Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 4.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(t);
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * log(y)) - y) - z) + log(t)
end function

Java

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

Python

def code(x, y, z, t):
	return (((x * math.log(y)) - y) - z) + math.log(t)

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(t);
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * log(y)) - y) - z) + log(t)
end function

Java

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

Python

def code(x, y, z, t):
	return (((x * math.log(y)) - y) - z) + math.log(t)

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 99.9%

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

3. Applied rewrites 99.9%

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

Alternative 2: 89.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq 1.9400327209735698 \cdot 10^{+31}:\\ \;\;\;\;\left(x \cdot \log y - z\right) + \log t\\ \mathbf{elif}\;y \leq 1.721387848480009 \cdot 10^{+248}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= y 1.9400327209735698e+31)
  (+ (- (* x (log y)) z) (log t))
  (if (<= y 1.721387848480009e+248)
    (- (log t) (+ y z))
    (fma x (log y) (- (log t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.9400327209735698e+31) {
		tmp = ((x * log(y)) - z) + log(t);
	} else if (y <= 1.721387848480009e+248) {
		tmp = log(t) - (y + z);
	} else {
		tmp = fma(x, log(y), (log(t) - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.9400327209735698e+31)
		tmp = Float64(Float64(Float64(x * log(y)) - z) + log(t));
	elseif (y <= 1.721387848480009e+248)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = fma(x, log(y), Float64(log(t) - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.9400327209735698e+31], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.721387848480009e+248], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (y <= (172138784848000910678784409119011237206298314965381906828690193615571084267346565904389242826559038341044754864056304444295696053129816752963291972220795393619411543965205101828526562124213876522311000020857282480043023351113822424735545765482463232)) THEN ((ln(t)) - (y + z)) ELSE ((x * (ln(y))) + ((ln(t)) - y)) ENDIF IN
	LET tmp = IF (y <= (19400327209735697715520610500608)) THEN (((x * (ln(y))) - z) + (ln(t))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y < 1.9400327209735698e31

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 71.2%

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

   if 1.9400327209735698e31 < y < 1.7213878484800091e248

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   if 1.7213878484800091e248 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 71.3%

      \[\leadsto \left(\log t + x \cdot \log y\right) - y \]
   5. Step-by-step derivation

   6. Applied rewrites 71.3%

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

Alternative 3: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \log t - \left(y + z\right)\\ \mathbf{if}\;z \leq -3.3950948268142874 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.0377994761209829 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (log t) (+ y z))))
  (if (<= z -3.3950948268142874e+74)
    t_1
    (if (<= z 2.0377994761209829e-13)
      (fma x (log y) (- (log t) y))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - (y + z);
	double tmp;
	if (z <= -3.3950948268142874e+74) {
		tmp = t_1;
	} else if (z <= 2.0377994761209829e-13) {
		tmp = fma(x, log(y), (log(t) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - Float64(y + z))
	tmp = 0.0
	if (z <= -3.3950948268142874e+74)
		tmp = t_1;
	elseif (z <= 2.0377994761209829e-13)
		tmp = fma(x, log(y), Float64(log(t) - y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3950948268142874e+74], t$95$1, If[LessEqual[z, 2.0377994761209829e-13], N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((ln(t)) - (y + z)) IN
		LET tmp_1 = IF (z <= (2037799476120982867987924073719547209712459057140421236908878199756145477294921875e-94)) THEN ((x * (ln(y))) + ((ln(t)) - y)) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-339509482681428740206532583944965862344874843797051379248844413982885281792)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -3.3950948268142874e74 or 2.0377994761209829e-13 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   if -3.3950948268142874e74 < z < 2.0377994761209829e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 71.3%

      \[\leadsto \left(\log t + x \cdot \log y\right) - y \]
   5. Step-by-step derivation

