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

Percentage Accurate: 98.1% → 100.0%

Time: 5.9s

Alternatives: 7

Speedup: 1.3×

• 20.6% 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: 98.1% 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 96.5%

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

   1. *-commutative 96.5%

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

   2. distribute-lft-out-- 96.5%

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

   3. *-rgt-identity 96.5%

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

   4. cancel-sign-sub-inv 96.5%

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

   5. +-commutative 96.5%

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

   6. associate-+r+ 96.5%

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

   7. +-commutative 96.5%

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

   8. *-commutative 96.5%

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

   9. distribute-rgt-out 100.0%

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

   10. fma-define 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: 54.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-22}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-91}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-144}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-196}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-188}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-43}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= y -1.2e-22)
     (* x y)
     (if (<= y -2.15e-91)
       z
       (if (<= y -1.35e-144)
         t_0
         (if (<= y -4.1e-196)
           z
           (if (<= y 5.2e-188) t_0 (if (<= y 2.9e-43) z (* x y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (y <= -1.2e-22) {
		tmp = x * y;
	} else if (y <= -2.15e-91) {
		tmp = z;
	} else if (y <= -1.35e-144) {
		tmp = t_0;
	} else if (y <= -4.1e-196) {
		tmp = z;
	} else if (y <= 5.2e-188) {
		tmp = t_0;
	} else if (y <= 2.9e-43) {
		tmp = z;
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (y <= (-1.2d-22)) then
        tmp = x * y
    else if (y <= (-2.15d-91)) then
        tmp = z
    else if (y <= (-1.35d-144)) then
        tmp = t_0
    else if (y <= (-4.1d-196)) then
        tmp = z
    else if (y <= 5.2d-188) then
        tmp = t_0
    else if (y <= 2.9d-43) then
        tmp = z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (y <= -1.2e-22) {
		tmp = x * y;
	} else if (y <= -2.15e-91) {
		tmp = z;
	} else if (y <= -1.35e-144) {
		tmp = t_0;
	} else if (y <= -4.1e-196) {
		tmp = z;
	} else if (y <= 5.2e-188) {
		tmp = t_0;
	} else if (y <= 2.9e-43) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if y <= -1.2e-22:
		tmp = x * y
	elif y <= -2.15e-91:
		tmp = z
	elif y <= -1.35e-144:
		tmp = t_0
	elif y <= -4.1e-196:
		tmp = z
	elif y <= 5.2e-188:
		tmp = t_0
	elif y <= 2.9e-43:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (y <= -1.2e-22)
		tmp = Float64(x * y);
	elseif (y <= -2.15e-91)
		tmp = z;
	elseif (y <= -1.35e-144)
		tmp = t_0;
	elseif (y <= -4.1e-196)
		tmp = z;
	elseif (y <= 5.2e-188)
		tmp = t_0;
	elseif (y <= 2.9e-43)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (y <= -1.2e-22)
		tmp = x * y;
	elseif (y <= -2.15e-91)
		tmp = z;
	elseif (y <= -1.35e-144)
		tmp = t_0;
	elseif (y <= -4.1e-196)
		tmp = z;
	elseif (y <= 5.2e-188)
		tmp = t_0;
	elseif (y <= 2.9e-43)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.2e-22], N[(x * y), $MachinePrecision], If[LessEqual[y, -2.15e-91], z, If[LessEqual[y, -1.35e-144], t$95$0, If[LessEqual[y, -4.1e-196], z, If[LessEqual[y, 5.2e-188], t$95$0, If[LessEqual[y, 2.9e-43], z, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.20000000000000001e-22 or 2.9000000000000001e-43 < y

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 72.5%

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

   if -1.20000000000000001e-22 < y < -2.15e-91 or -1.34999999999999988e-144 < y < -4.10000000000000021e-196 or 5.2000000000000001e-188 < y < 2.9000000000000001e-43

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 60.2%

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

   if -2.15e-91 < y < -1.34999999999999988e-144 or -4.10000000000000021e-196 < y < 5.2000000000000001e-188

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. sub-neg 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in y around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. distribute-lft-neg-out 65.9%

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

      3. *-commutative 65.9%

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

   8. Simplified 65.9%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-22}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-91}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-144}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-196}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-188}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-43}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-105} \lor \neg \left(x \leq 6.5 \cdot 10^{-134}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e-105) (not (<= x 6.5e-134))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e-105) || !(x <= 6.5e-134)) {
		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 <= (-1.7d-105)) .or. (.not. (x <= 6.5d-134))) 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 <= -1.7e-105) || !(x <= 6.5e-134)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e-105) or not (x <= 6.5e-134):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e-105) || !(x <= 6.5e-134))
		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 <= -1.7e-105) || ~((x <= 6.5e-134)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e-105], N[Not[LessEqual[x, 6.5e-134]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999996e-105 or 6.4999999999999998e-134 < x

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. sub-neg 91.7%

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

   5. Simplified 91.7%

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

   if -1.69999999999999996e-105 < x < 6.4999999999999998e-134

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-105} \lor \neg \left(x \leq 6.5 \cdot 10^{-134}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+22} \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.26e+22) (not (<= x 1.0))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.26e+22) || !(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 <= (-1.26d+22)) .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 <= -1.26e+22) || !(x <= 1.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.26e+22) 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 <= -1.26e+22) || !(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 <= -1.26e+22) || ~((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, -1.26e+22], 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 < -1.26e22 or 1 < x

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   if -1.26e22 < x < 1

   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. remove-double-neg 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-z\right)\right)} + x \cdot y \]

      5. neg-sub0 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-+l- 100.0%

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

      12. 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 98.7%

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

      1. mul-1-neg 98.7%

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

      2. distribute-rgt-neg-out 98.7%

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

   7. Simplified 98.7%

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

      1. *-commutative 98.7%

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

      2. cancel-sign-sub 98.7%

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

      3. +-commutative 98.7%

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

   9. Applied egg-rr 98.7%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+22} \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-71} \lor \neg \left(x \leq 4 \cdot 10^{-134}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.2e-71) (not (<= x 4e-134))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e-71) || !(x <= 4e-134)) {
		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 <= (-7.2d-71)) .or. (.not. (x <= 4d-134))) 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 <= -7.2e-71) || !(x <= 4e-134)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.2e-71) or not (x <= 4e-134):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.2e-71) || !(x <= 4e-134))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.2e-71) || ~((x <= 4e-134)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.2e-71], N[Not[LessEqual[x, 4e-134]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -7.2e-71 or 4.00000000000000016e-134 < x

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 55.8%

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

   if -7.2e-71 < x < 4.00000000000000016e-134

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.1%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-71} \lor \neg \left(x \leq 4 \cdot 10^{-134}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
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 96.5%

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

   1. +-commutative 96.5%

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

   2. remove-double-neg 96.5%

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

   3. distribute-rgt-neg-out 96.5%

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

   4. neg-sub0 96.5%

      \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-z\right)\right)} + x \cdot y \]

   5. neg-sub0 96.5%

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

   6. *-commutative 96.5%

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

   7. distribute-lft-neg-in 96.5%

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

   8. remove-double-neg 96.5%

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

   9. distribute-rgt-out-- 96.5%

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

   10. *-lft-identity 96.5%

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

   11. associate-+l- 96.5%

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

   12. 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: 36.5% 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 96.5%

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

3. Taylor expanded in x around 0 28.7%

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

4. Final simplification 28.7%

   \[\leadsto z \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024072 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))