Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Percentage Accurate: 97.9% → 100.0%

Time: 5.5s

Alternatives: 7

Speedup: 1.3×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * 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) + ((1.0d0 - x) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * 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) + ((1.0d0 - x) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. *-commutative 97.3%

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

   2. distribute-lft-out-- 97.3%

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

   3. *-rgt-identity 97.3%

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

   4. cancel-sign-sub-inv 97.3%

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

   5. +-commutative 97.3%

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

   6. associate-+r+ 97.3%

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

   7. +-commutative 97.3%

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

   8. *-commutative 97.3%

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

   9. distribute-rgt-out 100.0%

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

   10. fma-def 100.0%

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

   11. +-commutative 100.0%

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

   12. unsub-neg 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y - z, z\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, y - z, z\right) \]
6. Add Preprocessing

Alternative 2: 60.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-26}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-109}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-83}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+39} \lor \neg \left(x \leq 3 \cdot 10^{+101}\right) \land x \leq 2.3 \cdot 10^{+159}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.15e-26)
   (* x y)
   (if (<= x -1.6e-109)
     z
     (if (<= x -5.8e-125)
       (* x y)
       (if (<= x 2.1e-83)
         z
         (if (or (<= x 8.8e+39) (and (not (<= x 3e+101)) (<= x 2.3e+159)))
           (* x y)
           (* x (- z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.15e-26) {
		tmp = x * y;
	} else if (x <= -1.6e-109) {
		tmp = z;
	} else if (x <= -5.8e-125) {
		tmp = x * y;
	} else if (x <= 2.1e-83) {
		tmp = z;
	} else if ((x <= 8.8e+39) || (!(x <= 3e+101) && (x <= 2.3e+159))) {
		tmp = x * y;
	} else {
		tmp = x * -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 <= (-2.15d-26)) then
        tmp = x * y
    else if (x <= (-1.6d-109)) then
        tmp = z
    else if (x <= (-5.8d-125)) then
        tmp = x * y
    else if (x <= 2.1d-83) then
        tmp = z
    else if ((x <= 8.8d+39) .or. (.not. (x <= 3d+101)) .and. (x <= 2.3d+159)) then
        tmp = x * y
    else
        tmp = x * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.15e-26) {
		tmp = x * y;
	} else if (x <= -1.6e-109) {
		tmp = z;
	} else if (x <= -5.8e-125) {
		tmp = x * y;
	} else if (x <= 2.1e-83) {
		tmp = z;
	} else if ((x <= 8.8e+39) || (!(x <= 3e+101) && (x <= 2.3e+159))) {
		tmp = x * y;
	} else {
		tmp = x * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.15e-26:
		tmp = x * y
	elif x <= -1.6e-109:
		tmp = z
	elif x <= -5.8e-125:
		tmp = x * y
	elif x <= 2.1e-83:
		tmp = z
	elif (x <= 8.8e+39) or (not (x <= 3e+101) and (x <= 2.3e+159)):
		tmp = x * y
	else:
		tmp = x * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.15e-26)
		tmp = Float64(x * y);
	elseif (x <= -1.6e-109)
		tmp = z;
	elseif (x <= -5.8e-125)
		tmp = Float64(x * y);
	elseif (x <= 2.1e-83)
		tmp = z;
	elseif ((x <= 8.8e+39) || (!(x <= 3e+101) && (x <= 2.3e+159)))
		tmp = Float64(x * y);
	else
		tmp = Float64(x * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.15e-26)
		tmp = x * y;
	elseif (x <= -1.6e-109)
		tmp = z;
	elseif (x <= -5.8e-125)
		tmp = x * y;
	elseif (x <= 2.1e-83)
		tmp = z;
	elseif ((x <= 8.8e+39) || (~((x <= 3e+101)) && (x <= 2.3e+159)))
		tmp = x * y;
	else
		tmp = x * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.15e-26], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.6e-109], z, If[LessEqual[x, -5.8e-125], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.1e-83], z, If[Or[LessEqual[x, 8.8e+39], And[N[Not[LessEqual[x, 3e+101]], $MachinePrecision], LessEqual[x, 2.3e+159]]], N[(x * y), $MachinePrecision], N[(x * (-z)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.14999999999999994e-26 or -1.6000000000000001e-109 < x < -5.8000000000000004e-125 or 2.0999999999999999e-83 < x < 8.8000000000000006e39 or 2.99999999999999993e101 < x < 2.29999999999999995e159

   1. Initial program 96.4%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.0%

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

   if -2.14999999999999994e-26 < x < -1.6000000000000001e-109 or -5.8000000000000004e-125 < x < 2.0999999999999999e-83

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.5%

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

   if 8.8000000000000006e39 < x < 2.99999999999999993e101 or 2.29999999999999995e159 < x

