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

Percentage Accurate: 85.3% → 99.5%

Time: 8.5s

Alternatives: 10

Speedup: 1.6×

Specification

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (fma (log y) x (* (* z (fma -0.5 y -1.0)) y)) t))

C

double code(double x, double y, double z, double t) {
	return fma(log(y), x, ((z * fma(-0.5, y, -1.0)) * y)) - t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(log(y), x, Float64(Float64(z * fma(-0.5, y, -1.0)) * y)) - t)
end

Wolfram

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

Derivation

1. Initial program 85.3%

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

2. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. remove-double-neg N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

   3. log-rec N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

   4. mul-1-neg N/A

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

   5. lower-fma.f64 N/A

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

   6. mul-1-neg N/A

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

   7. log-rec N/A

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

   8. remove-double-neg N/A

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

   9. lift-log.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

4. Applied rewrites 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]
5. Add Preprocessing

Alternative 2: 99.2% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

2. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. remove-double-neg N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

   3. log-rec N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

   4. mul-1-neg N/A

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

   5. lower-fma.f64 N/A

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

   6. mul-1-neg N/A

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

   7. log-rec N/A

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

   8. remove-double-neg N/A

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

   9. lift-log.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

4. Applied rewrites 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]

5. Taylor expanded in y around 0

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

   1. associate--l+ N/A

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

   2. *-lft-identity N/A

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

   3. cancel-sign-sub-inv N/A

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

   4. metadata-eval N/A

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

   5. mul-1-neg N/A

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

   6. lift-neg.f64 N/A

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

   7. lift-neg.f64 N/A

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

   8. associate--l+ N/A

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

7. Applied rewrites 99.2%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-log.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-fma.f64 N/A

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

   6. *-commutative N/A

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

   7. +-commutative N/A

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

   8. associate--r+ N/A

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

   9. *-lft-identity N/A

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

   10. metadata-eval N/A

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

   11. fp-cancel-sign-sub-inv N/A

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

   12. mul-1-neg N/A

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

   13. associate--l+ N/A

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

   14. *-commutative N/A

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

   15. fp-cancel-sub-sign N/A

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

   16. mul-1-neg N/A

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

   17. associate-*r* N/A

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

   18. mul-1-neg N/A

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

   19. distribute-lft-in N/A

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

   20. lower-fma.f64 N/A

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

   21. lift-log.f64 N/A

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

   22. mul-1-neg N/A

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

   23. +-commutative N/A

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

   24. *-commutative N/A

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

9. Applied rewrites 99.2%

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

Alternative 3: 99.2% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

2. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. remove-double-neg N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

   3. log-rec N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

   4. mul-1-neg N/A

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

   5. lower-fma.f64 N/A

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

   6. mul-1-neg N/A

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

   7. log-rec N/A

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

   8. remove-double-neg N/A

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

   9. lift-log.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

4. Applied rewrites 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]

5. Taylor expanded in y around 0

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

   1. associate--l+ N/A

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

   2. *-lft-identity N/A

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

   3. cancel-sign-sub-inv N/A

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

   4. metadata-eval N/A

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

   5. mul-1-neg N/A

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

   6. lift-neg.f64 N/A

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

   7. lift-neg.f64 N/A

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

   8. associate--l+ N/A

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

7. Applied rewrites 99.2%

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

Alternative 4: 89.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-89}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -t\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-28}:\\ \;\;\;\;t\_1 - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= t -1.45e-89)
     (fma (log y) x (- t))
     (if (<= t 1.22e-28) (- t_1 (* z y)) (- t_1 t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (t <= -1.45e-89) {
		tmp = fma(log(y), x, -t);
	} else if (t <= 1.22e-28) {
		tmp = t_1 - (z * y);
	} else {
		tmp = t_1 - t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (t <= -1.45e-89)
		tmp = fma(log(y), x, Float64(-t));
	elseif (t <= 1.22e-28)
		tmp = Float64(t_1 - Float64(z * y));
	else
		tmp = Float64(t_1 - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -1.45e-89], N[(N[Log[y], $MachinePrecision] * x + (-t)), $MachinePrecision], If[LessEqual[t, 1.22e-28], N[(t$95$1 - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.44999999999999996e-89

   1. Initial program 91.3%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      3. log-rec N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. log-rec N/A

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

      8. remove-double-neg N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   4. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]

   5. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-lft-identity N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. associate--l+ N/A

