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

Percentage Accurate: 96.7% → 99.5%

Time: 6.2s

Alternatives: 11

Speedup: 0.6×

• 58.9% 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 (- 1.0 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

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[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 96.7% 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 (- 1.0 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

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[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<=
     (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
     INFINITY)
  (* (exp (- (* (- (- z) b) a) (* (- t (log z)) y))) x)
  (* x (pow z y))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (exp.f64 (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))))) < +inf.0

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 99.1%

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

   4. Applied rewrites 99.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.1%

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

   6. Applied rewrites 99.1%

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

   if +inf.0 < (*.f64 x (exp.f64 (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))))

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 19.5%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in t around 0

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

      1. lower-pow.f64 51.5%

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

   10. Applied rewrites 51.5%

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

Alternative 2: 93.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;e^{\left(\left(-z\right) - b\right) \cdot a - t \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot {\left(z \cdot e^{-t}\right)}^{y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= y -5.8e+47)
  (* x (exp (* y (- (log z) t))))
  (if (<= y 2e-10)
    (* (exp (- (* (- (- z) b) a) (* t y))) x)
    (* x (pow (* z (exp (- t))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.8e+47) {
		tmp = x * exp((y * (log(z) - t)));
	} else if (y <= 2e-10) {
		tmp = exp((((-z - b) * a) - (t * y))) * x;
	} else {
		tmp = x * pow((z * exp(-t)), y);
	}
	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) :: tmp
    if (y <= (-5.8d+47)) then
        tmp = x * exp((y * (log(z) - t)))
    else if (y <= 2d-10) then
        tmp = exp((((-z - b) * a) - (t * y))) * x
    else
        tmp = x * ((z * 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 <= -5.8e+47) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else if (y <= 2e-10) {
		tmp = Math.exp((((-z - b) * a) - (t * y))) * x;
	} else {
		tmp = x * Math.pow((z * Math.exp(-t)), y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.8e+47:
		tmp = x * math.exp((y * (math.log(z) - t)))
	elif y <= 2e-10:
		tmp = math.exp((((-z - b) * a) - (t * y))) * x
	else:
		tmp = x * math.pow((z * math.exp(-t)), y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.8e+47)
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	elseif (y <= 2e-10)
		tmp = Float64(exp(Float64(Float64(Float64(Float64(-z) - b) * a) - Float64(t * y))) * x);
	else
		tmp = Float64(x * (Float64(z * exp(Float64(-t))) ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.8e+47)
		tmp = x * exp((y * (log(z) - t)));
	elseif (y <= 2e-10)
		tmp = exp((((-z - b) * a) - (t * y))) * x;
	else
		tmp = x * ((z * exp(-t)) ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.8e+47], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-10], N[(N[Exp[N[(N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision] - N[(t * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], N[(x * N[Power[N[(z * N[Exp[(-t)], $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999996e47

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   if -5.7999999999999996e47 < y < 2.0000000000000001e-10

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 99.1%

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

   4. Applied rewrites 99.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.1%

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

   6. Applied rewrites 99.1%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 87.5%

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

   9. Applied rewrites 87.5%

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

   if 2.0000000000000001e-10 < y

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

      1. lift-exp.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. lift-neg.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-*.f64 N/A

