Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B

Percentage Accurate: 96.5% → 99.2%

Time: 4.1s

Alternatives: 15

Speedup: 1.1×

• 59.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

ReFlow

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

Initial Program: 96.5% accurate, 1.0× speedup

Math

\[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

ReFlow

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

Alternative 1: 99.2% accurate, 0.9× speedup

Math

\[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log1p (- z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log1p(-z) - b))));
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log1p(-z) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log1p(-z) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log1p(Float64(-z)) - b)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

ReFlow

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

Derivation

1. Initial program 96.5%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Step-by-step derivation

3. Applied rewrites 99.2%

   \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)} \]
4. Add Preprocessing

Alternative 2: 99.2% accurate, 1.0× speedup

Math

\[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(z \cdot \left(-0.5 \cdot z - 1\right) - b\right)} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (*
 x
 (exp (+ (* y (- (log z) t)) (* a (- (* z (- (* -0.5 z) 1.0)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * ((z * ((-0.5 * z) - 1.0)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * ((z * (((-0.5d0) * z) - 1.0d0)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * ((z * ((-0.5 * z) - 1.0)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * ((z * ((-0.5 * z) - 1.0)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(Float64(z * Float64(Float64(-0.5 * z) - 1.0)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * ((z * ((-0.5 * z) - 1.0)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * N[(N[(-0.5 * z), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	x * (exp(((y * ((ln(z)) - t)) + (a * ((z * (((-5e-1) * z) - (1))) - b)))))
END code

Derivation

1. Initial program 96.5%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

2. Taylor expanded in z around 0

   \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(z \cdot \left(\frac{-1}{2} \cdot z - 1\right) - b\right)} \]
3. Step-by-step derivation

4. Applied rewrites 99.2%

   \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(z \cdot \left(-0.5 \cdot z - 1\right) - b\right)} \]
5. Add Preprocessing

Alternative 3: 99.1% accurate, 1.1× speedup

Math

\[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(-1 \cdot z - b\right)} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (* x (exp (+ (* y (- (log z) t)) (* a (- (* -1.0 z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * ((-1.0 * z) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (((-1.0d0) * z) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * ((-1.0 * z) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * ((-1.0 * z) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(Float64(-1.0 * z) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * ((-1.0 * z) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(-1.0 * z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

ReFlow

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

Derivation

1. Initial program 96.5%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

2. Taylor expanded in z around 0

   \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(-1 \cdot z - b\right)} \]
3. Step-by-step derivation

4. Applied rewrites 99.1%

   \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(-1 \cdot z - b\right)} \]
5. Add Preprocessing

Alternative 4: 87.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{if}\;y \leq -1.3091999464162745 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 226065464659316450:\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* x (exp (* y (- (log z) t))))))
  (if (<= y -1.3091999464162745e-14)
    t_1
    (if (<= y 226065464659316450.0)
      (* x (exp (* a (- (log1p (- z)) b))))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((y * (log(z) - t)));
	double tmp;
	if (y <= -1.3091999464162745e-14) {
		tmp = t_1;
	} else if (y <= 226065464659316450.0) {
		tmp = x * exp((a * (log1p(-z) - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((y * (Math.log(z) - t)));
	double tmp;
	if (y <= -1.3091999464162745e-14) {
		tmp = t_1;
	} else if (y <= 226065464659316450.0) {
		tmp = x * Math.exp((a * (Math.log1p(-z) - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((y * (math.log(z) - t)))
	tmp = 0
	if y <= -1.3091999464162745e-14:
		tmp = t_1
	elif y <= 226065464659316450.0:
		tmp = x * math.exp((a * (math.log1p(-z) - b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(y * Float64(log(z) - t))))
	tmp = 0.0
	if (y <= -1.3091999464162745e-14)
		tmp = t_1;
	elseif (y <= 226065464659316450.0)
		tmp = Float64(x * exp(Float64(a * Float64(log1p(Float64(-z)) - b))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3091999464162745e-14], t$95$1, If[LessEqual[y, 226065464659316450.0], N[(x * N[Exp[N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET t_1 = (x * (exp((y * ((ln(z)) - t))))) IN
		LET tmp_1 = IF (y <= (226065464659316448)) THEN (x * (exp((a * ((ln(((- z) + (1)))) - b))))) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-13091999464162745474106964123472663879982368952126225991605679155327379703521728515625e-99)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.3091999464162745e-14 or 226065464659316450 < y

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   if -1.3091999464162745e-14 < y < 226065464659316450

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 59.1%

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   5. Step-by-step derivation

