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

Percentage Accurate: 96.7% → 99.6%

Time: 7.9s

Alternatives: 17

Speedup: 1.2×

• 41.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

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

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: 99.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, -0.5, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (*
  x
  (exp (fma (- a) b (fma (fma (* a z) -0.5 (- a)) z (* (- (log z) t) y))))))

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[((-a) * b + N[(N[(N[(a * z), $MachinePrecision] * -0.5 + (-a)), $MachinePrecision] * z + N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $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 z around 0

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

   1. associate-*r* N/A

      \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \left(\color{blue}{y \cdot \left(\log z - t\right)} + z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right)\right)} \]

   2. lower-fma.f64 N/A

      \[\leadsto x \cdot e^{\mathsf{fma}\left(-1 \cdot a, \color{blue}{b}, y \cdot \left(\log z - t\right) + z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right)\right)} \]

   3. mul-1-neg N/A

      \[\leadsto x \cdot e^{\mathsf{fma}\left(\mathsf{neg}\left(a\right), b, y \cdot \left(\log z - t\right) + z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right)\right)} \]

   4. lower-neg.f64 N/A

      \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, y \cdot \left(\log z - t\right) + z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right)\right)} \]

   5. +-commutative N/A

      \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right) + y \cdot \left(\log z - t\right)\right)} \]

   6. *-commutative N/A

      \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right) \cdot z + y \cdot \left(\log z - t\right)\right)} \]

   7. lower-fma.f64 N/A

      \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

   8. +-commutative N/A

      \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\frac{-1}{2} \cdot \left(a \cdot z\right) + -1 \cdot a, z, y \cdot \left(\log z - t\right)\right)\right)} \]

   9. *-commutative N/A

      \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\left(a \cdot z\right) \cdot \frac{-1}{2} + -1 \cdot a, z, y \cdot \left(\log z - t\right)\right)\right)} \]

   10. lower-fma.f64 N/A

       \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -1 \cdot a\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

   11. lower-*.f64 N/A

       \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -1 \cdot a\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

   12. mul-1-neg N/A

       \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, \mathsf{neg}\left(a\right)\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

   13. lower-neg.f64 N/A

       \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -a\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

   14. *-commutative N/A

       \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)} \]

   15. lower-*.f64 N/A

       \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)} \]

   16. lift-log.f64 N/A

       \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)} \]

   17. lift--.f64 99.6

       \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, -0.5, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)} \]

4. Applied rewrites 99.6%

   \[\leadsto x \cdot e^{\color{blue}{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, -0.5, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)}} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (+ (* y (- (log z) t)) (* a (- (* (- (* -0.5 z) 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 * ((((-0.5 * z) - 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 * (((((-0.5d0) * z) - 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 * ((((-0.5 * z) - 1.0) * z) - b))));
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * ((((-0.5 * z) - 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[(N[(N[(-0.5 * z), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $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 z around 0

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

   1. *-commutative N/A

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\left(\frac{-1}{2} \cdot z - 1\right) \cdot \color{blue}{z} - b\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\left(\frac{-1}{2} \cdot z - 1\right) \cdot \color{blue}{z} - b\right)} \]

   3. lower--.f64 N/A

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

   4. lower-*.f64 99.3

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

4. Applied rewrites 99.3%

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

Alternative 3: 99.3% accurate, 1.2× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (-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[((-z) - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $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 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. mul-1-neg N/A

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

   2. lower-neg.f64 99.3

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

4. Applied rewrites 99.3%

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

Alternative 4: 87.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{\left(\log z - t\right) \cdot y} \cdot x\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-6}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.5, z, 1\right), z, b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (exp (* (- (log z) t) y)) x)))
   (if (<= y -7.5e-11)
     t_1
     (if (<= y 2.2e-6) (* x (exp (* (- a) (fma (fma 0.5 z 1.0) z b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(((log(z) - t) * y)) * x;
	double tmp;
	if (y <= -7.5e-11) {
		tmp = t_1;
	} else if (y <= 2.2e-6) {
		tmp = x * exp((-a * fma(fma(0.5, z, 1.0), z, b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(log(z) - t) * y)) * x)
	tmp = 0.0
	if (y <= -7.5e-11)
		tmp = t_1;
	elseif (y <= 2.2e-6)
		tmp = Float64(x * exp(Float64(Float64(-a) * fma(fma(0.5, z, 1.0), z, b))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -7.5e-11], t$95$1, If[LessEqual[y, 2.2e-6], N[(x * N[Exp[N[((-a) * N[(N[(0.5 * z + 1.0), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e-11 or 2.2000000000000001e-6 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 88.6