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

   7. Applied rewrites 99.3%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sign-sub-inv N/A

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

      12. mul-1-neg N/A

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

      13. associate--l+ N/A

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

      14. *-commutative N/A

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

      15. fp-cancel-sub-sign N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. mul-1-neg N/A

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

      19. distribute-lft-in N/A

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

      20. lower-fma.f64 N/A

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

      21. lift-log.f64 N/A

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

      22. mul-1-neg N/A

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

      23. +-commutative N/A

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

      24. *-commutative N/A

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

   9. Applied rewrites 99.3%

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

   10. Taylor expanded in y around 0

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

   12. Applied rewrites 90.4%

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

   if -1.44999999999999996e-89 < t < 1.22e-28

   1. Initial program 74.9%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      3. log-rec N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. log-rec N/A

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

      8. remove-double-neg N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   4. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]

   5. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-lft-identity N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. associate--l+ N/A

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

   7. Applied rewrites 98.9%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 87.2

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

   10. Applied rewrites 87.2%

       \[\leadsto \log y \cdot x - z \cdot \color{blue}{y} \]

   if 1.22e-28 < t

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} - t \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \log y \cdot \color{blue}{x} - t \]

      2. remove-double-neg N/A

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

      3. log-rec N/A

         \[\leadsto \left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x - t \]

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x - t \]

      7. log-rec N/A

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

      8. remove-double-neg N/A

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

      9. lift-log.f64 92.8

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

   4. Applied rewrites 92.8%

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

Alternative 5: 85.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+185}:\\ \;\;\;\;-\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e+185) (- (fma z y t)) (fma (log y) x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+185) {
		tmp = -fma(z, y, t);
	} else {
		tmp = fma(log(y), x, -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e+185)
		tmp = Float64(-fma(z, y, t));
	else
		tmp = fma(log(y), x, Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e+185], (-N[(z * y + t), $MachinePrecision]), N[(N[Log[y], $MachinePrecision] * x + (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999996e185

   1. Initial program 56.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      3. log-rec N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. log-rec N/A

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

      8. remove-double-neg N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   4. Applied rewrites 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]

   5. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-lft-identity N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. associate--l+ N/A

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

   7. Applied rewrites 98.4%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-neg.f64 N/A

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

      5. lift-fma.f64 71.7

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

   10. Applied rewrites 71.7%

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

   if -5.4999999999999996e185 < z

   1. Initial program 88.3%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      3. log-rec N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. log-rec N/A

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

      8. remove-double-neg N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   4. Applied rewrites 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]

   5. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-lft-identity N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. associate--l+ N/A

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

   7. Applied rewrites 99.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sign-sub-inv N/A

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

      12. mul-1-neg N/A

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

      13. associate--l+ N/A

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

      14. *-commutative N/A

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

      15. fp-cancel-sub-sign N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. mul-1-neg N/A

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

      19. distribute-lft-in N/A

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

      20. lower-fma.f64 N/A

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

      21. lift-log.f64 N/A

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

      22. mul-1-neg N/A

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

      23. +-commutative N/A

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

      24. *-commutative N/A

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

   9. Applied rewrites 99.2%

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

   10. Taylor expanded in y around 0

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

   12. Applied rewrites 87.4%

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

Alternative 6: 85.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+185}:\\ \;\;\;\;-\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e+185) (- (fma z y t)) (- (* (log y) x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+185) {
		tmp = -fma(z, y, t);
	} else {
		tmp = (log(y) * x) - t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e+185)
		tmp = Float64(-fma(z, y, t));
	else
		tmp = Float64(Float64(log(y) * x) - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e+185], (-N[(z * y + t), $MachinePrecision]), N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999996e185

   1. Initial program 56.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      3. log-rec N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. log-rec N/A

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

      8. remove-double-neg N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   4. Applied rewrites 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]

   5. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-lft-identity N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. associate--l+ N/A

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

   7. Applied rewrites 98.4%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-neg.f64 N/A

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

      5. lift-fma.f64 71.7

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

   10. Applied rewrites 71.7%

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

   if -5.4999999999999996e185 < z

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} - t \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \log y \cdot \color{blue}{x} - t \]

      2. remove-double-neg N/A

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

      3. log-rec N/A

         \[\leadsto \left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x - t \]

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x - t \]