   6. Applied rewrites 62.9%

      \[\leadsto x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 87.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{if}\;y \leq -1.3091999464162745 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 226065464659316450:\\ \;\;\;\;x \cdot e^{a \cdot \left(z \cdot \left(-0.5 \cdot z - 1\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* x (exp (* y (- (log z) t))))))
  (if (<= y -1.3091999464162745e-14)
    t_1
    (if (<= y 226065464659316450.0)
      (* x (exp (* a (- (* z (- (* -0.5 z) 1.0)) b))))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((y * (log(z) - t)));
	double tmp;
	if (y <= -1.3091999464162745e-14) {
		tmp = t_1;
	} else if (y <= 226065464659316450.0) {
		tmp = x * exp((a * ((z * ((-0.5 * z) - 1.0)) - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * exp((y * (log(z) - t)))
    if (y <= (-1.3091999464162745d-14)) then
        tmp = t_1
    else if (y <= 226065464659316450.0d0) then
        tmp = x * exp((a * ((z * (((-0.5d0) * z) - 1.0d0)) - b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((y * (Math.log(z) - t)));
	double tmp;
	if (y <= -1.3091999464162745e-14) {
		tmp = t_1;
	} else if (y <= 226065464659316450.0) {
		tmp = x * Math.exp((a * ((z * ((-0.5 * z) - 1.0)) - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((y * (math.log(z) - t)))
	tmp = 0
	if y <= -1.3091999464162745e-14:
		tmp = t_1
	elif y <= 226065464659316450.0:
		tmp = x * math.exp((a * ((z * ((-0.5 * z) - 1.0)) - b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(y * Float64(log(z) - t))))
	tmp = 0.0
	if (y <= -1.3091999464162745e-14)
		tmp = t_1;
	elseif (y <= 226065464659316450.0)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(z * Float64(Float64(-0.5 * z) - 1.0)) - b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((y * (log(z) - t)));
	tmp = 0.0;
	if (y <= -1.3091999464162745e-14)
		tmp = t_1;
	elseif (y <= 226065464659316450.0)
		tmp = x * exp((a * ((z * ((-0.5 * z) - 1.0)) - b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3091999464162745e-14], t$95$1, If[LessEqual[y, 226065464659316450.0], N[(x * N[Exp[N[(a * N[(N[(z * N[(N[(-0.5 * z), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET t_1 = (x * (exp((y * ((ln(z)) - t))))) IN
		LET tmp_1 = IF (y <= (226065464659316448)) THEN (x * (exp((a * ((z * (((-5e-1) * z) - (1))) - b))))) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-13091999464162745474106964123472663879982368952126225991605679155327379703521728515625e-99)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.3091999464162745e-14 or 226065464659316450 < y

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   if -1.3091999464162745e-14 < y < 226065464659316450

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 59.1%

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto x \cdot e^{a \cdot \left(z \cdot \left(\frac{-1}{2} \cdot z - 1\right) - b\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 62.9%

      \[\leadsto x \cdot e^{a \cdot \left(z \cdot \left(-0.5 \cdot z - 1\right) - b\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 87.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_1 := x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{if}\;y \leq -1.3091999464162745 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 226065464659316450:\\ \;\;\;\;x \cdot e^{a \cdot \left(-1 \cdot z - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* x (exp (* y (- (log z) t))))))
  (if (<= y -1.3091999464162745e-14)
    t_1
    (if (<= y 226065464659316450.0)
      (* x (exp (* a (- (* -1.0 z) b))))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((y * (log(z) - t)));
	double tmp;
	if (y <= -1.3091999464162745e-14) {
		tmp = t_1;
	} else if (y <= 226065464659316450.0) {
		tmp = x * exp((a * ((-1.0 * z) - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * exp((y * (log(z) - t)))
    if (y <= (-1.3091999464162745d-14)) then
        tmp = t_1
    else if (y <= 226065464659316450.0d0) then
        tmp = x * exp((a * (((-1.0d0) * z) - b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((y * (Math.log(z) - t)));
	double tmp;
	if (y <= -1.3091999464162745e-14) {
		tmp = t_1;
	} else if (y <= 226065464659316450.0) {
		tmp = x * Math.exp((a * ((-1.0 * z) - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((y * (math.log(z) - t)))
	tmp = 0
	if y <= -1.3091999464162745e-14:
		tmp = t_1
	elif y <= 226065464659316450.0:
		tmp = x * math.exp((a * ((-1.0 * z) - b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(y * Float64(log(z) - t))))
	tmp = 0.0
	if (y <= -1.3091999464162745e-14)
		tmp = t_1;
	elseif (y <= 226065464659316450.0)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-1.0 * z) - b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((y * (log(z) - t)));
	tmp = 0.0;
	if (y <= -1.3091999464162745e-14)
		tmp = t_1;
	elseif (y <= 226065464659316450.0)
		tmp = x * exp((a * ((-1.0 * z) - b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3091999464162745e-14], t$95$1, If[LessEqual[y, 226065464659316450.0], N[(x * N[Exp[N[(a * N[(N[(-1.0 * z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET t_1 = (x * (exp((y * ((ln(z)) - t))))) IN
		LET tmp_1 = IF (y <= (226065464659316448)) THEN (x * (exp((a * (((-1) * z) - b))))) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-13091999464162745474106964123472663879982368952126225991605679155327379703521728515625e-99)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.3091999464162745e-14 or 226065464659316450 < y