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

   4. Applied rewrites 88.6%

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

   if -7.5e-11 < y < 2.2000000000000001e-6

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0

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

      1. associate-*r* N/A

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot b + \left(\color{blue}{y \cdot \left(\log z - t\right)} + z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto x \cdot e^{\mathsf{fma}\left(-1 \cdot a, \color{blue}{b}, y \cdot \left(\log z - t\right) + z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto x \cdot e^{\mathsf{fma}\left(\mathsf{neg}\left(a\right), b, y \cdot \left(\log z - t\right) + z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right)\right)} \]

      4. lower-neg.f64 N/A

         \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, y \cdot \left(\log z - t\right) + z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, z \cdot \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right) + y \cdot \left(\log z - t\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right)\right) \cdot z + y \cdot \left(\log z - t\right)\right)} \]

      7. lower-fma.f64 N/A

         \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(-1 \cdot a + \frac{-1}{2} \cdot \left(a \cdot z\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

      8. +-commutative N/A

         \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\frac{-1}{2} \cdot \left(a \cdot z\right) + -1 \cdot a, z, y \cdot \left(\log z - t\right)\right)\right)} \]

      9. *-commutative N/A

         \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\left(a \cdot z\right) \cdot \frac{-1}{2} + -1 \cdot a, z, y \cdot \left(\log z - t\right)\right)\right)} \]

      10. lower-fma.f64 N/A

          \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -1 \cdot a\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

      11. lower-*.f64 N/A

          \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -1 \cdot a\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, \mathsf{neg}\left(a\right)\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

      13. lower-neg.f64 N/A

          \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -a\right), z, y \cdot \left(\log z - t\right)\right)\right)} \]

      14. *-commutative N/A

          \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)} \]

      15. lower-*.f64 N/A

          \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)} \]

      16. lift-log.f64 N/A

          \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, \frac{-1}{2}, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)} \]

      17. lift--.f64 99.9

          \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, -0.5, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)} \]

   4. Applied rewrites 99.9%

      \[\leadsto x \cdot e^{\color{blue}{\mathsf{fma}\left(-a, b, \mathsf{fma}\left(\mathsf{fma}\left(a \cdot z, -0.5, -a\right), z, \left(\log z - t\right) \cdot y\right)\right)}} \]

   5. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot \left(b + \color{blue}{z \cdot \left(1 + \frac{1}{2} \cdot z\right)}\right)} \]

      2. mul-1-neg N/A

         \[\leadsto x \cdot e^{\left(\mathsf{neg}\left(a\right)\right) \cdot \left(b + \color{blue}{z} \cdot \left(1 + \frac{1}{2} \cdot z\right)\right)} \]

      3. lift-neg.f64 N/A

         \[\leadsto x \cdot e^{\left(-a\right) \cdot \left(b + \color{blue}{z} \cdot \left(1 + \frac{1}{2} \cdot z\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto x \cdot e^{\left(-a\right) \cdot \left(b + \color{blue}{z \cdot \left(1 + \frac{1}{2} \cdot z\right)}\right)} \]

      5. +-commutative N/A

         \[\leadsto x \cdot e^{\left(-a\right) \cdot \left(z \cdot \left(1 + \frac{1}{2} \cdot z\right) + b\right)} \]

      6. *-commutative N/A

         \[\leadsto x \cdot e^{\left(-a\right) \cdot \left(\left(1 + \frac{1}{2} \cdot z\right) \cdot z + b\right)} \]

      7. lower-fma.f64 N/A

         \[\leadsto x \cdot e^{\left(-a\right) \cdot \mathsf{fma}\left(1 + \frac{1}{2} \cdot z, z, b\right)} \]