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

      8. exp-sum N/A

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

      9. lower-exp.f64 N/A

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

      10. lower-*.f32 N/A

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

      11. lower-unsound-log.f64 N/A

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

      12. lower-unsound-*.f32 N/A

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

      13. lower-unsound-exp.f64 N/A

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

      14. pow-to-exp N/A

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

      15. lift-*.f64 N/A

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

      16. exp-prod N/A

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

      17. pow-prod-down N/A

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

      18. lower-pow.f64 N/A

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

      19. lower-*.f64 N/A

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

      20. lower-exp.f64 69.6%

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

   6. Applied rewrites 69.6%

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

Alternative 3: 93.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;e^{\left(\left(-z\right) - b\right) \cdot a - t \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* x (exp (* y (- (log z) t))))))
  (if (<= y -5.8e+47)
    t_1
    (if (<= y 2e-10) (* (exp (- (* (- (- z) b) a) (* t y))) 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 <= -5.8e+47) {
		tmp = t_1;
	} else if (y <= 2e-10) {
		tmp = exp((((-z - b) * a) - (t * y))) * 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 <= (-5.8d+47)) then
        tmp = t_1
    else if (y <= 2d-10) then
        tmp = exp((((-z - b) * a) - (t * y))) * 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 <= -5.8e+47) {
		tmp = t_1;
	} else if (y <= 2e-10) {
		tmp = Math.exp((((-z - b) * a) - (t * y))) * 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 <= -5.8e+47:
		tmp = t_1
	elif y <= 2e-10:
		tmp = math.exp((((-z - b) * a) - (t * y))) * 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 <= -5.8e+47)
		tmp = t_1;
	elseif (y <= 2e-10)
		tmp = Float64(exp(Float64(Float64(Float64(Float64(-z) - b) * a) - Float64(t * y))) * 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 <= -5.8e+47)
		tmp = t_1;
	elseif (y <= 2e-10)
		tmp = exp((((-z - b) * a) - (t * y))) * 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, -5.8e+47], t$95$1, If[LessEqual[y, 2e-10], N[(N[Exp[N[(N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision] - N[(t * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999996e47 or 2.0000000000000001e-10 < y

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   if -5.7999999999999996e47 < y < 2.0000000000000001e-10

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 99.1%

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

   4. Applied rewrites 99.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.1%

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

   6. Applied rewrites 99.1%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 87.5%

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

   9. Applied rewrites 87.5%

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

Alternative 4: 85.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} t_1 := e^{\left(\left(-z\right) - b\right) \cdot a - t \cdot y} \cdot x\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-166}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (exp (- (* (- (- z) b) a) (* t y))) x)))
  (if (<= t -1.4e-91) t_1 (if (<= t 9.8e-166) (* 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((((-z - b) * a) - (t * y))) * x;
	double tmp;
	if (t <= -1.4e-91) {
		tmp = t_1;
	} else if (t <= 9.8e-166) {
		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((((-z - b) * a) - (t * y))) * x
    if (t <= (-1.4d-91)) then
        tmp = t_1
    else if (t <= 9.8d-166) 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((((-z - b) * a) - (t * y))) * x;
	double tmp;
	if (t <= -1.4e-91) {
		tmp = t_1;
	} else if (t <= 9.8e-166) {
		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((((-z - b) * a) - (t * y))) * x
	tmp = 0
	if t <= -1.4e-91:
		tmp = t_1
	elif t <= 9.8e-166:
		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(Float64(Float64(-z) - b) * a) - Float64(t * y))) * x)
	tmp = 0.0
	if (t <= -1.4e-91)
		tmp = t_1;
	elseif (t <= 9.8e-166)
		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((((-z - b) * a) - (t * y))) * x;
	tmp = 0.0;
	if (t <= -1.4e-91)
		tmp = t_1;
	elseif (t <= 9.8e-166)
		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[(N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision] - N[(t * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -1.4e-91], t$95$1, If[LessEqual[t, 9.8e-166], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3999999999999999e-91 or 9.7999999999999998e-166 < t

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 99.1%

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

   4. Applied rewrites 99.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.1%

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

   6. Applied rewrites 99.1%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 87.5%

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

   9. Applied rewrites 87.5%

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

   if -1.3999999999999999e-91 < t < 9.7999999999999998e-166

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 19.5%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in t around 0

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

      1. lower-pow.f64 51.5%

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

   10. Applied rewrites 51.5%

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

Alternative 5: 71.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := e^{-1 \cdot \left(t \cdot y\right)} \cdot x\\ \mathbf{if}\;t \leq -1000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-81}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (exp (* -1.0 (* t y))) x)))
  (if (<= t -1000000000.0)
    t_1
    (if (<= t 1.7e-81) (* 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((-1.0 * (t * y))) * x;
	double tmp;
	if (t <= -1000000000.0) {
		tmp = t_1;
	} else if (t <= 1.7e-81) {
		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(((-1.0d0) * (t * y))) * x
    if (t <= (-1000000000.0d0)) then
        tmp = t_1
    else if (t <= 1.7d-81) 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((-1.0 * (t * y))) * x;
	double tmp;
	if (t <= -1000000000.0) {
		tmp = t_1;
	} else if (t <= 1.7e-81) {
		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((-1.0 * (t * y))) * x
	tmp = 0
	if t <= -1000000000.0:
		tmp = t_1
	elif t <= 1.7e-81:
		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(-1.0 * Float64(t * y))) * x)
	tmp = 0.0
	if (t <= -1000000000.0)
		tmp = t_1;
	elseif (t <= 1.7e-81)
		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((-1.0 * (t * y))) * x;
	tmp = 0.0;
	if (t <= -1000000000.0)
		tmp = t_1;
	elseif (t <= 1.7e-81)
		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[(-1.0 * N[(t * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -1000000000.0], t$95$1, If[LessEqual[t, 1.7e-81], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1e9 or 1.6999999999999999e-81 < t

