Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2

Percentage Accurate: 88.9% → 99.5%

Time: 12.9s

Alternatives: 18

Speedup: 1.8×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * 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 - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * 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 - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

3. Taylor expanded in y around 0

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

   1. associate--l+ N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. +-commutative N/A

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

   5. associate-*r* N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lift--.f64 N/A

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

   9. mul-1-neg N/A

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

   10. lower-neg.f64 N/A

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

   11. lift--.f64 N/A

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

   12. lower--.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. lift-log.f64 N/A

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

   15. lift--.f64 99.5

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

5. Applied rewrites 99.5%

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

Alternative 2: 85.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x - t\\ t_2 := \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 111:\\ \;\;\;\;\mathsf{fma}\left(1 - z, y, -t\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* (log y) x) t))
        (t_2 (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)))
   (if (<= t_2 -5e+41)
     t_1
     (if (<= t_2 111.0)
       (fma (- 1.0 z) y (- t))
       (if (<= t_2 2e+29) (- (- (log y)) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (log(y) * x) - t;
	double t_2 = (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
	double tmp;
	if (t_2 <= -5e+41) {
		tmp = t_1;
	} else if (t_2 <= 111.0) {
		tmp = fma((1.0 - z), y, -t);
	} else if (t_2 <= 2e+29) {
		tmp = -log(y) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(log(y) * x) - t)
	t_2 = Float64(Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * log(Float64(1.0 - y)))) - t)
	tmp = 0.0
	if (t_2 <= -5e+41)
		tmp = t_1;
	elseif (t_2 <= 111.0)
		tmp = fma(Float64(1.0 - z), y, Float64(-t));
	elseif (t_2 <= 2e+29)
		tmp = Float64(Float64(-log(y)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+41], t$95$1, If[LessEqual[t$95$2, 111.0], N[(N[(1.0 - z), $MachinePrecision] * y + (-t)), $MachinePrecision], If[LessEqual[t$95$2, 2e+29], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) t) < -5.00000000000000022e41 or 1.99999999999999983e29 < (-.f64 (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) t)

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 92.7

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

   5. Applied rewrites 92.7%

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

   if -5.00000000000000022e41 < (-.f64 (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) t) < 111

   1. Initial program 73.0%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.0

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, t \cdot \left(\frac{\log y \cdot \left(x - 1\right)}{t} - 1\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 97.4

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

   8. Applied rewrites 97.4%

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

   9. Taylor expanded in y around 0

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

       1. lower--.f64 97.0

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

   11. Applied rewrites 97.0%

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

   12. Taylor expanded in t around inf

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 47.3

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

   14. Applied rewrites 47.3%

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

   if 111 < (-.f64 (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) t) < 1.99999999999999983e29

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   8. Applied rewrites 94.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \log y - t \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

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

       2. lift-log.f64 N/A

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

       3. lift-neg.f64 73.4

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

   11. Applied rewrites 73.4%

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

Alternative 3: 99.5% accurate, 1.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * (((-0.5 * y) - 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 - 1.0d0) * log(y)) + ((z - 1.0d0) * ((((-0.5d0) * y) - 1.0d0) * y))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-*.f64 99.5

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(-0.5 \cdot y - 1\right) \cdot y\right)\right) - t \]