   1. Initial program 92.7%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 71.7%

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

      1. associate-*r* 71.7%

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

      2. mul-1-neg 71.7%

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

   8. Simplified 71.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-26}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-109}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-83}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+39} \lor \neg \left(x \leq 3 \cdot 10^{+101}\right) \land x \leq 2.3 \cdot 10^{+159}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-110}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-83}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y z))))
   (if (<= x -2.1e-25)
     t_0
     (if (<= x -5.4e-110)
       z
       (if (<= x -1.12e-125) (* x y) (if (<= x 3.6e-83) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -2.1e-25) {
		tmp = t_0;
	} else if (x <= -5.4e-110) {
		tmp = z;
	} else if (x <= -1.12e-125) {
		tmp = x * y;
	} else if (x <= 3.6e-83) {
		tmp = z;
	} 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 * (y - z)
    if (x <= (-2.1d-25)) then
        tmp = t_0
    else if (x <= (-5.4d-110)) then
        tmp = z
    else if (x <= (-1.12d-125)) then
        tmp = x * y
    else if (x <= 3.6d-83) then
        tmp = z
    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 * (y - z);
	double tmp;
	if (x <= -2.1e-25) {
		tmp = t_0;
	} else if (x <= -5.4e-110) {
		tmp = z;
	} else if (x <= -1.12e-125) {
		tmp = x * y;
	} else if (x <= 3.6e-83) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y - z)
	tmp = 0
	if x <= -2.1e-25:
		tmp = t_0
	elif x <= -5.4e-110:
		tmp = z
	elif x <= -1.12e-125:
		tmp = x * y
	elif x <= 3.6e-83:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y - z))
	tmp = 0.0
	if (x <= -2.1e-25)
		tmp = t_0;
	elseif (x <= -5.4e-110)
		tmp = z;
	elseif (x <= -1.12e-125)
		tmp = Float64(x * y);
	elseif (x <= 3.6e-83)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y - z);
	tmp = 0.0;
	if (x <= -2.1e-25)
		tmp = t_0;
	elseif (x <= -5.4e-110)
		tmp = z;
	elseif (x <= -1.12e-125)
		tmp = x * y;
	elseif (x <= 3.6e-83)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e-25], t$95$0, If[LessEqual[x, -5.4e-110], z, If[LessEqual[x, -1.12e-125], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.6e-83], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.10000000000000002e-25 or 3.60000000000000012e-83 < x

   1. Initial program 95.3%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.5%

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

      1. mul-1-neg 94.5%

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

      2. sub-neg 94.5%

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

   5. Simplified 94.5%

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

   if -2.10000000000000002e-25 < x < -5.3999999999999996e-110 or -1.11999999999999997e-125 < x < 3.60000000000000012e-83

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.5%

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

   if -5.3999999999999996e-110 < x < -1.11999999999999997e-125

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-110}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-83}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-25} \lor \neg \left(x \leq -5.1 \cdot 10^{-110} \lor \neg \left(x \leq -7.2 \cdot 10^{-125}\right) \land x \leq 3.3 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e-25)
         (not
          (or (<= x -5.1e-110) (and (not (<= x -7.2e-125)) (<= x 3.3e-83)))))
   (* x y)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e-25) || !((x <= -5.1e-110) || (!(x <= -7.2e-125) && (x <= 3.3e-83)))) {
		tmp = x * y;
	} 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 ((x <= (-1.9d-25)) .or. (.not. (x <= (-5.1d-110)) .or. (.not. (x <= (-7.2d-125))) .and. (x <= 3.3d-83))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e-25) || !((x <= -5.1e-110) || (!(x <= -7.2e-125) && (x <= 3.3e-83)))) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e-25) or not ((x <= -5.1e-110) or (not (x <= -7.2e-125) and (x <= 3.3e-83))):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e-25) || !((x <= -5.1e-110) || (!(x <= -7.2e-125) && (x <= 3.3e-83))))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.9e-25) || ~(((x <= -5.1e-110) || (~((x <= -7.2e-125)) && (x <= 3.3e-83)))))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e-25], N[Not[Or[LessEqual[x, -5.1e-110], And[N[Not[LessEqual[x, -7.2e-125]], $MachinePrecision], LessEqual[x, 3.3e-83]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999999e-25 or -5.1000000000000002e-110 < x < -7.2000000000000004e-125 or 3.2999999999999999e-83 < x

   1. Initial program 95.4%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.8%

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

   if -1.8999999999999999e-25 < x < -5.1000000000000002e-110 or -7.2000000000000004e-125 < x < 3.2999999999999999e-83

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.5%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-25} \lor \neg \left(x \leq -5.1 \cdot 10^{-110} \lor \neg \left(x \leq -7.2 \cdot 10^{-125}\right) \land x \leq 3.3 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -370000 \lor \neg \left(x \leq 1.1 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -370000.0) (not (<= x 1.1e-9))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -370000.0) || !(x <= 1.1e-9)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * 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 ((x <= (-370000.0d0)) .or. (.not. (x <= 1.1d-9))) then
        tmp = x * (y - z)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -370000.0) || !(x <= 1.1e-9)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -370000.0) or not (x <= 1.1e-9):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -370000.0) || !(x <= 1.1e-9))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -370000.0) || ~((x <= 1.1e-9)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -370000.0], N[Not[LessEqual[x, 1.1e-9]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7e5 or 1.0999999999999999e-9 < x

   1. Initial program 94.4%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. sub-neg 99.5%

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

   5. Simplified 99.5%

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

   if -3.7e5 < x < 1.0999999999999999e-9

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+l- 100.0%

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

      6. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z - x \cdot \left(z - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 98.8%

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

      1. mul-1-neg 98.8%

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

      2. *-commutative 98.8%

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

      3. distribute-rgt-neg-in 98.8%

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

   7. Simplified 98.8%

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

      1. sub-neg 98.8%

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

      2. +-commutative 98.8%

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

      3. distribute-rgt-neg-out 98.8%

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

      4. remove-double-neg 98.8%

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

   9. Applied egg-rr 98.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -370000 \lor \neg \left(x \leq 1.1 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. +-commutative 97.3%

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

   2. *-commutative 97.3%

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

   3. distribute-rgt-out-- 97.3%

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

   4. *-lft-identity 97.3%

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

   5. associate-+l- 97.3%

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

   6. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{z - x \cdot \left(z - y\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto z + x \cdot \left(y - z\right) \]
6. Add Preprocessing

Alternative 7: 36.2% accurate, 9.0× 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 97.3%

   \[x \cdot y + \left(1 - x\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0 36.6%

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

4. Final simplification 36.6%

   \[\leadsto z \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))