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 99.1%

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

   4. Applied rewrites 99.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.1%

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

   6. Applied rewrites 99.1%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 87.5%

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

   9. Applied rewrites 87.5%

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

   10. Taylor expanded in t around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 56.7%

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

   12. Applied rewrites 56.7%

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

   if -1e9 < t < 1.6999999999999999e-81

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 19.5%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in t around 0

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

      1. lower-pow.f64 51.5%

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

   10. Applied rewrites 51.5%

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

Alternative 6: 55.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -5000:\\ \;\;\;\;\left(\left(-t\right) \cdot y - -1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= t -5000.0) (* (- (* (- t) y) -1.0) x) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5000.0) {
		tmp = ((-t * y) - -1.0) * x;
	} else {
		tmp = x * pow(z, y);
	}
	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) :: tmp
    if (t <= (-5000.0d0)) then
        tmp = ((-t * y) - (-1.0d0)) * x
    else
        tmp = x * (z ** 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 (t <= -5000.0) {
		tmp = ((-t * y) - -1.0) * x;
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5000.0:
		tmp = ((-t * y) - -1.0) * x
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5000.0)
		tmp = Float64(Float64(Float64(Float64(-t) * y) - -1.0) * x);
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5000.0)
		tmp = ((-t * y) - -1.0) * x;
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5000.0], N[(N[(N[((-t) * y), $MachinePrecision] - -1.0), $MachinePrecision] * x), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5e3

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 29.7%

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

   7. Applied rewrites 29.7%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 27.7%

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

   10. Applied rewrites 27.7%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 27.7%

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

   12. Applied rewrites 27.7%

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

   if -5e3 < t

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 19.5%

      \[\leadsto x \cdot 1 \]