      8. +-commutative N/A

         \[\leadsto x \cdot e^{\left(-a\right) \cdot \mathsf{fma}\left(\frac{1}{2} \cdot z + 1, z, b\right)} \]

      9. lower-fma.f64 86.8

         \[\leadsto x \cdot e^{\left(-a\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.5, z, 1\right), z, b\right)} \]

   7. Applied rewrites 86.8%

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

Alternative 5: 87.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{\left(\log z - t\right) \cdot y} \cdot x\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-6}:\\ \;\;\;\;e^{\left(\left(-z\right) - b\right) \cdot a} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (exp (* (- (log z) t) y)) x)))
   (if (<= y -7.5e-11)
     t_1
     (if (<= y 2.2e-6) (* (exp (* (- (- z) b) a)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(((log(z) - t) * y)) * x;
	double tmp;
	if (y <= -7.5e-11) {
		tmp = t_1;
	} else if (y <= 2.2e-6) {
		tmp = exp(((-z - b) * a)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = exp(((log(z) - t) * y)) * x
    if (y <= (-7.5d-11)) then
        tmp = t_1
    else if (y <= 2.2d-6) then
        tmp = exp(((-z - b) * a)) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.exp(((Math.log(z) - t) * y)) * x;
	double tmp;
	if (y <= -7.5e-11) {
		tmp = t_1;
	} else if (y <= 2.2e-6) {
		tmp = Math.exp(((-z - b) * a)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp(((math.log(z) - t) * y)) * x
	tmp = 0
	if y <= -7.5e-11:
		tmp = t_1
	elif y <= 2.2e-6:
		tmp = math.exp(((-z - b) * a)) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(log(z) - t) * y)) * x)
	tmp = 0.0
	if (y <= -7.5e-11)
		tmp = t_1;
	elseif (y <= 2.2e-6)
		tmp = Float64(exp(Float64(Float64(Float64(-z) - b) * a)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp(((log(z) - t) * y)) * x;
	tmp = 0.0;
	if (y <= -7.5e-11)
		tmp = t_1;
	elseif (y <= 2.2e-6)
		tmp = exp(((-z - b) * a)) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -7.5e-11], t$95$1, If[LessEqual[y, 2.2e-6], N[(N[Exp[N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e-11 or 2.2000000000000001e-6 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 88.6

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

   4. Applied rewrites 88.6%

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

   if -7.5e-11 < y < 2.2000000000000001e-6

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 81.9

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

   4. Applied rewrites 81.9%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 86.8

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

   7. Applied rewrites 86.8%

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

Alternative 6: 73.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+122}:\\ \;\;\;\;e^{\left(-t\right) \cdot y} \cdot x\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+101}:\\ \;\;\;\;e^{\left(\left(-z\right) - b\right) \cdot a} \cdot x\\ \mathbf{else}:\\ \;\;\;\;{z}^{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.36e+122)
   (* (exp (* (- t) y)) x)
   (if (<= y 2.55e+101) (* (exp (* (- (- z) b) a)) x) (* (pow z y) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.36e+122) {
		tmp = exp((-t * y)) * x;
	} else if (y <= 2.55e+101) {
		tmp = exp(((-z - b) * a)) * x;
	} else {
		tmp = pow(z, y) * 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) :: tmp
    if (y <= (-1.36d+122)) then
        tmp = exp((-t * y)) * x
    else if (y <= 2.55d+101) then
        tmp = exp(((-z - b) * a)) * x
    else
        tmp = (z ** y) * 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 tmp;
	if (y <= -1.36e+122) {
		tmp = Math.exp((-t * y)) * x;
	} else if (y <= 2.55e+101) {
		tmp = Math.exp(((-z - b) * a)) * x;
	} else {
		tmp = Math.pow(z, y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.36e+122:
		tmp = math.exp((-t * y)) * x
	elif y <= 2.55e+101:
		tmp = math.exp(((-z - b) * a)) * x
	else:
		tmp = math.pow(z, y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.36e+122)
		tmp = Float64(exp(Float64(Float64(-t) * y)) * x);
	elseif (y <= 2.55e+101)
		tmp = Float64(exp(Float64(Float64(Float64(-z) - b) * a)) * x);
	else
		tmp = Float64((z ^ y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.36e+122)
		tmp = exp((-t * y)) * x;
	elseif (y <= 2.55e+101)
		tmp = exp(((-z - b) * a)) * x;
	else
		tmp = (z ^ y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.36e+122], N[(N[Exp[N[((-t) * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 2.55e+101], N[(N[Exp[N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.36000000000000004e122

