Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3

Percentage Accurate: 97.9% → 100.0%

Time: 1.6s

Alternatives: 7

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $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) + ((x - (1)) * z)
END code

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $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) + ((x - (1)) * z)
END code

Alternative 1: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $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 97.9%

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

3. Applied rewrites 100.0%

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

Alternative 2: 98.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -14298.649587223466:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.0005660629841236394:\\ \;\;\;\;\mathsf{fma}\left(z, -1, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

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 z -1.0 (* y x)) 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(z, -1.0, (y * x));
	} 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(z, -1.0, Float64(y * x));
	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[(z * -1.0 + N[(y * x), $MachinePrecision]), $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 ((z * (-1)) + (y * x)) 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 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.9%

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

   if -14298.649587223466 < x < 5.6606298412363945e-4

   1. Initial program 97.9%

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

   3. Applied rewrites 98.9%

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

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(z, -1, y \cdot x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 75.8%

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

Alternative 3: 84.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -2.8368855981903414 \cdot 10^{-51}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 464742860.8895076:\\ \;\;\;\;z \cdot \left(x - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (+ y z))))
  (if (<= x -2.8368855981903414e-51)
    t_0
    (if (<= x 464742860.8895076) (* z (- x 1.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -2.8368855981903414e-51) {
		tmp = t_0;
	} else if (x <= 464742860.8895076) {
		tmp = z * (x - 1.0);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * (y + z)
    if (x <= (-2.8368855981903414d-51)) then
        tmp = t_0
    else if (x <= 464742860.8895076d0) then
        tmp = z * (x - 1.0d0)
    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 <= -2.8368855981903414e-51) {
		tmp = t_0;
	} else if (x <= 464742860.8895076) {
		tmp = z * (x - 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -2.8368855981903414e-51:
		tmp = t_0
	elif x <= 464742860.8895076:
		tmp = z * (x - 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -2.8368855981903414e-51)
		tmp = t_0;
	elseif (x <= 464742860.8895076)
		tmp = Float64(z * Float64(x - 1.0));
	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 <= -2.8368855981903414e-51)
		tmp = t_0;
	elseif (x <= 464742860.8895076)
		tmp = z * (x - 1.0);
	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, -2.8368855981903414e-51], t$95$0, If[LessEqual[x, 464742860.8895076], N[(z * N[(x - 1.0), $MachinePrecision]), $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 <= (464742860889507591724395751953125e-24)) THEN (z * (x - (1))) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-28368855981903414102920337465896913142028897505741484614367286972627935745057502704794255345263793652131194254318143559929623156480593682005064692930318415164947509765625e-220)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -2.8368855981903414e-51 or 464742860.88950759 < x

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.9%

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

   if -2.8368855981903414e-51 < x < 464742860.88950759

   1. Initial program 97.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 62.4%

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

Alternative 4: 84.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -2.8368855981903414 \cdot 10^{-51}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.957315309628584 \cdot 10^{-34}:\\ \;\;\;\;z \cdot -1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (+ y z))))
  (if (<= x -2.8368855981903414e-51)
    t_0
    (if (<= x 9.957315309628584e-34) (* z -1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -2.8368855981903414e-51) {
		tmp = t_0;
	} else if (x <= 9.957315309628584e-34) {
		tmp = z * -1.0;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * (y + z)
    if (x <= (-2.8368855981903414d-51)) then
        tmp = t_0
    else if (x <= 9.957315309628584d-34) then
        tmp = z * (-1.0d0)
    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 <= -2.8368855981903414e-51) {
		tmp = t_0;
	} else if (x <= 9.957315309628584e-34) {
		tmp = z * -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -2.8368855981903414e-51:
		tmp = t_0
	elif x <= 9.957315309628584e-34:
		tmp = z * -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -2.8368855981903414e-51)
		tmp = t_0;
	elseif (x <= 9.957315309628584e-34)
		tmp = Float64(z * -1.0);
	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 <= -2.8368855981903414e-51)
		tmp = t_0;
	elseif (x <= 9.957315309628584e-34)
		tmp = z * -1.0;
	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, -2.8368855981903414e-51], t$95$0, If[LessEqual[x, 9.957315309628584e-34], N[(z * -1.0), $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 <= (995731530962858429324473884117268777133337992305983115666935440622549596510538661930608296535272216942757950164377689361572265625e-162)) THEN (z * (-1)) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-28368855981903414102920337465896913142028897505741484614367286972627935745057502704794255345263793652131194254318143559929623156480593682005064692930318415164947509765625e-220)) THEN t_0 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 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.9%

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

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

   1. Initial program 97.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 62.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 36.9%