   8. Taylor expanded in t around 0

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

      1. lower-pow.f64 51.5%

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

   10. Applied rewrites 51.5%

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

Alternative 7: 35.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \left(-t\right) \cdot y\\ t_2 := y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)\\ t_3 := \left(\left(-t\right) \cdot x\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -50000000:\\ \;\;\;\;\frac{t\_3 \cdot t\_3 - x \cdot x}{t\_3 - x}\\ \mathbf{elif}\;t\_2 \leq 10^{+275}:\\ \;\;\;\;x \cdot \frac{t\_1 \cdot t\_1 - 1 \cdot 1}{t\_1 - 1}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 - -1\right) \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (- t) y))
       (t_2 (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
       (t_3 (* (* (- t) x) y)))
  (if (<= t_2 -50000000.0)
    (/ (- (* t_3 t_3) (* x x)) (- t_3 x))
    (if (<= t_2 1e+275)
      (* x (/ (- (* t_1 t_1) (* 1.0 1.0)) (- t_1 1.0)))
      (* (- t_1 -1.0) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t * y;
	double t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	double t_3 = (-t * x) * y;
	double tmp;
	if (t_2 <= -50000000.0) {
		tmp = ((t_3 * t_3) - (x * x)) / (t_3 - x);
	} else if (t_2 <= 1e+275) {
		tmp = x * (((t_1 * t_1) - (1.0 * 1.0)) / (t_1 - 1.0));
	} else {
		tmp = (t_1 - -1.0) * x;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = -t * y
    t_2 = (y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))
    t_3 = (-t * x) * y
    if (t_2 <= (-50000000.0d0)) then
        tmp = ((t_3 * t_3) - (x * x)) / (t_3 - x)
    else if (t_2 <= 1d+275) then
        tmp = x * (((t_1 * t_1) - (1.0d0 * 1.0d0)) / (t_1 - 1.0d0))
    else
        tmp = (t_1 - (-1.0d0)) * x
    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 = -t * y;
	double t_2 = (y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b));
	double t_3 = (-t * x) * y;
	double tmp;
	if (t_2 <= -50000000.0) {
		tmp = ((t_3 * t_3) - (x * x)) / (t_3 - x);
	} else if (t_2 <= 1e+275) {
		tmp = x * (((t_1 * t_1) - (1.0 * 1.0)) / (t_1 - 1.0));
	} else {
		tmp = (t_1 - -1.0) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t * y
	t_2 = (y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))
	t_3 = (-t * x) * y
	tmp = 0
	if t_2 <= -50000000.0:
		tmp = ((t_3 * t_3) - (x * x)) / (t_3 - x)
	elif t_2 <= 1e+275:
		tmp = x * (((t_1 * t_1) - (1.0 * 1.0)) / (t_1 - 1.0))
	else:
		tmp = (t_1 - -1.0) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) * y)
	t_2 = Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))
	t_3 = Float64(Float64(Float64(-t) * x) * y)
	tmp = 0.0
	if (t_2 <= -50000000.0)
		tmp = Float64(Float64(Float64(t_3 * t_3) - Float64(x * x)) / Float64(t_3 - x));
	elseif (t_2 <= 1e+275)
		tmp = Float64(x * Float64(Float64(Float64(t_1 * t_1) - Float64(1.0 * 1.0)) / Float64(t_1 - 1.0)));
	else
		tmp = Float64(Float64(t_1 - -1.0) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t * y;
	t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	t_3 = (-t * x) * y;
	tmp = 0.0;
	if (t_2 <= -50000000.0)
		tmp = ((t_3 * t_3) - (x * x)) / (t_3 - x);
	elseif (t_2 <= 1e+275)
		tmp = x * (((t_1 * t_1) - (1.0 * 1.0)) / (t_1 - 1.0));
	else
		tmp = (t_1 - -1.0) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) * y), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(N[((-t) * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -50000000.0], N[(N[(N[(t$95$3 * t$95$3), $MachinePrecision] - N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(t$95$3 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+275], N[(x * N[(N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(1.0 * 1.0), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 - -1.0), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -5e7

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

   4. Applied rewrites 57.0%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 29.7%

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

   7. Applied rewrites 29.7%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 26.8%

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

   10. Applied rewrites 26.8%

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

       1. lift-+.f64 N/A

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

       2. +-commutative N/A

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

       3. flip-+ N/A

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

       4. lower-unsound-/.f64 N/A

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

   12. Applied rewrites 22.2%

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

   if -5e7 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < 9.9999999999999996e274

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 29.7%

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

   7. Applied rewrites 29.7%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 27.7%

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

   10. Applied rewrites 27.7%

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

       1. lift-+.f64 N/A

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

       2. +-commutative N/A

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

       3. flip-+ N/A

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

       4. lower-unsound-/.f64 N/A

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

   12. Applied rewrites 25.4%

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

   if 9.9999999999999996e274 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 29.7%