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   if -1.3091999464162745e-14 < y < 226065464659316450

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 59.1%

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto x \cdot e^{a \cdot \left(-1 \cdot z - b\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 62.8%

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

Alternative 7: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -4 \cdot 10^{+14}:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-1 \cdot z - b\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (if (<= (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))) -4e+14)
  (* 0.0 1.0)
  (* x (exp (* a (- (* -1.0 z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= -4e+14) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * exp((a * ((-1.0 * z) - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))) <= (-4d+14)) then
        tmp = 0.0d0 * 1.0d0
    else
        tmp = x * exp((a * (((-1.0d0) * z) - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))) <= -4e+14) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * Math.exp((a * ((-1.0 * z) - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))) <= -4e+14:
		tmp = 0.0 * 1.0
	else:
		tmp = x * math.exp((a * ((-1.0 * z) - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= -4e+14)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-1.0 * z) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= -4e+14)
		tmp = 0.0 * 1.0;
	else
		tmp = x * exp((a * ((-1.0 * z) - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -4e+14], N[(0.0 * 1.0), $MachinePrecision], N[(x * N[Exp[N[(a * N[(N[(-1.0 * z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET tmp = IF (((y * ((ln(z)) - t)) + (a * ((ln(((1) - z))) - b))) <= (-4e14)) THEN ((0) * (1)) ELSE (x * (exp((a * (((-1) * z) - b))))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -4e14

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 18.9%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 43.4%

       \[\leadsto 0 \cdot 1 \]

   if -4e14 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 59.1%

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto x \cdot e^{a \cdot \left(-1 \cdot z - b\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 62.8%

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

Alternative 8: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -4 \cdot 10^{+14}:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-b\right) \cdot a}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (if (<= (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))) -4e+14)
  (* 0.0 1.0)
  (* x (exp (* (- b) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= -4e+14) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * exp((-b * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))) <= (-4d+14)) then
        tmp = 0.0d0 * 1.0d0
    else
        tmp = x * exp((-b * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))) <= -4e+14) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * Math.exp((-b * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))) <= -4e+14:
		tmp = 0.0 * 1.0
	else:
		tmp = x * math.exp((-b * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= -4e+14)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = Float64(x * exp(Float64(Float64(-b) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= -4e+14)
		tmp = 0.0 * 1.0;
	else
		tmp = x * exp((-b * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -4e+14], N[(0.0 * 1.0), $MachinePrecision], N[(x * N[Exp[N[((-b) * a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET tmp = IF (((y * ((ln(z)) - t)) + (a * ((ln(((1) - z))) - b))) <= (-4e14)) THEN ((0) * (1)) ELSE (x * (exp(((- b) * a)))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -4e14

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 18.9%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 43.4%

       \[\leadsto 0 \cdot 1 \]

   if -4e14 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 59.1%

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto x \cdot e^{a \cdot \left(-1 \cdot b\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 58.5%

      \[\leadsto x \cdot e^{a \cdot \left(-1 \cdot b\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 58.5%

      \[\leadsto x \cdot e^{\left(-b\right) \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -20000:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-t\right) \cdot y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (if (<= (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))) -20000.0)
  (* 0.0 1.0)
  (* x (exp (* (- t) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= -20000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * exp((-t * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))) <= (-20000.0d0)) then
        tmp = 0.0d0 * 1.0d0
    else
        tmp = x * exp((-t * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))) <= -20000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * Math.exp((-t * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))) <= -20000.0:
		tmp = 0.0 * 1.0
	else:
		tmp = x * math.exp((-t * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= -20000.0)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = Float64(x * exp(Float64(Float64(-t) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= -20000.0)
		tmp = 0.0 * 1.0;
	else
		tmp = x * exp((-t * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -20000.0], N[(0.0 * 1.0), $MachinePrecision], N[(x * N[Exp[N[((-t) * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET tmp = IF (((y * ((ln(z)) - t)) + (a * ((ln(((1) - z))) - b))) <= (-2e4)) THEN ((0) * (1)) ELSE (x * (exp(((- t) * y)))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -2e4

