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

Percentage Accurate: 97.7% → 100.0%

Time: 5.1s

Alternatives: 6

Speedup: 1.7×

• 20.4% 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, 1.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. fp-cancel-sign-sub-inv N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{y - \left(\mathsf{neg}\left(-1\right)\right) \cdot z}, x, z\right) \]

   5. metadata-eval N/A

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

   6. *-lft-identity N/A

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

   7. lower--.f64 100.0

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

5. Applied rewrites 100.0%

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

Alternative 2: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-29} \lor \neg \left(x \leq 7.8 \cdot 10^{-79}\right):\\ \;\;\;\;\left(y - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.8e-29) (not (<= x 7.8e-79))) (* (- y z) x) (* (- 1.0 x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.8e-29) || !(x <= 7.8e-79)) {
		tmp = (y - z) * x;
	} else {
		tmp = (1.0 - 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 <= (-9.8d-29)) .or. (.not. (x <= 7.8d-79))) then
        tmp = (y - z) * x
    else
        tmp = (1.0d0 - x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.8e-29) || !(x <= 7.8e-79)) {
		tmp = (y - z) * x;
	} else {
		tmp = (1.0 - x) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.8e-29) or not (x <= 7.8e-79):
		tmp = (y - z) * x
	else:
		tmp = (1.0 - x) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.8e-29) || !(x <= 7.8e-79))
		tmp = Float64(Float64(y - z) * x);
	else
		tmp = Float64(Float64(1.0 - x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.8e-29) || ~((x <= 7.8e-79)))
		tmp = (y - z) * x;
	else
		tmp = (1.0 - x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.8e-29], N[Not[LessEqual[x, 7.8e-79]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.7999999999999997e-29 or 7.80000000000000011e-79 < x

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 94.0

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

   5. Applied rewrites 94.0%

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

   if -9.7999999999999997e-29 < x < 7.80000000000000011e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-29} \lor \neg \left(x \leq 7.8 \cdot 10^{-79}\right):\\ \;\;\;\;\left(y - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-133} \lor \neg \left(z \leq 6.8 \cdot 10^{-127}\right):\\ \;\;\;\;\left(1 - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.9e-133) (not (<= z 6.8e-127))) (* (- 1.0 x) z) (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.9e-133) || !(z <= 6.8e-127)) {
		tmp = (1.0 - x) * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.9d-133)) .or. (.not. (z <= 6.8d-127))) then
        tmp = (1.0d0 - x) * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.9e-133) || !(z <= 6.8e-127)) {
		tmp = (1.0 - x) * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.9e-133) or not (z <= 6.8e-127):
		tmp = (1.0 - x) * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.9e-133) || !(z <= 6.8e-127))
		tmp = Float64(Float64(1.0 - x) * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.9e-133) || ~((z <= 6.8e-127)))
		tmp = (1.0 - x) * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.9e-133], N[Not[LessEqual[z, 6.8e-127]], $MachinePrecision]], N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.89999999999999964e-133 or 6.7999999999999997e-127 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -5.89999999999999964e-133 < z < 6.7999999999999997e-127

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 27.9

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

   5. Applied rewrites 27.9%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 73.8

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

   8. Applied rewrites 73.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-133} \lor \neg \left(z \leq 6.8 \cdot 10^{-127}\right):\\ \;\;\;\;\left(1 - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-29} \lor \neg \left(x \leq 7.8 \cdot 10^{-79}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.8e-29) (not (<= x 7.8e-79))) (* y x) (* 1.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.8e-29) || !(x <= 7.8e-79)) {
		tmp = y * x;
	} else {
		tmp = 1.0 * 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 <= (-9.8d-29)) .or. (.not. (x <= 7.8d-79))) then
        tmp = y * x
    else
        tmp = 1.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.8e-29) || !(x <= 7.8e-79)) {
		tmp = y * x;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.8e-29) or not (x <= 7.8e-79):
		tmp = y * x
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.8e-29) || !(x <= 7.8e-79))
		tmp = Float64(y * x);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.8e-29) || ~((x <= 7.8e-79)))
		tmp = y * x;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.8e-29], N[Not[LessEqual[x, 7.8e-79]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.7999999999999997e-29 or 7.80000000000000011e-79 < x

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.2

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

   5. Applied rewrites 52.2%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 54.3

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

   8. Applied rewrites 54.3%

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

   if -9.7999999999999997e-29 < x < 7.80000000000000011e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 83.8%

      \[\leadsto 1 \cdot z \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-29} \lor \neg \left(x \leq 7.8 \cdot 10^{-79}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-6}:\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-79}:\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.7e-6) (* (- z) x) (if (<= x 7.8e-79) (* 1.0 z) (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e-6) {
		tmp = -z * x;
	} else if (x <= 7.8e-79) {
		tmp = 1.0 * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.7d-6)) then
        tmp = -z * x
    else if (x <= 7.8d-79) then
        tmp = 1.0d0 * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e-6) {
		tmp = -z * x;
	} else if (x <= 7.8e-79) {
		tmp = 1.0 * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.7e-6:
		tmp = -z * x
	elif x <= 7.8e-79:
		tmp = 1.0 * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.7e-6)
		tmp = Float64(Float64(-z) * x);
	elseif (x <= 7.8e-79)
		tmp = Float64(1.0 * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.7e-6)
		tmp = -z * x;
	elseif (x <= 7.8e-79)
		tmp = 1.0 * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.7e-6], N[((-z) * x), $MachinePrecision], If[LessEqual[x, 7.8e-79], N[(1.0 * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.70000000000000003e-6

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 58.2%

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

   if -1.70000000000000003e-6 < x < 7.80000000000000011e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.2

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 81.6%

      \[\leadsto 1 \cdot z \]

   if 7.80000000000000011e-79 < x

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 47.7

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

   5. Applied rewrites 47.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.6

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

   8. Applied rewrites 57.6%

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

Alternative 6: 41.5% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 66.2

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

5. Applied rewrites 66.2%

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

6. Taylor expanded in y around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 38.0

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

8. Applied rewrites 38.0%

   \[\leadsto \color{blue}{y \cdot x} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))