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 66.6

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

   4. Applied rewrites 66.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.6

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

   6. Applied rewrites 66.6%

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

   if -1.36000000000000004e122 < y < 2.54999999999999997e101

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 70.5

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

   4. Applied rewrites 70.5%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 75.0

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

   7. Applied rewrites 75.0%

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

   if 2.54999999999999997e101 < y

   1. Initial program 98.4%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 92.9

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

   4. Applied rewrites 92.9%

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

   5. Taylor expanded in t around 0

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

      1. lower-pow.f64 70.7

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

   7. Applied rewrites 70.7%

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

Alternative 7: 72.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+53}:\\ \;\;\;\;e^{\left(-t\right) \cdot y} \cdot x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;e^{\left(-a\right) \cdot b} \cdot x\\ \mathbf{else}:\\ \;\;\;\;{z}^{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.5e+53)
   (* (exp (* (- t) y)) x)
   (if (<= y 4.2e+15) (* (exp (* (- a) b)) x) (* (pow z y) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.5e+53) {
		tmp = exp((-t * y)) * x;
	} else if (y <= 4.2e+15) {
		tmp = exp((-a * b)) * x;
	} else {
		tmp = pow(z, y) * 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) :: tmp
    if (y <= (-7.5d+53)) then
        tmp = exp((-t * y)) * x
    else if (y <= 4.2d+15) then
        tmp = exp((-a * b)) * x
    else
        tmp = (z ** y) * 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 tmp;
	if (y <= -7.5e+53) {
		tmp = Math.exp((-t * y)) * x;
	} else if (y <= 4.2e+15) {
		tmp = Math.exp((-a * b)) * x;
	} else {
		tmp = Math.pow(z, y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.5e+53:
		tmp = math.exp((-t * y)) * x
	elif y <= 4.2e+15:
		tmp = math.exp((-a * b)) * x
	else:
		tmp = math.pow(z, y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.5e+53)
		tmp = Float64(exp(Float64(Float64(-t) * y)) * x);
	elseif (y <= 4.2e+15)
		tmp = Float64(exp(Float64(Float64(-a) * b)) * x);
	else
		tmp = Float64((z ^ y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.5e+53)
		tmp = exp((-t * y)) * x;
	elseif (y <= 4.2e+15)
		tmp = exp((-a * b)) * x;
	else
		tmp = (z ^ y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.5e+53], N[(N[Exp[N[((-t) * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 4.2e+15], N[(N[Exp[N[((-a) * b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999997e53