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 18.9%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 43.4%

       \[\leadsto 0 \cdot 1 \]

   if -2e4 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot e^{y \cdot \left(-1 \cdot t\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 56.8%

      \[\leadsto x \cdot e^{y \cdot \left(-1 \cdot t\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 56.8%

      \[\leadsto x \cdot e^{\left(-t\right) \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(\log z - t\right)\\ \mathbf{if}\;t\_1 + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -20000:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y (- (log z) t))))
  (if (<= (+ t_1 (* a (- (log (- 1.0 z)) b))) -20000.0)
    (* 0.0 1.0)
    (+ x (* x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (log(z) - t);
	double tmp;
	if ((t_1 + (a * (log((1.0 - z)) - b))) <= -20000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x + (x * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (log(z) - t)
    if ((t_1 + (a * (log((1.0d0 - z)) - b))) <= (-20000.0d0)) then
        tmp = 0.0d0 * 1.0d0
    else
        tmp = x + (x * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (Math.log(z) - t);
	double tmp;
	if ((t_1 + (a * (Math.log((1.0 - z)) - b))) <= -20000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x + (x * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (math.log(z) - t)
	tmp = 0
	if (t_1 + (a * (math.log((1.0 - z)) - b))) <= -20000.0:
		tmp = 0.0 * 1.0
	else:
		tmp = x + (x * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(log(z) - t))
	tmp = 0.0
	if (Float64(t_1 + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= -20000.0)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = Float64(x + Float64(x * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (log(z) - t);
	tmp = 0.0;
	if ((t_1 + (a * (log((1.0 - z)) - b))) <= -20000.0)
		tmp = 0.0 * 1.0;
	else
		tmp = x + (x * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -20000.0], N[(0.0 * 1.0), $MachinePrecision], N[(x + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET t_1 = (y * ((ln(z)) - t)) IN
		LET tmp = IF ((t_1 + (a * ((ln(((1) - z))) - b))) <= (-2e4)) THEN ((0) * (1)) ELSE (x + (x * t_1)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -2e4

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 18.9%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 43.4%

       \[\leadsto 0 \cdot 1 \]

   if -2e4 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} + x \cdot \left(y \cdot \left(e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \cdot \left(\log z - t\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 57.7%

      \[\leadsto \mathsf{fma}\left(x, e^{a \cdot \left(\log \left(1 - z\right) - b\right)}, x \cdot \left(y \cdot \left(e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \cdot \left(\log z - t\right)\right)\right)\right) \]

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 30.2%

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

Alternative 11: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(\log z - t\right)\\ \mathbf{if}\;t\_1 + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -20000:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + t\_1\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y (- (log z) t))))
  (if (<= (+ t_1 (* a (- (log (- 1.0 z)) b))) -20000.0)
    (* 0.0 1.0)
    (* x (+ 1.0 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (log(z) - t);
	double tmp;
	if ((t_1 + (a * (log((1.0 - z)) - b))) <= -20000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * (1.0 + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (log(z) - t)
    if ((t_1 + (a * (log((1.0d0 - z)) - b))) <= (-20000.0d0)) then
        tmp = 0.0d0 * 1.0d0
    else
        tmp = x * (1.0d0 + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (Math.log(z) - t);
	double tmp;
	if ((t_1 + (a * (Math.log((1.0 - z)) - b))) <= -20000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * (1.0 + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (math.log(z) - t)
	tmp = 0
	if (t_1 + (a * (math.log((1.0 - z)) - b))) <= -20000.0:
		tmp = 0.0 * 1.0
	else:
		tmp = x * (1.0 + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(log(z) - t))
	tmp = 0.0
	if (Float64(t_1 + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= -20000.0)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = Float64(x * Float64(1.0 + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (log(z) - t);
	tmp = 0.0;
	if ((t_1 + (a * (log((1.0 - z)) - b))) <= -20000.0)
		tmp = 0.0 * 1.0;
	else
		tmp = x * (1.0 + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -20000.0], N[(0.0 * 1.0), $MachinePrecision], N[(x * N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET t_1 = (y * ((ln(z)) - t)) IN
		LET tmp = IF ((t_1 + (a * ((ln(((1) - z))) - b))) <= (-2e4)) THEN ((0) * (1)) ELSE (x * ((1) + t_1)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -2e4