5. Applied rewrites 99.5%

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

Alternative 4: 88.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+285}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, -t\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(x - 1, \log y, -t\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+247}:\\ \;\;\;\;\left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - z, y, \log y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+285)
   (fma (fma (* -0.5 y) (- z 1.0) (- (- z 1.0))) y (- t))
   (if (<= z 8.5e+159)
     (fma (- x 1.0) (log y) (- t))
     (if (<= z 7.8e+247)
       (- (* (* (- (* -0.5 y) 1.0) z) y) t)
       (fma (- 1.0 z) y (* (log y) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+285) {
		tmp = fma(fma((-0.5 * y), (z - 1.0), -(z - 1.0)), y, -t);
	} else if (z <= 8.5e+159) {
		tmp = fma((x - 1.0), log(y), -t);
	} else if (z <= 7.8e+247) {
		tmp = ((((-0.5 * y) - 1.0) * z) * y) - t;
	} else {
		tmp = fma((1.0 - z), y, (log(y) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+285)
		tmp = fma(fma(Float64(-0.5 * y), Float64(z - 1.0), Float64(-Float64(z - 1.0))), y, Float64(-t));
	elseif (z <= 8.5e+159)
		tmp = fma(Float64(x - 1.0), log(y), Float64(-t));
	elseif (z <= 7.8e+247)
		tmp = Float64(Float64(Float64(Float64(Float64(-0.5 * y) - 1.0) * z) * y) - t);
	else
		tmp = fma(Float64(1.0 - z), y, Float64(log(y) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e+285], N[(N[(N[(-0.5 * y), $MachinePrecision] * N[(z - 1.0), $MachinePrecision] + (-N[(z - 1.0), $MachinePrecision])), $MachinePrecision] * y + (-t)), $MachinePrecision], If[LessEqual[z, 8.5e+159], N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision] + (-t)), $MachinePrecision], If[LessEqual[z, 7.8e+247], N[(N[(N[(N[(N[(-0.5 * y), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision] - t), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * y + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.9999999999999998e284

   1. Initial program 56.4%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.5

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, -1 \cdot t\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lift-neg.f64 62.2

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

   8. Applied rewrites 62.2%

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

   if -9.9999999999999998e284 < z < 8.50000000000000076e159

   1. Initial program 93.5%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate--l+ N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-log.f64 N/A

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

      14. lower--.f64 N/A

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

   4. Applied rewrites 93.5%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 92.6

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

   7. Applied rewrites 92.6%

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

   if 8.50000000000000076e159 < z < 7.80000000000000003e247

   1. Initial program 70.1%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.2

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   8. Applied rewrites 68.3%

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

   9. Taylor expanded in z around inf

      \[\leadsto y \cdot \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right) - t \]
   10. Step-by-step derivation

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. lower--.f64 N/A

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

       6. lower-*.f64 59.3

          \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y - t \]

   11. Applied rewrites 59.3%

       \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y - t \]

   if 7.80000000000000003e247 < z

   1. Initial program 50.4%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.2

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, t \cdot \left(\frac{\log y \cdot \left(x - 1\right)}{t} - 1\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 89.4

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

   8. Applied rewrites 89.4%

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

   9. Taylor expanded in y around 0

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

       1. lower--.f64 88.7

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

   11. Applied rewrites 88.7%

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

   12. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lift-log.f64 73.9

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

   14. Applied rewrites 73.9%

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

Alternative 5: 73.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -9 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, -t\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-14}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{+151}:\\ \;\;\;\;\left(-y\right) \cdot z - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -9e+162)
     t_1
     (if (<= x -2.9e-27)
       (fma (fma (* -0.5 y) (- z 1.0) (- (- z 1.0))) y (- t))
       (if (<= x 2.9e-14)
         (- (- (log y)) t)
         (if (<= x 1.28e+151) (- (* (- y) z) t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -9e+162) {
		tmp = t_1;
	} else if (x <= -2.9e-27) {
		tmp = fma(fma((-0.5 * y), (z - 1.0), -(z - 1.0)), y, -t);
	} else if (x <= 2.9e-14) {
		tmp = -log(y) - t;
	} else if (x <= 1.28e+151) {
		tmp = (-y * z) - 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 <= -9e+162)
		tmp = t_1;
	elseif (x <= -2.9e-27)
		tmp = fma(fma(Float64(-0.5 * y), Float64(z - 1.0), Float64(-Float64(z - 1.0))), y, Float64(-t));
	elseif (x <= 2.9e-14)
		tmp = Float64(Float64(-log(y)) - t);
	elseif (x <= 1.28e+151)
		tmp = Float64(Float64(Float64(-y) * z) - 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, -9e+162], t$95$1, If[LessEqual[x, -2.9e-27], N[(N[(N[(-0.5 * y), $MachinePrecision] * N[(z - 1.0), $MachinePrecision] + (-N[(z - 1.0), $MachinePrecision])), $MachinePrecision] * y + (-t)), $MachinePrecision], If[LessEqual[x, 2.9e-14], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision], If[LessEqual[x, 1.28e+151], N[(N[((-y) * z), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.99999999999999944e162 or 1.28000000000000006e151 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -8.99999999999999944e162 < x < -2.90000000000000004e-27