      7. log-rec N/A

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

      8. remove-double-neg N/A

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

      9. lift-log.f64 87.4

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

   4. Applied rewrites 87.4%

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

Alternative 7: 77.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+88}:\\ \;\;\;\;-\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -8.5e+114) t_1 (if (<= x 2.3e+88) (- (fma z y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -8.5e+114) {
		tmp = t_1;
	} else if (x <= 2.3e+88) {
		tmp = -fma(z, y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -8.5e+114)
		tmp = t_1;
	elseif (x <= 2.3e+88)
		tmp = Float64(-fma(z, y, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -8.5e+114], t$95$1, If[LessEqual[x, 2.3e+88], (-N[(z * y + t), $MachinePrecision]), t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000001e114 or 2.3000000000000002e88 < x

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      2. remove-double-neg N/A

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

      3. log-rec N/A

         \[\leadsto \left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x \]

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x \]

      7. log-rec N/A

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

      8. remove-double-neg N/A

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

      9. lift-log.f64 81.1

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

   4. Applied rewrites 81.1%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if -8.5000000000000001e114 < x < 2.3000000000000002e88

   1. Initial program 79.3%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      3. log-rec N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. log-rec N/A

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

      8. remove-double-neg N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   4. Applied rewrites 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]

   5. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-lft-identity N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. associate--l+ N/A

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

   7. Applied rewrites 99.1%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-neg.f64 N/A

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

      5. lift-fma.f64 76.4

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

   10. Applied rewrites 76.4%

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

Alternative 8: 57.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ -\mathsf{fma}\left(z, y, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

2. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. remove-double-neg N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

   3. log-rec N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right) \cdot x + y \cdot \left(-1 \cdot z + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) - t \]

   4. mul-1-neg N/A

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

   5. lower-fma.f64 N/A

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

   6. mul-1-neg N/A

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

   7. log-rec N/A

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

   8. remove-double-neg N/A

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

   9. lift-log.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

4. Applied rewrites 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(z \cdot \mathsf{fma}\left(-0.5, y, -1\right)\right) \cdot y\right)} - t \]

5. Taylor expanded in y around 0

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

   1. associate--l+ N/A

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

   2. *-lft-identity N/A

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

   3. cancel-sign-sub-inv N/A

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

   4. metadata-eval N/A

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

   5. mul-1-neg N/A

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

   6. lift-neg.f64 N/A

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

   7. lift-neg.f64 N/A

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

   8. associate--l+ N/A

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

7. Applied rewrites 99.2%

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

8. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. lower-neg.f64 N/A

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

   5. lift-fma.f64 57.4

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

10. Applied rewrites 57.4%

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

Alternative 9: 48.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-89}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-28}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.45e-89) (- t) (if (<= t 1.22e-28) (* (- y) z) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e-89) {
		tmp = -t;
	} else if (t <= 1.22e-28) {
		tmp = -y * z;
	} else {
		tmp = -t;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.45d-89)) then
        tmp = -t
    else if (t <= 1.22d-28) then
        tmp = -y * z
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e-89) {
		tmp = -t;
	} else if (t <= 1.22e-28) {
		tmp = -y * z;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.45e-89:
		tmp = -t
	elif t <= 1.22e-28:
		tmp = -y * z
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.45e-89)
		tmp = Float64(-t);
	elseif (t <= 1.22e-28)
		tmp = Float64(Float64(-y) * z);
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.45e-89)
		tmp = -t;
	elseif (t <= 1.22e-28)
		tmp = -y * z;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.45e-89], (-t), If[LessEqual[t, 1.22e-28], N[((-y) * z), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999996e-89 or 1.22e-28 < t

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot t} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 62.8

         \[\leadsto -t \]

   4. Applied rewrites 62.8%

      \[\leadsto \color{blue}{-t} \]

   if -1.44999999999999996e-89 < t < 1.22e-28

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. lift--.f64 4.3

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

   4. Applied rewrites 4.3%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 27.1

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

   7. Applied rewrites 27.1%

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

Alternative 10: 42.9% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ -t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- t))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-t)

Derivation

1. Initial program 85.3%

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

2. Taylor expanded in t around inf

   \[\leadsto \color{blue}{-1 \cdot t} \]
3. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. lower-neg.f64 42.9

      \[\leadsto -t \]

4. Applied rewrites 42.9%

   \[\leadsto \color{blue}{-t} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B"
  :precision binary64
  (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))