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 64.3

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

   4. Applied rewrites 64.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 64.3

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

   6. Applied rewrites 64.3%

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

   if -7.4999999999999997e53 < y < 4.2e15

   1. Initial program 95.6%

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

   2. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 76.5

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

   4. Applied rewrites 76.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 76.5

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

   6. Applied rewrites 76.5%

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

   if 4.2e15 < y

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 89.6

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

   4. Applied rewrites 89.6%

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

   5. Taylor expanded in t around 0

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

      1. lower-pow.f64 69.4

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

   7. Applied rewrites 69.4%

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

Alternative 8: 72.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{\left(-t\right) \cdot y} \cdot x\\ \mathbf{if}\;t \leq -6 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-25}:\\ \;\;\;\;e^{\left(-a\right) \cdot b} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (exp (* (- t) y)) x)))
   (if (<= t -6e+21) t_1 (if (<= t 1.7e-25) (* (exp (* (- a) b)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp((-t * y)) * x;
	double tmp;
	if (t <= -6e+21) {
		tmp = t_1;
	} else if (t <= 1.7e-25) {
		tmp = exp((-a * b)) * 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 = exp((-t * y)) * x
    if (t <= (-6d+21)) then
        tmp = t_1
    else if (t <= 1.7d-25) then
        tmp = exp((-a * b)) * 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 = Math.exp((-t * y)) * x;
	double tmp;
	if (t <= -6e+21) {
		tmp = t_1;
	} else if (t <= 1.7e-25) {
		tmp = Math.exp((-a * b)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp((-t * y)) * x
	tmp = 0
	if t <= -6e+21:
		tmp = t_1
	elif t <= 1.7e-25:
		tmp = math.exp((-a * b)) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(-t) * y)) * x)
	tmp = 0.0
	if (t <= -6e+21)
		tmp = t_1;
	elseif (t <= 1.7e-25)
		tmp = Float64(exp(Float64(Float64(-a) * b)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp((-t * y)) * x;
	tmp = 0.0;
	if (t <= -6e+21)
		tmp = t_1;
	elseif (t <= 1.7e-25)
		tmp = exp((-a * b)) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Exp[N[((-t) * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -6e+21], t$95$1, If[LessEqual[t, 1.7e-25], N[(N[Exp[N[((-a) * b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6e21 or 1.70000000000000001e-25 < t

   1. Initial program 96.8%

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

   2. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 77.7

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

   4. Applied rewrites 77.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 77.7

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

   6. Applied rewrites 77.7%

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

   if -6e21 < t < 1.70000000000000001e-25

   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 b around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 66.9

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

   4. Applied rewrites 66.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.9

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

   6. Applied rewrites 66.9%

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

Alternative 9: 58.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+112}:\\ \;\;\;\;\left(\left(\log z - t\right) \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;e^{\left(-a\right) \cdot b} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.62e+112) (* (* (- (log z) t) y) x) (* (exp (* (- a) b)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.62e+112) {
		tmp = ((log(z) - t) * y) * x;
	} else {
		tmp = exp((-a * b)) * 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) :: tmp
    if (y <= (-1.62d+112)) then
        tmp = ((log(z) - t) * y) * x
    else
        tmp = exp((-a * b)) * 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 tmp;
	if (y <= -1.62e+112) {
		tmp = ((Math.log(z) - t) * y) * x;
	} else {
		tmp = Math.exp((-a * b)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.62e+112:
		tmp = ((math.log(z) - t) * y) * x
	else:
		tmp = math.exp((-a * b)) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.62e+112)
		tmp = Float64(Float64(Float64(log(z) - t) * y) * x);
	else
		tmp = Float64(exp(Float64(Float64(-a) * b)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.62e+112)
		tmp = ((log(z) - t) * y) * x;
	else
		tmp = exp((-a * b)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.62e+112], N[(N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y), $MachinePrecision] * x), $MachinePrecision], N[(N[Exp[N[((-a) * b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.61999999999999994e112

   1. Initial program 97.7%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 91.8

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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 38.0

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

   7. Applied rewrites 38.0%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. lift--.f64 38.0

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

   10. Applied rewrites 38.0%

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

   if -1.61999999999999994e112 < y

   1. Initial program 96.5%

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

   2. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 62.9

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

   4. Applied rewrites 62.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 62.9

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

   6. Applied rewrites 62.9%

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

Alternative 10: 36.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;\left(\left(\log z - t\right) \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\left(-z\right) - b, a, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-a\right) \cdot b\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5e+38)
   (* (* (- (log z) t) y) x)
   (if (<= y 1.8e-39) (* (fma (- (- z) b) a 1.0) x) (* (* (- a) b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5e+38) {
		tmp = ((log(z) - t) * y) * x;
	} else if (y <= 1.8e-39) {
		tmp = fma((-z - b), a, 1.0) * x;
	} else {
		tmp = (-a * b) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5e+38)
		tmp = Float64(Float64(Float64(log(z) - t) * y) * x);
	elseif (y <= 1.8e-39)
		tmp = Float64(fma(Float64(Float64(-z) - b), a, 1.0) * x);
	else
		tmp = Float64(Float64(Float64(-a) * b) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5e+38], N[(N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.8e-39], N[(N[(N[((-z) - b), $MachinePrecision] * a + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[((-a) * b), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999997e38