   1. Initial program 87.9%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.5

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, -1 \cdot t\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lift-neg.f64 48.6

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

   8. Applied rewrites 48.6%

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

   if -2.90000000000000004e-27 < x < 2.9000000000000003e-14

   1. Initial program 84.5%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   8. Applied rewrites 99.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \log y - t \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

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

       2. lift-log.f64 N/A

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

       3. lift-neg.f64 83.0

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

   11. Applied rewrites 83.0%

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

   if 2.9000000000000003e-14 < x < 1.28000000000000006e151

   1. Initial program 87.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 99.2

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lift-neg.f64 47.8

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

   8. Applied rewrites 47.8%

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

Alternative 6: 97.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, \log y \cdot x\right) - t\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(1 - z, y, \left(-\log y\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (fma (- y) z (* (log y) x)) t)))
   (if (<= x -6.5e+31)
     t_1
     (if (<= x 2.9e-14) (fma (- 1.0 z) y (- (- (log y)) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(-y, z, (log(y) * x)) - t;
	double tmp;
	if (x <= -6.5e+31) {
		tmp = t_1;
	} else if (x <= 2.9e-14) {
		tmp = fma((1.0 - z), y, (-log(y) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(Float64(-y), z, Float64(log(y) * x)) - t)
	tmp = 0.0
	if (x <= -6.5e+31)
		tmp = t_1;
	elseif (x <= 2.9e-14)
		tmp = fma(Float64(1.0 - z), y, Float64(Float64(-log(y)) - t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-y) * z + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[x, -6.5e+31], t$95$1, If[LessEqual[x, 2.9e-14], N[(N[(1.0 - z), $MachinePrecision] * y + N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000004e31 or 2.9000000000000003e-14 < x

   1. Initial program 93.5%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 98.0%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 98.0%

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

   if -6.5000000000000004e31 < x < 2.9000000000000003e-14

   1. Initial program 84.6%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, t \cdot \left(\frac{\log y \cdot \left(x - 1\right)}{t} - 1\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 98.8

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

   8. Applied rewrites 98.8%

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

   9. Taylor expanded in y around 0

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

       1. lower--.f64 98.4

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

   11. Applied rewrites 98.4%

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

   12. Taylor expanded in x around 0

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

       1. lower--.f64 N/A

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

       2. mul-1-neg N/A

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

       3. lift-log.f64 N/A

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

       4. lift-neg.f64 96.5

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

   14. Applied rewrites 96.5%

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

Alternative 7: 94.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+31}:\\ \;\;\;\;\log y \cdot x - t\\ \mathbf{elif}\;x \leq 0.0265:\\ \;\;\;\;\mathsf{fma}\left(1 - z, y, \left(-\log y\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - 1, \log y, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.5e+31)
   (- (* (log y) x) t)
   (if (<= x 0.0265)
     (fma (- 1.0 z) y (- (- (log y)) t))
     (fma (- x 1.0) (log y) (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.5e+31) {
		tmp = (log(y) * x) - t;
	} else if (x <= 0.0265) {
		tmp = fma((1.0 - z), y, (-log(y) - t));
	} else {
		tmp = fma((x - 1.0), log(y), -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.5e+31)
		tmp = Float64(Float64(log(y) * x) - t);
	elseif (x <= 0.0265)
		tmp = fma(Float64(1.0 - z), y, Float64(Float64(-log(y)) - t));
	else
		tmp = fma(Float64(x - 1.0), log(y), Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.5e+31], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[x, 0.0265], N[(N[(1.0 - z), $MachinePrecision] * y + N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]), $MachinePrecision], N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision] + (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5000000000000004e31