   6. Applied rewrites 71.3%

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

Alternative 4: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3553147626182586 \cdot 10^{+106}:\\ \;\;\;\;\frac{1}{\frac{\frac{0.5}{x}}{\log \left(\sqrt{y}\right)}}\\ \mathbf{elif}\;x \leq 1.0136549878959845 \cdot 10^{+189}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= x -3.3553147626182586e+106)
  (/ 1.0 (/ (/ 0.5 x) (log (sqrt y))))
  (if (<= x 1.0136549878959845e+189)
    (- (log t) (+ y z))
    (* (log y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = 1.0 / ((0.5 / x) / log(sqrt(y)));
	} else if (x <= 1.0136549878959845e+189) {
		tmp = log(t) - (y + z);
	} else {
		tmp = log(y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.3553147626182586d+106)) then
        tmp = 1.0d0 / ((0.5d0 / x) / log(sqrt(y)))
    else if (x <= 1.0136549878959845d+189) then
        tmp = log(t) - (y + z)
    else
        tmp = log(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = 1.0 / ((0.5 / x) / Math.log(Math.sqrt(y)));
	} else if (x <= 1.0136549878959845e+189) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = Math.log(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.3553147626182586e+106:
		tmp = 1.0 / ((0.5 / x) / math.log(math.sqrt(y)))
	elif x <= 1.0136549878959845e+189:
		tmp = math.log(t) - (y + z)
	else:
		tmp = math.log(y) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.3553147626182586e+106)
		tmp = Float64(1.0 / Float64(Float64(0.5 / x) / log(sqrt(y))));
	elseif (x <= 1.0136549878959845e+189)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(log(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.3553147626182586e+106)
		tmp = 1.0 / ((0.5 / x) / log(sqrt(y)));
	elseif (x <= 1.0136549878959845e+189)
		tmp = log(t) - (y + z);
	else
		tmp = log(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.3553147626182586e+106], N[(1.0 / N[(N[(0.5 / x), $MachinePrecision] / N[Log[N[Sqrt[y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0136549878959845e+189], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (x <= (1013654987895984510930819536748060057011936254392728101032616601915457362985283915651363764121002113082029871351976696181650498247217107769133623148287600376891257947298171457715136358252544)) THEN ((ln(t)) - (y + z)) ELSE ((ln(y)) * x) ENDIF IN
	LET tmp = IF (x <= (-33553147626182586240847438317368570267580901609090972179257517970379359670654625604138917832625974763585536)) THEN ((1) / (((5e-1) / x) / (ln((sqrt(y)))))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -3.3553147626182586e106

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]

   8. Applied rewrites 31.0%

      \[\leadsto \frac{1}{\frac{\frac{0.5}{x}}{\log \left(\sqrt{y}\right)}} \]

   if -3.3553147626182586e106 < x < 1.0136549878959845e189

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   if 1.0136549878959845e189 < x

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]

   8. Applied rewrites 31.0%

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

Alternative 5: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3553147626182586 \cdot 10^{+106}:\\ \;\;\;\;\log \left(\sqrt{y}\right) \cdot \frac{-2}{\frac{-1}{x}}\\ \mathbf{elif}\;x \leq 1.0136549878959845 \cdot 10^{+189}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= x -3.3553147626182586e+106)
  (* (log (sqrt y)) (/ -2.0 (/ -1.0 x)))
  (if (<= x 1.0136549878959845e+189)
    (- (log t) (+ y z))
    (* (log y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = log(sqrt(y)) * (-2.0 / (-1.0 / x));
	} else if (x <= 1.0136549878959845e+189) {
		tmp = log(t) - (y + z);
	} else {
		tmp = log(y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.3553147626182586d+106)) then
        tmp = log(sqrt(y)) * ((-2.0d0) / ((-1.0d0) / x))
    else if (x <= 1.0136549878959845d+189) then
        tmp = log(t) - (y + z)
    else
        tmp = log(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = Math.log(Math.sqrt(y)) * (-2.0 / (-1.0 / x));
	} else if (x <= 1.0136549878959845e+189) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = Math.log(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.3553147626182586e+106:
		tmp = math.log(math.sqrt(y)) * (-2.0 / (-1.0 / x))
	elif x <= 1.0136549878959845e+189:
		tmp = math.log(t) - (y + z)
	else:
		tmp = math.log(y) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.3553147626182586e+106)
		tmp = Float64(log(sqrt(y)) * Float64(-2.0 / Float64(-1.0 / x)));
	elseif (x <= 1.0136549878959845e+189)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(log(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.3553147626182586e+106)
		tmp = log(sqrt(y)) * (-2.0 / (-1.0 / x));
	elseif (x <= 1.0136549878959845e+189)
		tmp = log(t) - (y + z);
	else
		tmp = log(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.3553147626182586e+106], N[(N[Log[N[Sqrt[y], $MachinePrecision]], $MachinePrecision] * N[(-2.0 / N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0136549878959845e+189], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (x <= (1013654987895984510930819536748060057011936254392728101032616601915457362985283915651363764121002113082029871351976696181650498247217107769133623148287600376891257947298171457715136358252544)) THEN ((ln(t)) - (y + z)) ELSE ((ln(y)) * x) ENDIF IN
	LET tmp = IF (x <= (-33553147626182586240847438317368570267580901609090972179257517970379359670654625604138917832625974763585536)) THEN ((ln((sqrt(y)))) * ((-2) / ((-1) / x))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -3.3553147626182586e106

