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

Percentage Accurate: 98.0% → 100.0%

Time: 1.3s

Alternatives: 6

Speedup: 1.4×

Specification

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+ (* 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * y) + (((1) - x) * z)
END code

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+ (* 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * y) + (((1) - x) * z)
END code

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (y - z)) + z
END code

Derivation

1. Initial program 98.0%

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

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(-x, z - y, z\right) \]
4. Step-by-step derivation

5. Applied rewrites 100.0%

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

Alternative 2: 98.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -14298.649587223466:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.0005660629841236394:\\ \;\;\;\;\mathsf{fma}\left(x, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (- y z))))
  (if (<= x -14298.649587223466)
    t_0
    (if (<= x 0.0005660629841236394) (fma x y z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -14298.649587223466) {
		tmp = t_0;
	} else if (x <= 0.0005660629841236394) {
		tmp = fma(x, y, 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 <= -14298.649587223466)
		tmp = t_0;
	elseif (x <= 0.0005660629841236394)
		tmp = fma(x, y, z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -14298.649587223466], t$95$0, If[LessEqual[x, 0.0005660629841236394], N[(x * y + z), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (x * (y - z)) IN
		LET tmp_1 = IF (x <= (566062984123639448448550570702764161978848278522491455078125e-63)) THEN ((x * y) + z) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-14298649587223466369323432445526123046875e-36)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -14298.649587223466 or 5.6606298412363945e-4 < x

   1. Initial program 98.0%

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

   3. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(-x, z - y, z\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 64.9%

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

   if -14298.649587223466 < x < 5.6606298412363945e-4

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto x \cdot y + z \]
   3. Step-by-step derivation

   4. Applied rewrites 75.9%

      \[\leadsto x \cdot y + z \]
   5. Step-by-step derivation

   6. Applied rewrites 76.0%

      \[\leadsto \mathsf{fma}\left(x, y, z\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -6.742668220036118 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z\right)\\ \mathbf{elif}\;y \leq 3.07342713026798 \cdot 10^{-110}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -6.742668220036118e+82)
  (fma x y z)
  (if (<= y 3.07342713026798e-110) (* z (- 1.0 x)) (fma x y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.742668220036118e+82) {
		tmp = fma(x, y, z);
	} else if (y <= 3.07342713026798e-110) {
		tmp = z * (1.0 - x);
	} else {
		tmp = fma(x, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.742668220036118e+82)
		tmp = fma(x, y, z);
	elseif (y <= 3.07342713026798e-110)
		tmp = Float64(z * Float64(1.0 - x));
	else
		tmp = fma(x, y, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.742668220036118e+82], N[(x * y + z), $MachinePrecision], If[LessEqual[y, 3.07342713026798e-110], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * y + z), $MachinePrecision]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp_1 = IF (y <= (3073427130267980153005627182190657993395790266346178807683912839381824716108030662403918387306509888781507111484986848945374899460134021774697330315701930108353347326619958155595922805617888049569222363859348691391916452399978367507736953548628895889670962497363109096337741021898182225413620471954345703125e-416)) THEN (z * ((1) - x)) ELSE ((x * y) + z) ENDIF IN
	LET tmp = IF (y <= (-67426682200361176120268859113156867640057346737471876670647569701482367024229253120)) THEN ((x * y) + z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -6.7426682200361176e82 or 3.0734271302679802e-110 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto x \cdot y + z \]
   3. Step-by-step derivation

   4. Applied rewrites 75.9%

      \[\leadsto x \cdot y + z \]
   5. Step-by-step derivation

   6. Applied rewrites 76.0%

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

   if -6.7426682200361176e82 < y < 3.0734271302679802e-110

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 62.3%

      \[\leadsto z \cdot \left(1 - x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 76.0% accurate, 2.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma x y z))

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * y) + z
END code

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in x around 0

   \[\leadsto x \cdot y + z \]
3. Step-by-step derivation

4. Applied rewrites 75.9%

   \[\leadsto x \cdot y + z \]
5. Step-by-step derivation

6. Applied rewrites 76.0%

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

Alternative 5: 61.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -2.8368855981903414 \cdot 10^{-51}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.957315309628584 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x -2.8368855981903414e-51)
  (* x y)
  (if (<= x 9.957315309628584e-34) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8368855981903414e-51) {
		tmp = x * y;
	} else if (x <= 9.957315309628584e-34) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.8368855981903414d-51)) then
        tmp = x * y
    else if (x <= 9.957315309628584d-34) 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 tmp;
	if (x <= -2.8368855981903414e-51) {
		tmp = x * y;
	} else if (x <= 9.957315309628584e-34) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.8368855981903414e-51:
		tmp = x * y
	elif x <= 9.957315309628584e-34:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8368855981903414e-51)
		tmp = Float64(x * y);
	elseif (x <= 9.957315309628584e-34)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.8368855981903414e-51)
		tmp = x * y;
	elseif (x <= 9.957315309628584e-34)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8368855981903414e-51], N[(x * y), $MachinePrecision], If[LessEqual[x, 9.957315309628584e-34], z, N[(x * y), $MachinePrecision]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp_1 = IF (x <= (995731530962858429324473884117268777133337992305983115666935440622549596510538661930608296535272216942757950164377689361572265625e-162)) THEN z ELSE (x * y) ENDIF IN
	LET tmp = IF (x <= (-28368855981903414102920337465896913142028897505741484614367286972627935745057502704794255345263793652131194254318143559929623156480593682005064692930318415164947509765625e-220)) THEN (x * y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -2.8368855981903414e-51 or 9.9573153096285843e-34 < x

   1. Initial program 98.0%

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

   3. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(-x, z - y, z\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 41.5%

      \[\leadsto x \cdot y \]

   if -2.8368855981903414e-51 < x < 9.9573153096285843e-34

   1. Initial program 98.0%

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

   3. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(-x, z - y, z\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 64.9%

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

   9. Taylor expanded in x around 0

      \[\leadsto z \]
   10. Step-by-step derivation

   11. Applied rewrites 36.9%

       \[\leadsto z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 36.9% accurate, 12.2× speedup

Math

\[z \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	z
END code

Derivation

1. Initial program 98.0%

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

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(-x, z - y, z\right) \]
4. Step-by-step derivation

5. Applied rewrites 100.0%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 64.9%

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

9. Taylor expanded in x around 0

   \[\leadsto z \]
10. Step-by-step derivation

11. Applied rewrites 36.9%

    \[\leadsto z \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))