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

Percentage Accurate: 96.8% → 99.2%

Time: 6.8s

Alternatives: 7

Speedup: 1.3×

• 58.6% 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
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 96.8% 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
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.2% accurate, 1.3× speedup

Math

\[x \cdot e^{\left(a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right) + y \cdot \log z\right) - t \cdot y} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (* x (exp (- (+ (* a (- (30-log1z0 z) b)) (* y (log z))) (* t y)))))

Derivation

1. Initial program 96.8%

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

2. Taylor expanded in y around inf

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

   1. lower-exp.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-+.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower--.f64 N/A

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

   6. lower-30-log1z0 N/A

      \[\leadsto x \cdot e^{\left(a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right) + y \cdot \log z\right) - t \cdot y} \]

   7. lower-*.f64 N/A

      \[\leadsto x \cdot e^{\left(a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right) + y \cdot \log z\right) - t \cdot y} \]

   8. lower-log.f64 N/A

      \[\leadsto x \cdot e^{\left(a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right) + y \cdot \log z\right) - t \cdot y} \]

   9. lower-*.f64 99.2%

      \[\leadsto x \cdot e^{\left(a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right) + y \cdot \log z\right) - t \cdot y} \]

4. Applied rewrites 99.2%

   \[\leadsto x \cdot \color{blue}{e^{\left(a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right) + y \cdot \log z\right) - t \cdot y}} \]
5. Add Preprocessing

Alternative 2: 85.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{if}\;y \leq -94999999999999995027949442561445199872:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9200:\\ \;\;\;\;e^{\left(\left(-z\right) - b\right) \cdot a} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* x (exp (* y (- (log z) t))))))
  (if (<= y -94999999999999995027949442561445199872)
    t_1
    (if (<= y 9200) (* (exp (* (- (- z) b) a)) x) 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 <= -9.5e+37) {
		tmp = t_1;
	} else if (y <= 9200.0) {
		tmp = exp(((-z - b) * a)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 <= (-9.5d+37)) then
        tmp = t_1
    else if (y <= 9200.0d0) then
        tmp = exp(((-z - b) * a)) * x
    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 <= -9.5e+37) {
		tmp = t_1;
	} else if (y <= 9200.0) {
		tmp = Math.exp(((-z - b) * a)) * x;
	} 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 <= -9.5e+37:
		tmp = t_1
	elif y <= 9200.0:
		tmp = math.exp(((-z - b) * a)) * x
	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 <= -9.5e+37)
		tmp = t_1;
	elseif (y <= 9200.0)
		tmp = Float64(exp(Float64(Float64(Float64(-z) - b) * a)) * x);
	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 <= -9.5e+37)
		tmp = t_1;
	elseif (y <= 9200.0)
		tmp = exp(((-z - b) * a)) * x;
	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, -94999999999999995027949442561445199872], t$95$1, If[LessEqual[y, 9200], N[(N[Exp[N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999995e37 or 9200 < y

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 72.5%

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

   4. Applied rewrites 72.5%

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

   if -9.4999999999999995e37 < y < 9200

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-30-log1z0 62.5%

         \[\leadsto x \cdot e^{a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right)} \]

   4. Applied rewrites 62.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right)}} \]

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 62.5%

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

   7. Applied rewrites 62.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 62.5%

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

   9. Applied rewrites 62.5%

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

Alternative 3: 73.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} t_1 := e^{\left(-t\right) \cdot y} \cdot x\\ \mathbf{if}\;y \leq -94999999999999995027949442561445199872:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 12000:\\ \;\;\;\;e^{\left(\left(-z\right) - b\right) \cdot a} \cdot x\\ \mathbf{elif}\;y \leq 10199999999999999168735447530637548288280156818942794594306261329182187057441323244557076267008:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (exp (* (- t) y)) x)))
  (if (<= y -94999999999999995027949442561445199872)
    t_1
    (if (<= y 12000)
      (* (exp (* (- (- z) b) a)) x)
      (if (<=
           y
           10199999999999999168735447530637548288280156818942794594306261329182187057441323244557076267008)
        (* x (pow z y))
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp((-t * y)) * x;
	double tmp;
	if (y <= -9.5e+37) {
		tmp = t_1;
	} else if (y <= 12000.0) {
		tmp = exp(((-z - b) * a)) * x;
	} else if (y <= 1.02e+94) {
		tmp = x * pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 = exp((-t * y)) * x
    if (y <= (-9.5d+37)) then
        tmp = t_1
    else if (y <= 12000.0d0) then
        tmp = exp(((-z - b) * a)) * x
    else if (y <= 1.02d+94) then
        tmp = x * (z ** y)
    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 = Math.exp((-t * y)) * x;
	double tmp;
	if (y <= -9.5e+37) {
		tmp = t_1;
	} else if (y <= 12000.0) {
		tmp = Math.exp(((-z - b) * a)) * x;
	} else if (y <= 1.02e+94) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp((-t * y)) * x
	tmp = 0
	if y <= -9.5e+37:
		tmp = t_1
	elif y <= 12000.0:
		tmp = math.exp(((-z - b) * a)) * x
	elif y <= 1.02e+94:
		tmp = x * math.pow(z, y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(-t) * y)) * x)
	tmp = 0.0
	if (y <= -9.5e+37)
		tmp = t_1;
	elseif (y <= 12000.0)
		tmp = Float64(exp(Float64(Float64(Float64(-z) - b) * a)) * x);
	elseif (y <= 1.02e+94)
		tmp = Float64(x * (z ^ y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp((-t * y)) * x;
	tmp = 0.0;
	if (y <= -9.5e+37)
		tmp = t_1;
	elseif (y <= 12000.0)
		tmp = exp(((-z - b) * a)) * x;
	elseif (y <= 1.02e+94)
		tmp = x * (z ^ y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Exp[N[((-t) * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -94999999999999995027949442561445199872], t$95$1, If[LessEqual[y, 12000], N[(N[Exp[N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 10199999999999999168735447530637548288280156818942794594306261329182187057441323244557076267008], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999995e37 or 1.0199999999999999e94 < y

