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

Percentage Accurate: 97.7% → 100.0%

Time: 4.1s

Alternatives: 8

Speedup: 1.3×

• 21.3% 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: 97.7% 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 98.8%

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

   1. *-commutative 98.8%

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

   2. distribute-lft-out-- 98.8%

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

   3. *-rgt-identity 98.8%

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

   4. cancel-sign-sub-inv 98.8%

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

   5. +-commutative 98.8%

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

   6. associate-+r+ 98.8%

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

   7. +-commutative 98.8%

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

   8. *-commutative 98.8%

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

   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. Final simplification 100.0%

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

Alternative 2: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+208}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.54 \cdot 10^{+91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4200000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-63}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+246}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= x -4.5e+208)
     (* x y)
     (if (<= x -1.8e+143)
       t_0
       (if (<= x -1.54e+91)
         (* x y)
         (if (<= x -4200000.0)
           t_0
           (if (<= x -5e-24)
             (* x y)
             (if (<= x 7.6e-63) z (if (<= x 9.6e+246) (* x y) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -4.5e+208) {
		tmp = x * y;
	} else if (x <= -1.8e+143) {
		tmp = t_0;
	} else if (x <= -1.54e+91) {
		tmp = x * y;
	} else if (x <= -4200000.0) {
		tmp = t_0;
	} else if (x <= -5e-24) {
		tmp = x * y;
	} else if (x <= 7.6e-63) {
		tmp = z;
	} else if (x <= 9.6e+246) {
		tmp = x * 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 * -z
    if (x <= (-4.5d+208)) then
        tmp = x * y
    else if (x <= (-1.8d+143)) then
        tmp = t_0
    else if (x <= (-1.54d+91)) then
        tmp = x * y
    else if (x <= (-4200000.0d0)) then
        tmp = t_0
    else if (x <= (-5d-24)) then
        tmp = x * y
    else if (x <= 7.6d-63) then
        tmp = z
    else if (x <= 9.6d+246) then
        tmp = x * 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 * -z;
	double tmp;
	if (x <= -4.5e+208) {
		tmp = x * y;
	} else if (x <= -1.8e+143) {
		tmp = t_0;
	} else if (x <= -1.54e+91) {
		tmp = x * y;
	} else if (x <= -4200000.0) {
		tmp = t_0;
	} else if (x <= -5e-24) {
		tmp = x * y;
	} else if (x <= 7.6e-63) {
		tmp = z;
	} else if (x <= 9.6e+246) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if x <= -4.5e+208:
		tmp = x * y
	elif x <= -1.8e+143:
		tmp = t_0
	elif x <= -1.54e+91:
		tmp = x * y
	elif x <= -4200000.0:
		tmp = t_0
	elif x <= -5e-24:
		tmp = x * y
	elif x <= 7.6e-63:
		tmp = z
	elif x <= 9.6e+246:
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (x <= -4.5e+208)
		tmp = Float64(x * y);
	elseif (x <= -1.8e+143)
		tmp = t_0;
	elseif (x <= -1.54e+91)
		tmp = Float64(x * y);
	elseif (x <= -4200000.0)
		tmp = t_0;
	elseif (x <= -5e-24)
		tmp = Float64(x * y);
	elseif (x <= 7.6e-63)
		tmp = z;
	elseif (x <= 9.6e+246)
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (x <= -4.5e+208)
		tmp = x * y;
	elseif (x <= -1.8e+143)
		tmp = t_0;
	elseif (x <= -1.54e+91)
		tmp = x * y;
	elseif (x <= -4200000.0)
		tmp = t_0;
	elseif (x <= -5e-24)
		tmp = x * y;
	elseif (x <= 7.6e-63)
		tmp = z;
	elseif (x <= 9.6e+246)
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[x, -4.5e+208], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.8e+143], t$95$0, If[LessEqual[x, -1.54e+91], N[(x * y), $MachinePrecision], If[LessEqual[x, -4200000.0], t$95$0, If[LessEqual[x, -5e-24], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.6e-63], z, If[LessEqual[x, 9.6e+246], N[(x * y), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.50000000000000015e208 or -1.8e143 < x < -1.54000000000000007e91 or -4.2e6 < x < -4.9999999999999998e-24 or 7.60000000000000034e-63 < x < 9.6e246

