:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 3.1:\\ \;\;\;\;\mathsf{fma}\left(y, \left(y \cdot y\right) \cdot \left(z \cdot \mathsf{fma}\left(y \cdot y, -0.008333333333333333, 0.16666666666666666\right)\right) - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -35.0)
   (+ x 1.0)
   (if (<= y 3.1)
     (fma
      y
      (-
       (*
        (* y y)
        (* z (fma (* y y) -0.008333333333333333 0.16666666666666666)))
       z)
      (+ x 1.0))
     (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -35.0) {
		tmp = x + 1.0;
	} else if (y <= 3.1) {
		tmp = fma(y, (((y * y) * (z * fma((y * y), -0.008333333333333333, 0.16666666666666666))) - z), (x + 1.0));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -35.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 3.1)
		tmp = fma(y, Float64(Float64(Float64(y * y) * Float64(z * fma(Float64(y * y), -0.008333333333333333, 0.16666666666666666))) - z), Float64(x + 1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -35.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 3.1], N[(y * N[(N[(N[(y * y), $MachinePrecision] * N[(z * N[(N[(y * y), $MachinePrecision] * -0.008333333333333333 + 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -35 or 3.10000000000000009 < y

   1. Initial program 99.8%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 37.7

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

   5. Simplified 37.7%

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

   if -35 < y < 3.10000000000000009

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(1 + x\right)} - z \cdot \sin y \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left({y}^{2} \cdot \left(\frac{-1}{120} \cdot \left({y}^{2} \cdot z\right) - \frac{-1}{6} \cdot z\right) - z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(1 + x\right) + y \cdot \left({y}^{2} \cdot \left(\frac{-1}{120} \cdot \left({y}^{2} \cdot z\right) - \frac{-1}{6} \cdot z\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left({y}^{2} \cdot \left(\frac{-1}{120} \cdot \left({y}^{2} \cdot z\right) - \frac{-1}{6} \cdot z\right) - z\right) + \left(1 + x\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, {y}^{2} \cdot \left(\frac{-1}{120} \cdot \left({y}^{2} \cdot z\right) - \frac{-1}{6} \cdot z\right) - z, 1 + x\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(y \cdot y\right) \cdot \left(z \cdot \mathsf{fma}\left(y \cdot y, -0.008333333333333333, 0.16666666666666666\right)\right) - z, x + 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 69.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -360000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 2.4:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \mathsf{fma}\left(0.16666666666666666, y \cdot y, -1\right), x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -360000.0)
   (+ x 1.0)
   (if (<= y 2.4)
     (fma y (* z (fma 0.16666666666666666 (* y y) -1.0)) (+ x 1.0))
     (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -360000.0) {
		tmp = x + 1.0;
	} else if (y <= 2.4) {
		tmp = fma(y, (z * fma(0.16666666666666666, (y * y), -1.0)), (x + 1.0));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -360000.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 2.4)
		tmp = fma(y, Float64(z * fma(0.16666666666666666, Float64(y * y), -1.0)), Float64(x + 1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -360000.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 2.4], N[(y * N[(z * N[(0.16666666666666666 * N[(y * y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e5 or 2.39999999999999991 < y

   1. Initial program 99.8%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 37.7

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

   5. Simplified 37.7%

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

   if -3.6e5 < y < 2.39999999999999991

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(1 + x\right)} - z \cdot \sin y \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(\frac{1}{6} \cdot \left({y}^{2} \cdot z\right) - z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(1 + x\right) + y \cdot \left(\frac{1}{6} \cdot \left({y}^{2} \cdot z\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left(\frac{1}{6} \cdot \left({y}^{2} \cdot z\right) - z\right) + \left(1 + x\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1}{6} \cdot \left({y}^{2} \cdot z\right) - z, 1 + x\right)} \]

      4. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{1}{6} \cdot \left({y}^{2} \cdot z\right) + \left(\mathsf{neg}\left(z\right)\right)}, 1 + x\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\frac{1}{6} \cdot {y}^{2}\right) \cdot z} + \left(\mathsf{neg}\left(z\right)\right), 1 + x\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{1}{6} \cdot {y}^{2}\right) \cdot z + \color{blue}{-1 \cdot z}, 1 + x\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot \left(\frac{1}{6} \cdot {y}^{2} + -1\right)}, 1 + x\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot \left(\frac{1}{6} \cdot {y}^{2} + -1\right)}, 1 + x\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, z \cdot \color{blue}{\mathsf{fma}\left(\frac{1}{6}, {y}^{2}, -1\right)}, 1 + x\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{fma}\left(y, z \cdot \mathsf{fma}\left(\frac{1}{6}, \color{blue}{y \cdot y}, -1\right), 1 + x\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, z \cdot \mathsf{fma}\left(\frac{1}{6}, \color{blue}{y \cdot y}, -1\right), 1 + x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, z \cdot \mathsf{fma}\left(\frac{1}{6}, y \cdot y, -1\right), \color{blue}{x + 1}\right) \]

      13. lower-+.f64 99.9

          \[\leadsto \mathsf{fma}\left(y, z \cdot \mathsf{fma}\left(0.16666666666666666, y \cdot y, -1\right), \color{blue}{x + 1}\right) \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot \mathsf{fma}\left(0.16666666666666666, y \cdot y, -1\right), x + 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 69.6% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -35:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+57}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -35.0)
   (+ x 1.0)
   (if (<= y 1.2e+57) (- x (fma y z -1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -35.0) {
		tmp = x + 1.0;
	} else if (y <= 1.2e+57) {
		tmp = x - fma(y, z, -1.0);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -35.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.2e+57)
		tmp = Float64(x - fma(y, z, -1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -35.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.2e+57], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -35 or 1.20000000000000002e57 < y

   1. Initial program 99.8%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 36.2

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

   5. Simplified 36.2%

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

   if -35 < y < 1.20000000000000002e57

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)}\right) + 1 \]

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 94.8

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

   5. Simplified 94.8%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y, z, -1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 61.6% accurate, 53.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 59.8

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

5. Simplified 59.8%

   \[\leadsto \color{blue}{x + 1} \]
6. Add Preprocessing

Alternative 13: 21.6% accurate, 212.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 59.8

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

5. Simplified 59.8%

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

6. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
7. Step-by-step derivation

8. Simplified 21.3%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024212 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))