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

   7. Applied rewrites 29.7%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 27.7%

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

   10. Applied rewrites 27.7%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 27.7%

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

   12. Applied rewrites 27.7%

       \[\leadsto \color{blue}{\left(\left(-t\right) \cdot y - -1\right) \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 30.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \left(-t\right) \cdot y\\ \mathbf{if}\;y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right) \leq 10^{+275}:\\ \;\;\;\;x \cdot \frac{t\_1 \cdot t\_1 - 1 \cdot 1}{t\_1 - 1}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 - -1\right) \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (- t) y)))
  (if (<= (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))) 1e+275)
    (* x (/ (- (* t_1 t_1) (* 1.0 1.0)) (- t_1 1.0)))
    (* (- t_1 -1.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t * y;
	double tmp;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= 1e+275) {
		tmp = x * (((t_1 * t_1) - (1.0 * 1.0)) / (t_1 - 1.0));
	} else {
		tmp = (t_1 - -1.0) * x;
	}
	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 = -t * y
    if (((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))) <= 1d+275) then
        tmp = x * (((t_1 * t_1) - (1.0d0 * 1.0d0)) / (t_1 - 1.0d0))
    else
        tmp = (t_1 - (-1.0d0)) * x
    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 = -t * y;
	double tmp;
	if (((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))) <= 1e+275) {
		tmp = x * (((t_1 * t_1) - (1.0 * 1.0)) / (t_1 - 1.0));
	} else {
		tmp = (t_1 - -1.0) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t * y
	tmp = 0
	if ((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))) <= 1e+275:
		tmp = x * (((t_1 * t_1) - (1.0 * 1.0)) / (t_1 - 1.0))
	else:
		tmp = (t_1 - -1.0) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) * y)
	tmp = 0.0
	if (Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= 1e+275)
		tmp = Float64(x * Float64(Float64(Float64(t_1 * t_1) - Float64(1.0 * 1.0)) / Float64(t_1 - 1.0)));
	else
		tmp = Float64(Float64(t_1 - -1.0) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t * y;
	tmp = 0.0;
	if (((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))) <= 1e+275)
		tmp = x * (((t_1 * t_1) - (1.0 * 1.0)) / (t_1 - 1.0));
	else
		tmp = (t_1 - -1.0) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) * y), $MachinePrecision]}, 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], 1e+275], N[(x * N[(N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(1.0 * 1.0), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 - -1.0), $MachinePrecision] * x), $MachinePrecision]]]

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))) < 9.9999999999999996e274

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 29.7%

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

   7. Applied rewrites 29.7%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 27.7%

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

   10. Applied rewrites 27.7%

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

       1. lift-+.f64 N/A

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

       2. +-commutative N/A

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

       3. flip-+ N/A

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

       4. lower-unsound-/.f64 N/A

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

   12. Applied rewrites 25.4%

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

   if 9.9999999999999996e274 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.7%

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

   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 71.6%

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 29.7%

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

   7. Applied rewrites 29.7%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 27.7%

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

   10. Applied rewrites 27.7%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 27.7%

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

   12. Applied rewrites 27.7%

       \[\leadsto \color{blue}{\left(\left(-t\right) \cdot y - -1\right) \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 27.7% accurate, 20.5× speedup

Math

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

FPCore

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

C

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

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 = ((-t * y) - (-1.0d0)) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

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 71.6%

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

4. Applied rewrites 71.6%

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

5. Taylor expanded in y around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-log.f64 29.7%

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

7. Applied rewrites 29.7%

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

8. Taylor expanded in t around inf

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

   1. lower-*.f64 27.7%

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

10. Applied rewrites 27.7%

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

    1. lift-*.f64 N/A

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

    2. *-commutative N/A

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

    3. lower-*.f64 27.7%

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

12. Applied rewrites 27.7%

    \[\leadsto \color{blue}{\left(\left(-t\right) \cdot y - -1\right) \cdot x} \]
13. Add Preprocessing

Alternative 10: 26.8% accurate, 20.5× speedup

Math

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

FPCore

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

C

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

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 + ((x * y) * -t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

2. Taylor expanded in y around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-exp.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower--.f64 N/A

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

   6. lower-log.f64 N/A

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

   7. lower--.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. lower-*.f64 N/A

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

4. Applied rewrites 57.0%

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

5. Taylor expanded in a around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower--.f64 N/A

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

   5. lower-log.f64 29.7%

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

7. Applied rewrites 29.7%

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

8. Taylor expanded in t around inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-*.f64 26.8%

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

10. Applied rewrites 26.8%

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

    1. lift-*.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. associate-*r* N/A

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

    4. lift-*.f64 N/A

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

    5. *-commutative N/A

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

    6. lower-*.f64 26.8%

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

    7. lift-*.f64 N/A

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

    8. mul-1-neg N/A

       \[\leadsto x + \left(x \cdot y\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

    9. lower-neg.f64 26.8%

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

12. Applied rewrites 26.8%

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

Alternative 11: 19.5% accurate, 54.7× speedup

Math

\[x \cdot 1 \]

FPCore

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

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 * 1.0), $MachinePrecision]

Derivation

1. Initial program 96.7%

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

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 71.6%

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

4. Applied rewrites 71.6%

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

5. Taylor expanded in y around 0

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

7. Applied rewrites 19.5%

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

Reproduce

herbie shell --seed 2025258 
(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))))))