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 31.0%

      \[\leadsto \log \left(\sqrt{y}\right) \cdot \left(x + x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 31.0%

       \[\leadsto \log \left(\sqrt{y}\right) \cdot \frac{-2}{\frac{-1}{x}} \]

   if -3.3553147626182586e106 < x < 1.0136549878959845e189

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   if 1.0136549878959845e189 < x

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]

   8. Applied rewrites 31.0%

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

Alternative 6: 82.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3553147626182586 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{\frac{1}{\log y}}\\ \mathbf{elif}\;x \leq 1.0136549878959845 \cdot 10^{+189}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= x -3.3553147626182586e+106)
  (/ x (/ 1.0 (log y)))
  (if (<= x 1.0136549878959845e+189)
    (- (log t) (+ y z))
    (* (log y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = x / (1.0 / log(y));
	} else if (x <= 1.0136549878959845e+189) {
		tmp = log(t) - (y + z);
	} else {
		tmp = log(y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.3553147626182586d+106)) then
        tmp = x / (1.0d0 / log(y))
    else if (x <= 1.0136549878959845d+189) then
        tmp = log(t) - (y + z)
    else
        tmp = log(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = x / (1.0 / Math.log(y));
	} else if (x <= 1.0136549878959845e+189) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = Math.log(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.3553147626182586e+106:
		tmp = x / (1.0 / math.log(y))
	elif x <= 1.0136549878959845e+189:
		tmp = math.log(t) - (y + z)
	else:
		tmp = math.log(y) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.3553147626182586e+106)
		tmp = Float64(x / Float64(1.0 / log(y)));
	elseif (x <= 1.0136549878959845e+189)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(log(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.3553147626182586e+106)
		tmp = x / (1.0 / log(y));
	elseif (x <= 1.0136549878959845e+189)
		tmp = log(t) - (y + z);
	else
		tmp = log(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.3553147626182586e+106], N[(x / N[(1.0 / N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0136549878959845e+189], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (x <= (1013654987895984510930819536748060057011936254392728101032616601915457362985283915651363764121002113082029871351976696181650498247217107769133623148287600376891257947298171457715136358252544)) THEN ((ln(t)) - (y + z)) ELSE ((ln(y)) * x) ENDIF IN
	LET tmp = IF (x <= (-33553147626182586240847438317368570267580901609090972179257517970379359670654625604138917832625974763585536)) THEN (x / ((1) / (ln(y)))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -3.3553147626182586e106

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 31.0%

      \[\leadsto \frac{x}{\frac{1}{\log y}} \]

   if -3.3553147626182586e106 < x < 1.0136549878959845e189

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   if 1.0136549878959845e189 < x

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]

   8. Applied rewrites 31.0%

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

Alternative 7: 82.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3553147626182586 \cdot 10^{+106}:\\ \;\;\;\;\log \left(\sqrt{y}\right) \cdot \left(x + x\right)\\ \mathbf{elif}\;x \leq 1.0136549878959845 \cdot 10^{+189}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= x -3.3553147626182586e+106)
  (* (log (sqrt y)) (+ x x))
  (if (<= x 1.0136549878959845e+189)
    (- (log t) (+ y z))
    (* (log y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = log(sqrt(y)) * (x + x);
	} else if (x <= 1.0136549878959845e+189) {
		tmp = log(t) - (y + z);
	} else {
		tmp = log(y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.3553147626182586d+106)) then
        tmp = log(sqrt(y)) * (x + x)
    else if (x <= 1.0136549878959845d+189) then
        tmp = log(t) - (y + z)
    else
        tmp = log(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = Math.log(Math.sqrt(y)) * (x + x);
	} else if (x <= 1.0136549878959845e+189) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = Math.log(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.3553147626182586e+106:
		tmp = math.log(math.sqrt(y)) * (x + x)
	elif x <= 1.0136549878959845e+189:
		tmp = math.log(t) - (y + z)
	else:
		tmp = math.log(y) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.3553147626182586e+106)
		tmp = Float64(log(sqrt(y)) * Float64(x + x));
	elseif (x <= 1.0136549878959845e+189)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(log(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.3553147626182586e+106)
		tmp = log(sqrt(y)) * (x + x);
	elseif (x <= 1.0136549878959845e+189)
		tmp = log(t) - (y + z);
	else
		tmp = log(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.3553147626182586e+106], N[(N[Log[N[Sqrt[y], $MachinePrecision]], $MachinePrecision] * N[(x + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0136549878959845e+189], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (x <= (1013654987895984510930819536748060057011936254392728101032616601915457362985283915651363764121002113082029871351976696181650498247217107769133623148287600376891257947298171457715136358252544)) THEN ((ln(t)) - (y + z)) ELSE ((ln(y)) * x) ENDIF IN
	LET tmp = IF (x <= (-33553147626182586240847438317368570267580901609090972179257517970379359670654625604138917832625974763585536)) THEN ((ln((sqrt(y)))) * (x + x)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -3.3553147626182586e106