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 90.4

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

   4. Applied rewrites 90.4%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 33.1

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

   7. Applied rewrites 33.1%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. lift--.f64 33.1

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

   10. Applied rewrites 33.1%

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

   if -4.9999999999999997e38 < y < 1.8e-39

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 79.7

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

   4. Applied rewrites 79.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 42.8

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

   7. Applied rewrites 42.8%

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

   8. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 43.4

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

   10. Applied rewrites 43.4%

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

   if 1.8e-39 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 40.4

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

   4. Applied rewrites 40.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 13.4

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

   7. Applied rewrites 13.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot b\right)\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot b\right)\right) \cdot x \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      4. lift-neg.f64 25.3

         \[\leadsto \left(\left(-a\right) \cdot b\right) \cdot x \]

   10. Applied rewrites 25.3%

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

Alternative 11: 34.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\left(\log z \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\left(-z\right) - b, a, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-a\right) \cdot b\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1e+109)
   (* (* (log z) y) x)
   (if (<= y 1.8e-39) (* (fma (- (- z) b) a 1.0) x) (* (* (- a) b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1e+109) {
		tmp = (log(z) * y) * x;
	} else if (y <= 1.8e-39) {
		tmp = fma((-z - b), a, 1.0) * x;
	} else {
		tmp = (-a * b) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1e+109)
		tmp = Float64(Float64(log(z) * y) * x);
	elseif (y <= 1.8e-39)
		tmp = Float64(fma(Float64(Float64(-z) - b), a, 1.0) * x);
	else
		tmp = Float64(Float64(Float64(-a) * b) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1e+109], N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.8e-39], N[(N[(N[((-z) - b), $MachinePrecision] * a + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[((-a) * b), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999982e108

   1. Initial program 97.7%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 91.6

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

   4. Applied rewrites 91.6%

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

   5. Taylor expanded in t around 0

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

      1. lower-pow.f64 69.5

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

   7. Applied rewrites 69.5%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 29.4

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

   10. Applied rewrites 29.4%

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

   11. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lift-log.f64 29.4

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

   13. Applied rewrites 29.4%

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

   if -9.99999999999999982e108 < y < 1.8e-39

   1. Initial program 95.8%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 75.4

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 39.8

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

   7. Applied rewrites 39.8%

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

   8. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 40.4

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

   10. Applied rewrites 40.4%

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

   if 1.8e-39 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 40.4

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

   4. Applied rewrites 40.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 13.4

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

   7. Applied rewrites 13.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot b\right)\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot b\right)\right) \cdot x \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      4. lift-neg.f64 25.3

         \[\leadsto \left(\left(-a\right) \cdot b\right) \cdot x \]

   10. Applied rewrites 25.3%

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

Alternative 12: 33.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(-t, y, 1\right) \cdot x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\left(-z\right) - b, a, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-a\right) \cdot b\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5e+38)
   (* (fma (- t) y 1.0) x)
   (if (<= y 1.8e-39) (* (fma (- (- z) b) a 1.0) x) (* (* (- a) b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5e+38) {
		tmp = fma(-t, y, 1.0) * x;
	} else if (y <= 1.8e-39) {
		tmp = fma((-z - b), a, 1.0) * x;
	} else {
		tmp = (-a * b) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5e+38)
		tmp = Float64(fma(Float64(-t), y, 1.0) * x);
	elseif (y <= 1.8e-39)
		tmp = Float64(fma(Float64(Float64(-z) - b), a, 1.0) * x);
	else
		tmp = Float64(Float64(Float64(-a) * b) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5e+38], N[(N[((-t) * y + 1.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.8e-39], N[(N[(N[((-z) - b), $MachinePrecision] * a + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[((-a) * b), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999997e38

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 90.4

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

   4. Applied rewrites 90.4%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 33.1

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

   7. Applied rewrites 33.1%

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

   8. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 21.4

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

   10. Applied rewrites 21.4%

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

   if -4.9999999999999997e38 < y < 1.8e-39

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 79.7

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

   4. Applied rewrites 79.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 42.8

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

   7. Applied rewrites 42.8%

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

   8. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 43.4

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

   10. Applied rewrites 43.4%

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

   if 1.8e-39 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 40.4

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

   4. Applied rewrites 40.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 13.4

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

   7. Applied rewrites 13.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot b\right)\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot b\right)\right) \cdot x \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      4. lift-neg.f64 25.3

         \[\leadsto \left(\left(-a\right) \cdot b\right) \cdot x \]