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 93.0

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

   5. Applied rewrites 93.0%

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

   if -6.5000000000000004e31 < x < 0.0264999999999999993

   1. Initial program 84.5%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, t \cdot \left(\frac{\log y \cdot \left(x - 1\right)}{t} - 1\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 98.8

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

   8. Applied rewrites 98.8%

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

   9. Taylor expanded in y around 0

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

       1. lower--.f64 98.5

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

   11. Applied rewrites 98.5%

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

   12. Taylor expanded in x around 0

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

       1. lower--.f64 N/A

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

       2. mul-1-neg N/A

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

       3. lift-log.f64 N/A

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

       4. lift-neg.f64 96.2

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

   14. Applied rewrites 96.2%

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

   if 0.0264999999999999993 < x

   1. Initial program 93.8%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate--l+ N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-log.f64 N/A

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

      14. lower--.f64 N/A

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

   4. Applied rewrites 93.8%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 93.2

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

   7. Applied rewrites 93.2%

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

Alternative 8: 88.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, -t\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(x - 1, \log y, -t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (fma (* -0.5 y) (- z 1.0) (- (- z 1.0))) y (- t))))
   (if (<= z -1e+285)
     t_1
     (if (<= z 8.5e+159) (fma (- x 1.0) (log y) (- t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(fma((-0.5 * y), (z - 1.0), -(z - 1.0)), y, -t);
	double tmp;
	if (z <= -1e+285) {
		tmp = t_1;
	} else if (z <= 8.5e+159) {
		tmp = fma((x - 1.0), log(y), -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(fma(Float64(-0.5 * y), Float64(z - 1.0), Float64(-Float64(z - 1.0))), y, Float64(-t))
	tmp = 0.0
	if (z <= -1e+285)
		tmp = t_1;
	elseif (z <= 8.5e+159)
		tmp = fma(Float64(x - 1.0), log(y), Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(-0.5 * y), $MachinePrecision] * N[(z - 1.0), $MachinePrecision] + (-N[(z - 1.0), $MachinePrecision])), $MachinePrecision] * y + (-t)), $MachinePrecision]}, If[LessEqual[z, -1e+285], t$95$1, If[LessEqual[z, 8.5e+159], N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision] + (-t)), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999998e284 or 8.50000000000000076e159 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, -1 \cdot t\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lift-neg.f64 63.1

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

   8. Applied rewrites 63.1%

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

   if -9.9999999999999998e284 < z < 8.50000000000000076e159

   1. Initial program 93.5%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate--l+ N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-log.f64 N/A

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

      14. lower--.f64 N/A

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

   4. Applied rewrites 93.5%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 92.6

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

   7. Applied rewrites 92.6%

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

Alternative 9: 88.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, -t\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+159}:\\ \;\;\;\;\log y \cdot \left(x - 1\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (fma (* -0.5 y) (- z 1.0) (- (- z 1.0))) y (- t))))
   (if (<= z -1e+285)
     t_1
     (if (<= z 8.5e+159) (- (* (log y) (- x 1.0)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(fma((-0.5 * y), (z - 1.0), -(z - 1.0)), y, -t);
	double tmp;
	if (z <= -1e+285) {
		tmp = t_1;
	} else if (z <= 8.5e+159) {
		tmp = (log(y) * (x - 1.0)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(fma(Float64(-0.5 * y), Float64(z - 1.0), Float64(-Float64(z - 1.0))), y, Float64(-t))
	tmp = 0.0
	if (z <= -1e+285)
		tmp = t_1;
	elseif (z <= 8.5e+159)
		tmp = Float64(Float64(log(y) * Float64(x - 1.0)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(-0.5 * y), $MachinePrecision] * N[(z - 1.0), $MachinePrecision] + (-N[(z - 1.0), $MachinePrecision])), $MachinePrecision] * y + (-t)), $MachinePrecision]}, If[LessEqual[z, -1e+285], t$95$1, If[LessEqual[z, 8.5e+159], N[(N[(N[Log[y], $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999998e284 or 8.50000000000000076e159 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, -1 \cdot t\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lift-neg.f64 63.1

