Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B

Percentage Accurate: 99.8% → 99.8%

Time: 11.0s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot \sin y + z \cdot \cos y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(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 * sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \sin y + z \cdot \cos y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(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 * sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\cos y, z, x \cdot \sin y\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-def 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)} \]

3. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)} \]

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(\cos y, z, x \cdot \sin y\right) \]

Alternative 2: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \sin y + \cos y \cdot z \end{array} \]

FPCore

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

C

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

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 * sin(y)) + (cos(y) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[x \cdot \sin y + z \cdot \cos y \]

2. Final simplification 99.9%

   \[\leadsto x \cdot \sin y + \cos y \cdot z \]

Alternative 3: 74.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := \cos y \cdot z\\ \mathbf{if}\;y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.02:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0019:\\ \;\;\;\;z + y \cdot x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+55} \lor \neg \left(y \leq 1.35 \cdot 10^{+165}\right) \land y \leq 5.5 \cdot 10^{+260}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* (cos y) z)))
   (if (<= y -2e+87)
     t_0
     (if (<= y -0.02)
       t_1
       (if (<= y 0.0019)
         (+ z (* y x))
         (if (or (<= y 6.4e+55) (and (not (<= y 1.35e+165)) (<= y 5.5e+260)))
           t_1
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double t_1 = cos(y) * z;
	double tmp;
	if (y <= -2e+87) {
		tmp = t_0;
	} else if (y <= -0.02) {
		tmp = t_1;
	} else if (y <= 0.0019) {
		tmp = z + (y * x);
	} else if ((y <= 6.4e+55) || (!(y <= 1.35e+165) && (y <= 5.5e+260))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x * sin(y)
    t_1 = cos(y) * z
    if (y <= (-2d+87)) then
        tmp = t_0
    else if (y <= (-0.02d0)) then
        tmp = t_1
    else if (y <= 0.0019d0) then
        tmp = z + (y * x)
    else if ((y <= 6.4d+55) .or. (.not. (y <= 1.35d+165)) .and. (y <= 5.5d+260)) then
        tmp = t_1
    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 * Math.sin(y);
	double t_1 = Math.cos(y) * z;
	double tmp;
	if (y <= -2e+87) {
		tmp = t_0;
	} else if (y <= -0.02) {
		tmp = t_1;
	} else if (y <= 0.0019) {
		tmp = z + (y * x);
	} else if ((y <= 6.4e+55) || (!(y <= 1.35e+165) && (y <= 5.5e+260))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	t_1 = math.cos(y) * z
	tmp = 0
	if y <= -2e+87:
		tmp = t_0
	elif y <= -0.02:
		tmp = t_1
	elif y <= 0.0019:
		tmp = z + (y * x)
	elif (y <= 6.4e+55) or (not (y <= 1.35e+165) and (y <= 5.5e+260)):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	t_1 = Float64(cos(y) * z)
	tmp = 0.0
	if (y <= -2e+87)
		tmp = t_0;
	elseif (y <= -0.02)
		tmp = t_1;
	elseif (y <= 0.0019)
		tmp = Float64(z + Float64(y * x));
	elseif ((y <= 6.4e+55) || (!(y <= 1.35e+165) && (y <= 5.5e+260)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	t_1 = cos(y) * z;
	tmp = 0.0;
	if (y <= -2e+87)
		tmp = t_0;
	elseif (y <= -0.02)
		tmp = t_1;
	elseif (y <= 0.0019)
		tmp = z + (y * x);
	elseif ((y <= 6.4e+55) || (~((y <= 1.35e+165)) && (y <= 5.5e+260)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -2e+87], t$95$0, If[LessEqual[y, -0.02], t$95$1, If[LessEqual[y, 0.0019], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 6.4e+55], And[N[Not[LessEqual[y, 1.35e+165]], $MachinePrecision], LessEqual[y, 5.5e+260]]], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e87 or 6.4000000000000005e55 < y < 1.35e165 or 5.49999999999999961e260 < y

   1. Initial program 99.7%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in x around inf 62.3%

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

   if -1.9999999999999999e87 < y < -0.0200000000000000004 or 0.0019 < y < 6.4000000000000005e55 or 1.35e165 < y < 5.49999999999999961e260