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 72.5%

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

   4. Applied rewrites 72.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 57.7%

         \[\leadsto x \cdot e^{y \cdot \left(-1 \cdot t\right)} \]

   7. Applied rewrites 57.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 57.7%

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

   9. Applied rewrites 57.7%

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

   if -9.4999999999999995e37 < y < 12000

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-30-log1z0 62.5%

         \[\leadsto x \cdot e^{a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right)} \]

   4. Applied rewrites 62.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right)}} \]

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 62.5%

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

   7. Applied rewrites 62.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 62.5%

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

   9. Applied rewrites 62.5%

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

   if 12000 < y < 1.0199999999999999e94

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 72.5%

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

   4. Applied rewrites 72.5%

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

   5. Taylor expanded in t around 0

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

      1. lower-pow.f64 51.7%

         \[\leadsto x \cdot {z}^{y} \]

   7. Applied rewrites 51.7%

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

Alternative 4: 70.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} t_1 := e^{\left(-t\right) \cdot y} \cdot x\\ \mathbf{if}\;y \leq -94999999999999995027949442561445199872:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1800:\\ \;\;\;\;e^{\left(-b\right) \cdot a} \cdot x\\ \mathbf{elif}\;y \leq 10199999999999999168735447530637548288280156818942794594306261329182187057441323244557076267008:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (exp (* (- t) y)) x)))
  (if (<= y -94999999999999995027949442561445199872)
    t_1
    (if (<= y 1800)
      (* (exp (* (- b) a)) x)
      (if (<=
           y
           10199999999999999168735447530637548288280156818942794594306261329182187057441323244557076267008)
        (* x (pow z y))
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp((-t * y)) * x;
	double tmp;
	if (y <= -9.5e+37) {
		tmp = t_1;
	} else if (y <= 1800.0) {
		tmp = exp((-b * a)) * x;
	} else if (y <= 1.02e+94) {
		tmp = x * pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 = exp((-t * y)) * x
    if (y <= (-9.5d+37)) then
        tmp = t_1
    else if (y <= 1800.0d0) then
        tmp = exp((-b * a)) * x
    else if (y <= 1.02d+94) then
        tmp = x * (z ** y)
    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 = Math.exp((-t * y)) * x;
	double tmp;
	if (y <= -9.5e+37) {
		tmp = t_1;
	} else if (y <= 1800.0) {
		tmp = Math.exp((-b * a)) * x;
	} else if (y <= 1.02e+94) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp((-t * y)) * x
	tmp = 0
	if y <= -9.5e+37:
		tmp = t_1
	elif y <= 1800.0:
		tmp = math.exp((-b * a)) * x
	elif y <= 1.02e+94:
		tmp = x * math.pow(z, y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(-t) * y)) * x)
	tmp = 0.0
	if (y <= -9.5e+37)
		tmp = t_1;
	elseif (y <= 1800.0)
		tmp = Float64(exp(Float64(Float64(-b) * a)) * x);
	elseif (y <= 1.02e+94)
		tmp = Float64(x * (z ^ y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp((-t * y)) * x;
	tmp = 0.0;
	if (y <= -9.5e+37)
		tmp = t_1;
	elseif (y <= 1800.0)
		tmp = exp((-b * a)) * x;
	elseif (y <= 1.02e+94)
		tmp = x * (z ^ y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Exp[N[((-t) * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -94999999999999995027949442561445199872], t$95$1, If[LessEqual[y, 1800], N[(N[Exp[N[((-b) * a), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 10199999999999999168735447530637548288280156818942794594306261329182187057441323244557076267008], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999995e37 or 1.0199999999999999e94 < y