   1. Initial program 97.9%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 70.3%

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

   if -4.50000000000000015e208 < x < -1.8e143 or -1.54000000000000007e91 < x < -4.2e6 or 9.6e246 < x

   1. Initial program 98.1%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 97.5%

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

      1. neg-mul-1 97.5%

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

      2. unsub-neg 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in y around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. distribute-lft-neg-out 63.0%

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

      3. *-commutative 63.0%

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

   7. Simplified 63.0%

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

   if -4.9999999999999998e-24 < x < 7.60000000000000034e-63

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 74.5%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+208}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -1.54 \cdot 10^{+91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4200000:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-63}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+246}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-24} \lor \neg \left(x \leq -9 \cdot 10^{-44}\right) \land \left(x \leq -5.3 \cdot 10^{-111} \lor \neg \left(x \leq 2.3 \cdot 10^{-60}\right)\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.2e-24)
         (and (not (<= x -9e-44)) (or (<= x -5.3e-111) (not (<= x 2.3e-60)))))
   (* x (- y z))
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-24) || (!(x <= -9e-44) && ((x <= -5.3e-111) || !(x <= 2.3e-60)))) {
		tmp = x * (y - z);
	} 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 <= (-2.2d-24)) .or. (.not. (x <= (-9d-44))) .and. (x <= (-5.3d-111)) .or. (.not. (x <= 2.3d-60))) then
        tmp = x * (y - z)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-24) || (!(x <= -9e-44) && ((x <= -5.3e-111) || !(x <= 2.3e-60)))) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.2e-24) or (not (x <= -9e-44) and ((x <= -5.3e-111) or not (x <= 2.3e-60))):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.2e-24) || (!(x <= -9e-44) && ((x <= -5.3e-111) || !(x <= 2.3e-60))))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.2e-24) || (~((x <= -9e-44)) && ((x <= -5.3e-111) || ~((x <= 2.3e-60)))))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.2e-24], And[N[Not[LessEqual[x, -9e-44]], $MachinePrecision], Or[LessEqual[x, -5.3e-111], N[Not[LessEqual[x, 2.3e-60]], $MachinePrecision]]]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000002e-24 or -8.9999999999999997e-44 < x < -5.2999999999999997e-111 or 2.3000000000000001e-60 < x

   1. Initial program 98.2%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 93.4%

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

      1. neg-mul-1 93.4%

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

      2. unsub-neg 93.4%

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

   4. Simplified 93.4%

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

   if -2.20000000000000002e-24 < x < -8.9999999999999997e-44 or -5.2999999999999997e-111 < x < 2.3000000000000001e-60

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 80.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-24} \lor \neg \left(x \leq -9 \cdot 10^{-44}\right) \land \left(x \leq -5.3 \cdot 10^{-111} \lor \neg \left(x \leq 2.3 \cdot 10^{-60}\right)\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-25} \lor \neg \left(x \leq -2.7 \cdot 10^{-42}\right) \land \left(x \leq -3.5 \cdot 10^{-113} \lor \neg \left(x \leq 1.65 \cdot 10^{-60}\right)\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e-25)
         (and (not (<= x -2.7e-42))
              (or (<= x -3.5e-113) (not (<= x 1.65e-60)))))
   (* x (- y z))
   (* z (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e-25) || (!(x <= -2.7e-42) && ((x <= -3.5e-113) || !(x <= 1.65e-60)))) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - 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 ((x <= (-5.2d-25)) .or. (.not. (x <= (-2.7d-42))) .and. (x <= (-3.5d-113)) .or. (.not. (x <= 1.65d-60))) then
        tmp = x * (y - z)
    else
        tmp = z * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e-25) || (!(x <= -2.7e-42) && ((x <= -3.5e-113) || !(x <= 1.65e-60)))) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e-25) or (not (x <= -2.7e-42) and ((x <= -3.5e-113) or not (x <= 1.65e-60))):
		tmp = x * (y - z)
	else:
		tmp = z * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e-25) || (!(x <= -2.7e-42) && ((x <= -3.5e-113) || !(x <= 1.65e-60))))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.2e-25) || (~((x <= -2.7e-42)) && ((x <= -3.5e-113) || ~((x <= 1.65e-60)))))
		tmp = x * (y - z);
	else
		tmp = z * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e-25], And[N[Not[LessEqual[x, -2.7e-42]], $MachinePrecision], Or[LessEqual[x, -3.5e-113], N[Not[LessEqual[x, 1.65e-60]], $MachinePrecision]]]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2e-25 or -2.69999999999999999e-42 < x < -3.50000000000000029e-113 or 1.6499999999999999e-60 < x