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 31.0%

      \[\leadsto \log \left(\sqrt{y}\right) \cdot \left(x + x\right) \]

   if -3.3553147626182586e106 < x < 1.0136549878959845e189

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   if 1.0136549878959845e189 < x

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]

   8. Applied rewrites 31.0%

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

Alternative 8: 82.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -3.3553147626182586 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.0136549878959845 \cdot 10^{+189}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (log y) x)))
  (if (<= x -3.3553147626182586e+106)
    t_1
    (if (<= x 1.0136549878959845e+189) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = t_1;
	} else if (x <= 1.0136549878959845e+189) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(y) * x
    if (x <= (-3.3553147626182586d+106)) then
        tmp = t_1
    else if (x <= 1.0136549878959845d+189) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * x;
	double tmp;
	if (x <= -3.3553147626182586e+106) {
		tmp = t_1;
	} else if (x <= 1.0136549878959845e+189) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -3.3553147626182586e+106:
		tmp = t_1
	elif x <= 1.0136549878959845e+189:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -3.3553147626182586e+106)
		tmp = t_1;
	elseif (x <= 1.0136549878959845e+189)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	tmp = 0.0;
	if (x <= -3.3553147626182586e+106)
		tmp = t_1;
	elseif (x <= 1.0136549878959845e+189)
		tmp = log(t) - (y + z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -3.3553147626182586e+106], t$95$1, If[LessEqual[x, 1.0136549878959845e+189], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((ln(y)) * x) IN
		LET tmp_1 = IF (x <= (1013654987895984510930819536748060057011936254392728101032616601915457362985283915651363764121002113082029871351976696181650498247217107769133623148287600376891257947298171457715136358252544)) THEN ((ln(t)) - (y + z)) ELSE t_1 ENDIF IN
		LET tmp = IF (x <= (-33553147626182586240847438317368570267580901609090972179257517970379359670654625604138917832625974763585536)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -3.3553147626182586e106 or 1.0136549878959845e189 < x

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]

   8. Applied rewrites 31.0%

      \[\leadsto \log y \cdot x \]

   if -3.3553147626182586e106 < x < 1.0136549878959845e189

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot -1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (* x (log y)) y)))
  (if (<= t_1 -2e+29)
    (* y -1.0)
    (if (<= t_1 5e+108) (- (log t) z) (* (log y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if (t_1 <= -2e+29) {
		tmp = y * -1.0;
	} else if (t_1 <= 5e+108) {
		tmp = log(t) - z;
	} else {
		tmp = log(y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - y
    if (t_1 <= (-2d+29)) then
        tmp = y * (-1.0d0)
    else if (t_1 <= 5d+108) then
        tmp = log(t) - z
    else
        tmp = log(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - y;
	double tmp;
	if (t_1 <= -2e+29) {
		tmp = y * -1.0;
	} else if (t_1 <= 5e+108) {
		tmp = Math.log(t) - z;
	} else {
		tmp = Math.log(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if t_1 <= -2e+29:
		tmp = y * -1.0
	elif t_1 <= 5e+108:
		tmp = math.log(t) - z
	else:
		tmp = math.log(y) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (t_1 <= -2e+29)
		tmp = Float64(y * -1.0);
	elseif (t_1 <= 5e+108)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(log(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if (t_1 <= -2e+29)
		tmp = y * -1.0;
	elseif (t_1 <= 5e+108)
		tmp = log(t) - z;
	else
		tmp = log(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+29], N[(y * -1.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+108], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x * (ln(y))) - y) IN
		LET tmp_1 = IF (t_1 <= (4999999999999999909254353594199903932358825482164085623979199184949536277190026649102901712196568838131679232)) THEN ((ln(t)) - z) ELSE ((ln(y)) * x) ENDIF IN
		LET tmp = IF (t_1 <= (-199999999999999982866301714432)) THEN (y * (-1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.9999999999999998e29