   10. Applied rewrites 25.3%

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

Alternative 13: 33.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(-t, y, 1\right) \cdot x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(-b, a, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-a\right) \cdot b\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.65e+37)
   (* (fma (- t) y 1.0) x)
   (if (<= y 1.8e-39) (* (fma (- b) a 1.0) x) (* (* (- a) b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.65e+37) {
		tmp = fma(-t, y, 1.0) * x;
	} else if (y <= 1.8e-39) {
		tmp = fma(-b, a, 1.0) * x;
	} else {
		tmp = (-a * b) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.65e+37)
		tmp = Float64(fma(Float64(-t), y, 1.0) * x);
	elseif (y <= 1.8e-39)
		tmp = Float64(fma(Float64(-b), a, 1.0) * x);
	else
		tmp = Float64(Float64(Float64(-a) * b) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.65e+37], N[(N[((-t) * y + 1.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.8e-39], N[(N[((-b) * a + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[((-a) * b), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e37

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 90.5

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

   4. Applied rewrites 90.5%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 33.0

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

   7. Applied rewrites 33.0%

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

   8. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 21.3

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

   10. Applied rewrites 21.3%

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

   if -1.65e37 < y < 1.8e-39

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 79.7

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

   4. Applied rewrites 79.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 42.9

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

   7. Applied rewrites 42.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(-1 \cdot b, a, 1\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(b\right), a, 1\right) \cdot x \]

      2. lower-neg.f64 42.8

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

   10. Applied rewrites 42.8%

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

   if 1.8e-39 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 40.4

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

   4. Applied rewrites 40.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 13.4

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

   7. Applied rewrites 13.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot b\right)\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot b\right)\right) \cdot x \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      4. lift-neg.f64 25.3

         \[\leadsto \left(\left(-a\right) \cdot b\right) \cdot x \]

   10. Applied rewrites 25.3%

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

Alternative 14: 33.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-a\right) \cdot b\right) \cdot x\\ t_2 := y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)\\ \mathbf{if}\;t\_2 \leq -4000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+301}:\\ \;\;\;\;\mathsf{fma}\left(-t, y, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (- a) b) x))
        (t_2 (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
   (if (<= t_2 -4000000000000.0)
     t_1
     (if (<= t_2 1e+301) (* (fma (- t) y 1.0) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-a * b) * x;
	double t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	double tmp;
	if (t_2 <= -4000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+301) {
		tmp = fma(-t, y, 1.0) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(-a) * b) * x)
	t_2 = Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))
	tmp = 0.0
	if (t_2 <= -4000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+301)
		tmp = Float64(fma(Float64(-t), y, 1.0) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[((-a) * b), $MachinePrecision] * x), $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]}, If[LessEqual[t$95$2, -4000000000000.0], t$95$1, If[LessEqual[t$95$2, 1e+301], N[(N[((-t) * y + 1.0), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

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))) < -4e12 or 1.00000000000000005e301 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 55.2

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

   4. Applied rewrites 55.2%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 15.2

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

   7. Applied rewrites 15.2%

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

   8. Taylor expanded in b around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot b\right)\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot b\right)\right) \cdot x \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      4. lift-neg.f64 26.3

         \[\leadsto \left(\left(-a\right) \cdot b\right) \cdot x \]

   10. Applied rewrites 26.3%

       \[\leadsto \left(\left(-a\right) \cdot b\right) \cdot x \]

   if -4e12 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < 1.00000000000000005e301