   1. Initial program 98.2%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 93.4%

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

      1. neg-mul-1 93.4%

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

      2. unsub-neg 93.4%

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

   4. Simplified 93.4%

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

   if -5.2e-25 < x < -2.69999999999999999e-42 or -3.50000000000000029e-113 < x < 1.6499999999999999e-60

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around 0 80.1%

      \[\leadsto \color{blue}{z \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-25} \lor \neg \left(x \leq -2.7 \cdot 10^{-42}\right) \land \left(x \leq -3.5 \cdot 10^{-113} \lor \neg \left(x \leq 1.65 \cdot 10^{-60}\right)\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -38 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -38.0) (not (<= x 1.0))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -38.0) || !(x <= 1.0)) {
		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 <= (-38.0d0)) .or. (.not. (x <= 1.0d0))) 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 <= -38.0) || !(x <= 1.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -38.0) or not (x <= 1.0):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -38.0) || !(x <= 1.0))
		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 <= -38.0) || ~((x <= 1.0)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -38.0], N[Not[LessEqual[x, 1.0]], $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 < -38 or 1 < x

   1. Initial program 97.8%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 98.4%

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

      1. neg-mul-1 98.4%

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

      2. unsub-neg 98.4%

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

   4. Simplified 98.4%

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

   if -38 < x < 1

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 100.0%

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

      1. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. distribute-lft-neg-out 100.0%

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

      5. mul-1-neg 100.0%

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

      6. *-lft-identity 100.0%

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

      7. associate-+r+ 100.0%

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

      8. mul-1-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. distribute-lft-out-- 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 99.1%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -38 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 6: 60.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-24} \lor \neg \left(x \leq 2.55 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.8e-24) (not (<= x 2.55e-63))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e-24) || !(x <= 2.55e-63)) {
		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 <= (-4.8d-24)) .or. (.not. (x <= 2.55d-63))) 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 <= -4.8e-24) || !(x <= 2.55e-63)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.8e-24) or not (x <= 2.55e-63):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.8e-24) || !(x <= 2.55e-63))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.8e-24) || ~((x <= 2.55e-63)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.8e-24], N[Not[LessEqual[x, 2.55e-63]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -4.7999999999999996e-24 or 2.55000000000000012e-63 < x

   1. Initial program 98.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 58.1%

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

   if -4.7999999999999996e-24 < x < 2.55000000000000012e-63

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 74.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-24} \lor \neg \left(x \leq 2.55 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 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 98.8%

   \[x \cdot y + \left(1 - x\right) \cdot z \]

2. Taylor expanded in x around 0 100.0%

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

   1. neg-mul-1 100.0%

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

4. Simplified 100.0%

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

5. Taylor expanded in z around 0 98.8%

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

   1. neg-mul-1 98.8%

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

   2. +-commutative 98.8%

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

   3. distribute-rgt-in 98.8%

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

   4. distribute-lft-neg-out 98.8%

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

   5. mul-1-neg 98.8%

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

   6. *-lft-identity 98.8%

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

   7. associate-+r+ 98.8%

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

   8. mul-1-neg 98.8%

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

   9. sub-neg 98.8%

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

   10. +-commutative 98.8%

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

   11. distribute-lft-out-- 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

   \[\leadsto z + x \cdot \left(y - z\right) \]

Alternative 8: 35.6% 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 98.8%

   \[x \cdot y + \left(1 - x\right) \cdot z \]

2. Taylor expanded in x around 0 33.8%

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

3. Final simplification 33.8%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023311 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))