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

Percentage Accurate: 99.8% → 99.8%

Time: 10.8s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

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: 99.8% accurate, 1.0× speedup

Math

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

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: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   3. *-commutative 99.9%

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

   4. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 3: 74.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -0.013:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.28:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+230} \lor \neg \left(y \leq 1.5 \cdot 10^{+238}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= y -0.013)
     t_0
     (if (<= y 0.28)
       (- x (* y z))
       (if (or (<= y 3.15e+230) (not (<= y 1.5e+238))) (* x (cos y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (y <= -0.013) {
		tmp = t_0;
	} else if (y <= 0.28) {
		tmp = x - (y * z);
	} else if ((y <= 3.15e+230) || !(y <= 1.5e+238)) {
		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 (y <= (-0.013d0)) then
        tmp = t_0
    else if (y <= 0.28d0) then
        tmp = x - (y * z)
    else if ((y <= 3.15d+230) .or. (.not. (y <= 1.5d+238))) 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 (y <= -0.013) {
		tmp = t_0;
	} else if (y <= 0.28) {
		tmp = x - (y * z);
	} else if ((y <= 3.15e+230) || !(y <= 1.5e+238)) {
		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 y <= -0.013:
		tmp = t_0
	elif y <= 0.28:
		tmp = x - (y * z)
	elif (y <= 3.15e+230) or not (y <= 1.5e+238):
		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 (y <= -0.013)
		tmp = t_0;
	elseif (y <= 0.28)
		tmp = Float64(x - Float64(y * z));
	elseif ((y <= 3.15e+230) || !(y <= 1.5e+238))
		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 (y <= -0.013)
		tmp = t_0;
	elseif (y <= 0.28)
		tmp = x - (y * z);
	elseif ((y <= 3.15e+230) || ~((y <= 1.5e+238)))
		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[y, -0.013], t$95$0, If[LessEqual[y, 0.28], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.15e+230], N[Not[LessEqual[y, 1.5e+238]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0129999999999999994 or 3.1500000000000001e230 < y < 1.5e238

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. distribute-lft-neg-in 64.1%

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

      3. *-commutative 64.1%

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

   4. Simplified 64.1%

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

   if -0.0129999999999999994 < y < 0.28000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. distribute-rgt-neg-in 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in x around 0 98.5%

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

      1. *-commutative 98.5%

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

      2. mul-1-neg 98.5%

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

      3. sub-neg 98.5%

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

   7. Simplified 98.5%

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

   if 0.28000000000000003 < y < 3.1500000000000001e230 or 1.5e238 < y

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 65.0%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.013:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 0.28:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+230} \lor \neg \left(y \leq 1.5 \cdot 10^{+238}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 85.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+47} \lor \neg \left(x \leq 4.2 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - \sin y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.6e+47) (not (<= x 4.2e+138)))
   (* x (cos y))
   (- x (* (sin y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.6e+47) || !(x <= 4.2e+138)) {
		tmp = x * cos(y);
	} else {
		tmp = x - (sin(y) * 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 ((x <= (-2.6d+47)) .or. (.not. (x <= 4.2d+138))) then
        tmp = x * cos(y)
    else
        tmp = x - (sin(y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.6e+47) || !(x <= 4.2e+138)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (Math.sin(y) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.6e+47) or not (x <= 4.2e+138):
		tmp = x * math.cos(y)
	else:
		tmp = x - (math.sin(y) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.6e+47) || !(x <= 4.2e+138))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(sin(y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.6e+47) || ~((x <= 4.2e+138)))
		tmp = x * cos(y);
	else
		tmp = x - (sin(y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.6e+47], N[Not[LessEqual[x, 4.2e+138]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000003e47 or 4.20000000000000014e138 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 93.5%

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

   if -2.60000000000000003e47 < x < 4.20000000000000014e138

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 92.5%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+47} \lor \neg \left(x \leq 4.2 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - \sin y \cdot z\\ \end{array} \]

Alternative 5: 74.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0034 \lor \neg \left(y \leq 0.28\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0034) (not (<= y 0.28))) (* x (cos y)) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0034) || !(y <= 0.28)) {
		tmp = x * cos(y);
	} else {
		tmp = x - (y * 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 ((y <= (-0.0034d0)) .or. (.not. (y <= 0.28d0))) then
        tmp = x * cos(y)
    else
        tmp = x - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0034) || !(y <= 0.28)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0034) or not (y <= 0.28):
		tmp = x * math.cos(y)
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0034) || !(y <= 0.28))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0034) || ~((y <= 0.28)))
		tmp = x * cos(y);
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0034], N[Not[LessEqual[y, 0.28]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00339999999999999981 or 0.28000000000000003 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 51.5%

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

   if -0.00339999999999999981 < y < 0.28000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-in 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in x around 0 98.9%

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

      1. *-commutative 98.9%

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

      2. mul-1-neg 98.9%

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

      3. sub-neg 98.9%

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

   7. Simplified 98.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0034 \lor \neg \left(y \leq 0.28\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]

Alternative 6: 40.5% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+132}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z -1.16e+132) (* y (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e+132) {
		tmp = y * -z;
	} 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) :: tmp
    if (z <= (-1.16d+132)) then
        tmp = y * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e+132) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.16e+132:
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.16e+132)
		tmp = Float64(y * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.16e+132)
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.16e+132], N[(y * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.16000000000000004e132

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. distribute-rgt-neg-in 53.6%

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

   4. Simplified 53.6%

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

   5. Taylor expanded in x around 0 37.2%

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

      1. associate-*r* 37.2%

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

      2. neg-mul-1 37.2%

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

   7. Simplified 37.2%

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

   if -1.16000000000000004e132 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-rgt-neg-in 58.9%

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

   4. Simplified 58.9%

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

   5. Taylor expanded in x around inf 48.2%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+132}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 52.7% accurate, 41.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x - (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 - (y * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 58.1%

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

   1. mul-1-neg 58.1%

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

   2. distribute-rgt-neg-in 58.1%

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

4. Simplified 58.1%

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

5. Taylor expanded in x around 0 58.1%

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

   1. *-commutative 58.1%

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

   2. mul-1-neg 58.1%

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

   3. sub-neg 58.1%

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

7. Simplified 58.1%

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

8. Final simplification 58.1%

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

Alternative 8: 38.3% accurate, 207.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 58.1%

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

   1. mul-1-neg 58.1%

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

   2. distribute-rgt-neg-in 58.1%

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

4. Simplified 58.1%

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

5. Taylor expanded in x around inf 43.2%

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

6. Final simplification 43.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))