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 72.5%

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

   4. Applied rewrites 72.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 57.7%

         \[\leadsto x \cdot e^{y \cdot \left(-1 \cdot t\right)} \]

   7. Applied rewrites 57.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 57.7%

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

   9. Applied rewrites 57.7%

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

   if -9.4999999999999995e37 < y < 1800

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-30-log1z0 62.5%

         \[\leadsto x \cdot e^{a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right)} \]

   4. Applied rewrites 62.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{30\_log1z0}\left(z\right) - b\right)}} \]

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 58.1%

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

   7. Applied rewrites 58.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.1%

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

   9. Applied rewrites 58.1%

      \[\leadsto \color{blue}{e^{\left(-b\right) \cdot a} \cdot x} \]

   if 1800 < y < 1.0199999999999999e94

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 72.5%

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

   4. Applied rewrites 72.5%

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

   5. Taylor expanded in t around 0

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

      1. lower-pow.f64 51.7%

         \[\leadsto x \cdot {z}^{y} \]

   7. Applied rewrites 51.7%

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

Alternative 5: 70.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := e^{\left(-t\right) \cdot y} \cdot x\\ \mathbf{if}\;t \leq \frac{-5440166188265831}{75557863725914323419136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 24999999999999998821833863412802751999361545695464520794771346937446488059801446767248924750854127694096827515373733105246240827891950550502659321931910610944:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (exp (* (- t) y)) x)))
  (if (<= t -5440166188265831/75557863725914323419136)
    t_1
    (if (<=
         t
         24999999999999998821833863412802751999361545695464520794771346937446488059801446767248924750854127694096827515373733105246240827891950550502659321931910610944)
      (* x (pow z y))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp((-t * y)) * x;
	double tmp;
	if (t <= -7.2e-8) {
		tmp = t_1;
	} else if (t <= 2.5e+157) {
		tmp = x * pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 = exp((-t * y)) * x
    if (t <= (-7.2d-8)) then
        tmp = t_1
    else if (t <= 2.5d+157) then
        tmp = x * (z ** y)
    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 = Math.exp((-t * y)) * x;
	double tmp;
	if (t <= -7.2e-8) {
		tmp = t_1;
	} else if (t <= 2.5e+157) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp((-t * y)) * x
	tmp = 0
	if t <= -7.2e-8:
		tmp = t_1
	elif t <= 2.5e+157:
		tmp = x * math.pow(z, y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(-t) * y)) * x)
	tmp = 0.0
	if (t <= -7.2e-8)
		tmp = t_1;
	elseif (t <= 2.5e+157)
		tmp = Float64(x * (z ^ y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp((-t * y)) * x;
	tmp = 0.0;
	if (t <= -7.2e-8)
		tmp = t_1;
	elseif (t <= 2.5e+157)
		tmp = x * (z ^ y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Exp[N[((-t) * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -5440166188265831/75557863725914323419136], t$95$1, If[LessEqual[t, 24999999999999998821833863412802751999361545695464520794771346937446488059801446767248924750854127694096827515373733105246240827891950550502659321931910610944], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.1999999999999996e-8 or 2.4999999999999999e157 < t

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 72.5%

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

   4. Applied rewrites 72.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 57.7%

         \[\leadsto x \cdot e^{y \cdot \left(-1 \cdot t\right)} \]

   7. Applied rewrites 57.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 57.7%

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

   9. Applied rewrites 57.7%

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

   if -7.1999999999999996e-8 < t < 2.4999999999999999e157

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 72.5%

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

   4. Applied rewrites 72.5%

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

   5. Taylor expanded in t around 0

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

      1. lower-pow.f64 51.7%

         \[\leadsto x \cdot {z}^{y} \]

   7. Applied rewrites 51.7%

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 51.7% accurate, 3.1× speedup

Math

\[x \cdot {z}^{y} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (* x (pow z y)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 * (z ** y)
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return x * math.pow(z, y)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

2. Taylor expanded in a around 0

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

   1. lower-exp.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-log.f64 72.5%

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

4. Applied rewrites 72.5%

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

5. Taylor expanded in t around 0

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

   1. lower-pow.f64 51.7%

      \[\leadsto x \cdot {z}^{y} \]

7. Applied rewrites 51.7%

   \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
8. Add Preprocessing

Alternative 7: 19.0% accurate, 54.7× speedup

Math

\[x \cdot 1 \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (* x 1))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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), $MachinePrecision]

Derivation

1. Initial program 96.8%

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

2. Taylor expanded in a around 0

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

   1. lower-exp.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-log.f64 72.5%

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

4. Applied rewrites 72.5%

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

5. Taylor expanded in y around 0

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

7. Applied rewrites 19.0%

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

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(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 z)) b))))))