      \[\leadsto z \cdot -1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.5035300976793776 \cdot 10^{+239}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.8368855981903414 \cdot 10^{-51}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.957315309628584 \cdot 10^{-34}:\\ \;\;\;\;z \cdot -1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x -1.5035300976793776e+239)
  (* x z)
  (if (<= x -2.8368855981903414e-51)
    (* x y)
    (if (<= x 9.957315309628584e-34) (* z -1.0) (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5035300976793776e+239) {
		tmp = x * z;
	} else if (x <= -2.8368855981903414e-51) {
		tmp = x * y;
	} else if (x <= 9.957315309628584e-34) {
		tmp = z * -1.0;
	} 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 <= (-1.5035300976793776d+239)) then
        tmp = x * z
    else if (x <= (-2.8368855981903414d-51)) then
        tmp = x * y
    else if (x <= 9.957315309628584d-34) then
        tmp = z * (-1.0d0)
    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 <= -1.5035300976793776e+239) {
		tmp = x * z;
	} else if (x <= -2.8368855981903414e-51) {
		tmp = x * y;
	} else if (x <= 9.957315309628584e-34) {
		tmp = z * -1.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5035300976793776e+239:
		tmp = x * z
	elif x <= -2.8368855981903414e-51:
		tmp = x * y
	elif x <= 9.957315309628584e-34:
		tmp = z * -1.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5035300976793776e+239)
		tmp = Float64(x * z);
	elseif (x <= -2.8368855981903414e-51)
		tmp = Float64(x * y);
	elseif (x <= 9.957315309628584e-34)
		tmp = Float64(z * -1.0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5035300976793776e+239)
		tmp = x * z;
	elseif (x <= -2.8368855981903414e-51)
		tmp = x * y;
	elseif (x <= 9.957315309628584e-34)
		tmp = z * -1.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5035300976793776e+239], N[(x * z), $MachinePrecision], If[LessEqual[x, -2.8368855981903414e-51], N[(x * y), $MachinePrecision], If[LessEqual[x, 9.957315309628584e-34], N[(z * -1.0), $MachinePrecision], 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_2 = IF (x <= (995731530962858429324473884117268777133337992305983115666935440622549596510538661930608296535272216942757950164377689361572265625e-162)) THEN (z * (-1)) ELSE (x * y) ENDIF IN
	LET tmp_1 = IF (x <= (-28368855981903414102920337465896913142028897505741484614367286972627935745057502704794255345263793652131194254318143559929623156480593682005064692930318415164947509765625e-220)) THEN (x * y) ELSE tmp_2 ENDIF IN
	LET tmp = IF (x <= (-150353009767937760884154711860257714387891541855886104115194725250238209157055610191370157512538108171292045452085945712819285768336718498601584906828263806694983474966458656621376604065417300474854092836554645825468703895493522125781729280)) THEN (x * z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -1.5035300976793776e239

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto x \cdot z \]
   6. Step-by-step derivation

   7. Applied rewrites 27.9%

      \[\leadsto x \cdot z \]

   if -1.5035300976793776e239 < x < -2.8368855981903414e-51 or 9.9573153096285843e-34 < x

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto x \cdot z \]
   6. Step-by-step derivation

   7. Applied rewrites 27.9%

      \[\leadsto x \cdot z \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot z \]
   9. Step-by-step derivation

   10. Applied rewrites 2.6%

       \[\leadsto 0 \cdot z \]

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 41.3%

       \[\leadsto x \cdot y \]

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

   1. Initial program 97.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 62.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 36.9%

      \[\leadsto z \cdot -1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -8.429824474477093 \cdot 10^{-68}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.07342713026798 \cdot 10^{-110}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -8.429824474477093e-68)
  (* x y)
  (if (<= y 3.07342713026798e-110) (* x z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.429824474477093e-68) {
		tmp = x * y;
	} else if (y <= 3.07342713026798e-110) {
		tmp = x * 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 (y <= (-8.429824474477093d-68)) then
        tmp = x * y
    else if (y <= 3.07342713026798d-110) then
        tmp = x * 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 (y <= -8.429824474477093e-68) {
		tmp = x * y;
	} else if (y <= 3.07342713026798e-110) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.429824474477093e-68:
		tmp = x * y
	elif y <= 3.07342713026798e-110:
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.429824474477093e-68)
		tmp = Float64(x * y);
	elseif (y <= 3.07342713026798e-110)
		tmp = Float64(x * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.429824474477093e-68)
		tmp = x * y;
	elseif (y <= 3.07342713026798e-110)
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.429824474477093e-68], N[(x * y), $MachinePrecision], If[LessEqual[y, 3.07342713026798e-110], N[(x * z), $MachinePrecision], 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 (y <= (3073427130267980153005627182190657993395790266346178807683912839381824716108030662403918387306509888781507111484986848945374899460134021774697330315701930108353347326619958155595922805617888049569222363859348691391916452399978367507736953548628895889670962497363109096337741021898182225413620471954345703125e-416)) THEN (x * z) ELSE (x * y) ENDIF IN
	LET tmp = IF (y <= (-84298244744770933169202899367670995163693774118542341362793512875956795725840722784332340093490592411985259885516636098652107019404335476668413384352593432461903176326767361814518153551034629344940185546875e-273)) THEN (x * y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -8.4298244744770933e-68 or 3.0734271302679802e-110 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto x \cdot z \]
   6. Step-by-step derivation

   7. Applied rewrites 27.9%

      \[\leadsto x \cdot z \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot z \]
   9. Step-by-step derivation

   10. Applied rewrites 2.6%

       \[\leadsto 0 \cdot z \]

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 41.3%

       \[\leadsto x \cdot y \]

   if -8.4298244744770933e-68 < y < 3.0734271302679802e-110

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto x \cdot z \]
   6. Step-by-step derivation

   7. Applied rewrites 27.9%

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

Alternative 7: 41.3% accurate, 3.0× speedup

Math

\[x \cdot y \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, 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 =
	x * y
END code

Derivation

1. Initial program 97.9%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 64.9%

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

5. Taylor expanded in y around 0

   \[\leadsto x \cdot z \]
6. Step-by-step derivation

7. Applied rewrites 27.9%

   \[\leadsto x \cdot z \]

8. Taylor expanded in undef-var around zero

   \[\leadsto 0 \cdot z \]
9. Step-by-step derivation

10. Applied rewrites 2.6%

    \[\leadsto 0 \cdot z \]

11. Taylor expanded in y around inf

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

13. Applied rewrites 41.3%

    \[\leadsto x \cdot y \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))