   1. Initial program 95.6%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 76.8

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

   4. Applied rewrites 76.8%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 46.5

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

   7. Applied rewrites 46.5%

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

   8. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 41.5

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

   10. Applied rewrites 41.5%

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

Alternative 15: 32.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-a\right) \cdot b\right) \cdot x\\ t_2 := y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)\\ \mathbf{if}\;t\_2 \leq -4000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (- a) b) x))
        (t_2 (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
   (if (<= t_2 -4000000000000.0) t_1 (if (<= t_2 2e+153) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-a * b) * x;
	double t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	double tmp;
	if (t_2 <= -4000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+153) {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = (-a * b) * x
    t_2 = (y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))
    if (t_2 <= (-4000000000000.0d0)) then
        tmp = t_1
    else if (t_2 <= 2d+153) then
        tmp = 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 = (-a * b) * x;
	double t_2 = (y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b));
	double tmp;
	if (t_2 <= -4000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+153) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-a * b) * x
	t_2 = (y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))
	tmp = 0
	if t_2 <= -4000000000000.0:
		tmp = t_1
	elif t_2 <= 2e+153:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(-a) * b) * x)
	t_2 = Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))
	tmp = 0.0
	if (t_2 <= -4000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 2e+153)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-a * b) * x;
	t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	tmp = 0.0;
	if (t_2 <= -4000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 2e+153)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[((-a) * b), $MachinePrecision] * x), $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]}, If[LessEqual[t$95$2, -4000000000000.0], t$95$1, If[LessEqual[t$95$2, 2e+153], x, t$95$1]]]]

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))) < -4e12 or 2e153 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 54.3

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

   4. Applied rewrites 54.3%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

         \[\leadsto \left(a \cdot \left(\log \left(1 - z\right) - b\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log \left(1 - z\right) - b\right) \cdot a + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 16.1

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

   7. Applied rewrites 16.1%

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

   8. Taylor expanded in b around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot b\right)\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot b\right)\right) \cdot x \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(a\right)\right) \cdot b\right) \cdot x \]

      4. lift-neg.f64 24.5

         \[\leadsto \left(\left(-a\right) \cdot b\right) \cdot x \]

   10. Applied rewrites 24.5%

       \[\leadsto \left(\left(-a\right) \cdot b\right) \cdot x \]

   if -4e12 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < 2e153

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 51.1%

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

Alternative 16: 31.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-t\right) \cdot y\right) \cdot x\\ t_2 := y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)\\ \mathbf{if}\;t\_2 \leq -4000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+184}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (- t) y) x))
        (t_2 (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
   (if (<= t_2 -4000000000000.0) t_1 (if (<= t_2 1e+184) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-t * y) * x;
	double t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	double tmp;
	if (t_2 <= -4000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+184) {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = (-t * y) * x
    t_2 = (y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))
    if (t_2 <= (-4000000000000.0d0)) then
        tmp = t_1
    else if (t_2 <= 1d+184) then
        tmp = 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 = (-t * y) * x;
	double t_2 = (y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b));
	double tmp;
	if (t_2 <= -4000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+184) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-t * y) * x
	t_2 = (y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))
	tmp = 0
	if t_2 <= -4000000000000.0:
		tmp = t_1
	elif t_2 <= 1e+184:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(-t) * y) * x)
	t_2 = Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))
	tmp = 0.0
	if (t_2 <= -4000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+184)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-t * y) * x;
	t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	tmp = 0.0;
	if (t_2 <= -4000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+184)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[((-t) * y), $MachinePrecision] * x), $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]}, If[LessEqual[t$95$2, -4000000000000.0], t$95$1, If[LessEqual[t$95$2, 1e+184], x, t$95$1]]]]

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))) < -4e12 or 1.00000000000000002e184 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 69.1

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

   4. Applied rewrites 69.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 18.2

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

   7. Applied rewrites 18.2%

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

   8. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-neg-out N/A

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

      3. lift-neg.f64 N/A

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

      4. lift-*.f64 23.3

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

   10. Applied rewrites 23.3%

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

   if -4e12 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < 1.00000000000000002e184

   1. Initial program 94.1%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 46.9%

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

Alternative 17: 18.7% accurate, 42.1× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return 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 = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

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

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower-exp.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lift-log.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lift--.f64 59.3

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

4. Applied rewrites 59.3%

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

5. Taylor expanded in a around 0

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

7. Applied rewrites 18.7%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025120 
(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))))))