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 18.9%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 43.4%

       \[\leadsto 0 \cdot 1 \]

   if -2e4 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 30.2%

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

Alternative 12: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \log z - t\\ \mathbf{if}\;y \cdot t\_1 + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -20000:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, t\_1 \cdot x, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (log z) t)))
  (if (<= (+ (* y t_1) (* a (- (log (- 1.0 z)) b))) -20000.0)
    (* 0.0 1.0)
    (fma y (* t_1 x) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(z) - t;
	double tmp;
	if (((y * t_1) + (a * (log((1.0 - z)) - b))) <= -20000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = fma(y, (t_1 * x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(z) - t)
	tmp = 0.0
	if (Float64(Float64(y * t_1) + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= -20000.0)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = fma(y, Float64(t_1 * x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$1), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -20000.0], N[(0.0 * 1.0), $MachinePrecision], N[(y * N[(t$95$1 * x), $MachinePrecision] + x), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET t_1 = ((ln(z)) - t) IN
		LET tmp = IF (((y * t_1) + (a * ((ln(((1) - z))) - b))) <= (-2e4)) THEN ((0) * (1)) ELSE ((y * (t_1 * x)) + x) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -2e4

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 18.9%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 43.4%

       \[\leadsto 0 \cdot 1 \]

   if -2e4 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} + x \cdot \left(y \cdot \left(e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \cdot \left(\log z - t\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 57.7%

      \[\leadsto \mathsf{fma}\left(x, e^{a \cdot \left(\log \left(1 - z\right) - b\right)}, x \cdot \left(y \cdot \left(e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \cdot \left(\log z - t\right)\right)\right)\right) \]

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 30.2%

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

   9. Applied rewrites 28.5%

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

Alternative 13: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -20000:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t \cdot y, x, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (if (<= (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))) -20000.0)
  (* 0.0 1.0)
  (fma (- (* t y)) x x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= -20000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = fma(-(t * y), x, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= -20000.0)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = fma(Float64(-Float64(t * y)), x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -20000.0], N[(0.0 * 1.0), $MachinePrecision], N[((-N[(t * y), $MachinePrecision]) * x + x), $MachinePrecision]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET tmp = IF (((y * ((ln(z)) - t)) + (a * ((ln(((1) - z))) - b))) <= (-2e4)) THEN ((0) * (1)) ELSE (((- (t * y)) * x) + x) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -2e4

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 18.9%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 43.4%

       \[\leadsto 0 \cdot 1 \]

   if -2e4 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)} + x \cdot \left(y \cdot \left(e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \cdot \left(\log z - t\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 57.7%

      \[\leadsto \mathsf{fma}\left(x, e^{a \cdot \left(\log \left(1 - z\right) - b\right)}, x \cdot \left(y \cdot \left(e^{a \cdot \left(\log \left(1 - z\right) - b\right)} \cdot \left(\log z - t\right)\right)\right)\right) \]

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 30.2%

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

   8. Taylor expanded in t around inf

      \[\leadsto x + x \cdot \left(-1 \cdot \left(t \cdot y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 27.7%

       \[\leadsto x + x \cdot \left(-1 \cdot \left(t \cdot y\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 27.7%

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

Alternative 14: 57.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -25.801916055828222:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  :pre TRUE
  (if (<=
     (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
     -25.801916055828222)
  (* 0.0 1.0)
  (* x 1.0)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= -25.801916055828222) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))) <= (-25.801916055828222d0)) then
        tmp = 0.0d0 * 1.0d0
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))) <= -25.801916055828222) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))) <= -25.801916055828222:
		tmp = 0.0 * 1.0
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= -25.801916055828222)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= -25.801916055828222)
		tmp = 0.0 * 1.0;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -25.801916055828222], N[(0.0 * 1.0), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]

ReFlow

f(x, y, z, t, a, b):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b: real): real =
	LET tmp = IF (((y * ((ln(z)) - t)) + (a * ((ln(((1) - z))) - b))) <= (-2580191605582822234055129229091107845306396484375e-47)) THEN ((0) * (1)) ELSE (x * (1)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -25.801916055828222

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 18.9%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 43.4%

       \[\leadsto 0 \cdot 1 \]

   if -25.801916055828222 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 72.0%

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 18.9%

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

Alternative 15: 18.9% accurate, 10.8× speedup

Math

\[x \cdot 1 \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    code = x * 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * 1.0), $MachinePrecision]

ReFlow

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

Derivation

1. Initial program 96.5%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

2. Taylor expanded in a around 0

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

4. Applied rewrites 72.0%

   \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right)} \]

5. Taylor expanded in y around 0

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

7. Applied rewrites 18.9%

   \[\leadsto x \cdot 1 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))