   1. Initial program 99.7%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in x around 0 69.5%

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

   if -0.0200000000000000004 < y < 0.0019

   1. Initial program 100.0%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq -0.02:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;y \leq 0.0019:\\ \;\;\;\;z + y \cdot x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+55} \lor \neg \left(y \leq 1.35 \cdot 10^{+165}\right) \land y \leq 5.5 \cdot 10^{+260}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]

Alternative 4: 85.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+86} \lor \neg \left(z \leq 4.6 \cdot 10^{+153}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.5e+86) (not (<= z 4.6e+153)))
   (* (cos y) z)
   (+ z (* x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e+86) || !(z <= 4.6e+153)) {
		tmp = cos(y) * z;
	} else {
		tmp = z + (x * 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 <= (-7.5d+86)) .or. (.not. (z <= 4.6d+153))) then
        tmp = cos(y) * z
    else
        tmp = z + (x * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e+86) || !(z <= 4.6e+153)) {
		tmp = Math.cos(y) * z;
	} else {
		tmp = z + (x * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.5e+86) or not (z <= 4.6e+153):
		tmp = math.cos(y) * z
	else:
		tmp = z + (x * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.5e+86) || !(z <= 4.6e+153))
		tmp = Float64(cos(y) * z);
	else
		tmp = Float64(z + Float64(x * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.5e+86) || ~((z <= 4.6e+153)))
		tmp = cos(y) * z;
	else
		tmp = z + (x * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.5e+86], N[Not[LessEqual[z, 4.6e+153]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4999999999999997e86 or 4.6000000000000003e153 < z

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in x around 0 91.2%

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

   if -7.4999999999999997e86 < z < 4.6000000000000003e153

   1. Initial program 99.9%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in y around 0 89.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+86} \lor \neg \left(z \leq 4.6 \cdot 10^{+153}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot \sin y\\ \end{array} \]

Alternative 5: 73.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-6} \lor \neg \left(y \leq 9.5 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e-6) (not (<= y 9.5e+30))) (* x (sin y)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e-6) || !(y <= 9.5e+30)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * 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) :: tmp
    if ((y <= (-5.2d-6)) .or. (.not. (y <= 9.5d+30))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e-6) || !(y <= 9.5e+30)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e-6) or not (y <= 9.5e+30):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e-6) || !(y <= 9.5e+30))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.2e-6) || ~((y <= 9.5e+30)))
		tmp = x * sin(y);
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e-6], N[Not[LessEqual[y, 9.5e+30]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.20000000000000019e-6 or 9.5000000000000003e30 < y

   1. Initial program 99.7%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in x around inf 51.8%

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

   if -5.20000000000000019e-6 < y < 9.5000000000000003e30

   1. Initial program 100.0%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in y around 0 97.6%

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

      1. +-commutative 97.6%

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

   4. Simplified 97.6%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-6} \lor \neg \left(y \leq 9.5 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 6: 41.0% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-58}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 10^{-105}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e-58) z (if (<= z 1e-105) (* y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e-58) {
		tmp = z;
	} else if (z <= 1e-105) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	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 <= (-1d-58)) then
        tmp = z
    else if (z <= 1d-105) then
        tmp = y * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e-58) {
		tmp = z;
	} else if (z <= 1e-105) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e-58:
		tmp = z
	elif z <= 1e-105:
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e-58)
		tmp = z;
	elseif (z <= 1e-105)
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1e-58)
		tmp = z;
	elseif (z <= 1e-105)
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e-58], z, If[LessEqual[z, 1e-105], N[(y * x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1e-58 or 9.99999999999999965e-106 < z

   1. Initial program 99.9%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)} \]

   3. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)} \]

   4. Taylor expanded in y around 0 53.1%

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

   if -1e-58 < z < 9.99999999999999965e-106

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in x around inf 73.5%

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

   3. Taylor expanded in y around 0 34.0%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-58}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 10^{-105}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 52.6% accurate, 41.4× speedup

Math

\[\begin{array}{l} \\ z + y \cdot x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[x \cdot \sin y + z \cdot \cos y \]

2. Taylor expanded in y around 0 53.2%

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

   1. +-commutative 53.2%

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

4. Simplified 53.2%

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

5. Final simplification 53.2%

   \[\leadsto z + y \cdot x \]

Alternative 8: 39.4% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-def 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)} \]

3. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)} \]

4. Taylor expanded in y around 0 40.2%

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

5. Final simplification 40.2%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))