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   5. Taylor expanded in y around inf

      \[\leadsto y \cdot \left(\frac{\log t}{y} - \left(1 + \frac{z}{y}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 60.3%

      \[\leadsto y \cdot \left(\frac{\log t}{y} - \left(1 + \frac{z}{y}\right)\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto y \cdot -1 \]
   9. Step-by-step derivation

   10. Applied rewrites 29.7%

       \[\leadsto y \cdot -1 \]

   if -1.9999999999999998e29 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.9999999999999999e108

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \log t - z \]
   6. Step-by-step derivation

   7. Applied rewrites 41.8%

      \[\leadsto \log t - z \]

   if 4.9999999999999999e108 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.9%

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

   3. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(x \cdot 2, \log \left(\sqrt{y}\right), \left(\log t - z\right) - y\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 31.0%

      \[\leadsto 2 \cdot \left(x \cdot \log \left(\sqrt{y}\right)\right) \]

   8. Applied rewrites 31.0%

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

Alternative 10: 60.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq 6.908300660868751 \cdot 10^{+47}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot -1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= y 6.908300660868751e+47) (- (log t) z) (* y -1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.908300660868751e+47) {
		tmp = log(t) - z;
	} else {
		tmp = y * -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 6.908300660868751d+47) then
        tmp = log(t) - z
    else
        tmp = y * (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.908300660868751e+47) {
		tmp = Math.log(t) - z;
	} else {
		tmp = y * -1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 6.908300660868751e+47:
		tmp = math.log(t) - z
	else:
		tmp = y * -1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6.908300660868751e+47)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(y * -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 6.908300660868751e+47)
		tmp = log(t) - z;
	else
		tmp = y * -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6.908300660868751e+47], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(y * -1.0), $MachinePrecision]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp = IF (y <= (690830066086875074461239755593732369843675463680)) THEN ((ln(t)) - z) ELSE (y * (-1)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < 6.9083006608687507e47

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \log t - z \]
   6. Step-by-step derivation

   7. Applied rewrites 41.8%

      \[\leadsto \log t - z \]

   if 6.9083006608687507e47 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 69.8%

      \[\leadsto \log t - \left(y + z\right) \]

   5. Taylor expanded in y around inf

      \[\leadsto y \cdot \left(\frac{\log t}{y} - \left(1 + \frac{z}{y}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 60.3%

      \[\leadsto y \cdot \left(\frac{\log t}{y} - \left(1 + \frac{z}{y}\right)\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto y \cdot -1 \]
   9. Step-by-step derivation

   10. Applied rewrites 29.7%

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

Alternative 11: 41.8% accurate, 2.5× speedup

Math

\[\log t - y \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (- (log t) y))

C

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

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = log(t) - y
end function

Java

public static double code(double x, double y, double z, double t) {
	return Math.log(t) - y;
}

Python

def code(x, y, z, t):
	return math.log(t) - y

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = log(t) - y;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]

ReFlow

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around 0

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

4. Applied rewrites 71.3%

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

5. Taylor expanded in x around 0

   \[\leadsto \log t - y \]
6. Step-by-step derivation

7. Applied rewrites 41.8%

   \[\leadsto \log t - y \]
8. Add Preprocessing

Alternative 12: 29.7% accurate, 6.0× speedup

Math

\[y \cdot -1 \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return y * -1.0;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y * (-1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(y * -1.0), $MachinePrecision]

ReFlow

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 69.8%

   \[\leadsto \log t - \left(y + z\right) \]

5. Taylor expanded in y around inf

   \[\leadsto y \cdot \left(\frac{\log t}{y} - \left(1 + \frac{z}{y}\right)\right) \]
6. Step-by-step derivation

7. Applied rewrites 60.3%

   \[\leadsto y \cdot \left(\frac{\log t}{y} - \left(1 + \frac{z}{y}\right)\right) \]

8. Taylor expanded in y around inf

   \[\leadsto y \cdot -1 \]
9. Step-by-step derivation

10. Applied rewrites 29.7%

    \[\leadsto y \cdot -1 \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))