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

   8. Applied rewrites 63.1%

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

   if -9.9999999999999998e284 < z < 8.50000000000000076e159

   1. Initial program 93.5%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 92.6

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

   5. Applied rewrites 92.6%

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

Alternative 10: 99.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

3. Taylor expanded in y around 0

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

   1. associate-*r* N/A

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

   2. mul-1-neg N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-neg.f64 N/A

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

   5. lift--.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lift-log.f64 N/A

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

   8. lift--.f64 99.1

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

5. Applied rewrites 99.1%

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

Alternative 11: 60.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, -t\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+153}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (fma (* -0.5 y) (- z 1.0) (- (- z 1.0))) y (- t))))
   (if (<= z -7.2e+116) t_1 (if (<= z 1.15e+153) (- (- (log y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(fma((-0.5 * y), (z - 1.0), -(z - 1.0)), y, -t);
	double tmp;
	if (z <= -7.2e+116) {
		tmp = t_1;
	} else if (z <= 1.15e+153) {
		tmp = -log(y) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(fma(Float64(-0.5 * y), Float64(z - 1.0), Float64(-Float64(z - 1.0))), y, Float64(-t))
	tmp = 0.0
	if (z <= -7.2e+116)
		tmp = t_1;
	elseif (z <= 1.15e+153)
		tmp = Float64(Float64(-log(y)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(-0.5 * y), $MachinePrecision] * N[(z - 1.0), $MachinePrecision] + (-N[(z - 1.0), $MachinePrecision])), $MachinePrecision] * y + (-t)), $MachinePrecision]}, If[LessEqual[z, -7.2e+116], t$95$1, If[LessEqual[z, 1.15e+153], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999941e116 or 1.1500000000000001e153 < z

   1. Initial program 66.3%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.1

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, -1 \cdot t\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lift-neg.f64 61.0

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

   8. Applied rewrites 61.0%

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

   if -7.19999999999999941e116 < z < 1.1500000000000001e153

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.6

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   8. Applied rewrites 62.5%

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

   9. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \log y - t \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

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

       2. lift-log.f64 N/A

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

       3. lift-neg.f64 60.3

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

   11. Applied rewrites 60.3%

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

Alternative 12: 45.9% accurate, 8.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

3. Taylor expanded in y around 0

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

   1. associate--l+ N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. +-commutative N/A

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

   5. associate-*r* N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lift--.f64 N/A

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

   9. mul-1-neg N/A

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

   10. lower-neg.f64 N/A

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

   11. lift--.f64 N/A

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

   12. lower--.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. lift-log.f64 N/A

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

   15. lift--.f64 99.5

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

5. Applied rewrites 99.5%

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

6. Taylor expanded in t around inf

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, -1 \cdot t\right) \]
7. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. lift-neg.f64 45.9

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

8. Applied rewrites 45.9%

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, -t\right) \]
9. Add Preprocessing

Alternative 13: 45.7% accurate, 10.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((((-0.5 * y) - 1.0) * z) * 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 = (((((-0.5d0) * y) - 1.0d0) * z) * y) - t
end function

Java

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

Python

def code(x, y, z, t):
	return ((((-0.5 * y) - 1.0) * z) * y) - t

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((((-0.5 * y) - 1.0) * z) * y) - t;
end

Wolfram

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

Derivation

1. Initial program 88.9%

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

3. Taylor expanded in y around 0

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

   1. associate--l+ N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. +-commutative N/A

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

   5. associate-*r* N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lift--.f64 N/A

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

   9. mul-1-neg N/A

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

   10. lower-neg.f64 N/A

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

   11. lift--.f64 N/A

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

   12. lower--.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. lift-log.f64 N/A

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

   15. lift--.f64 99.5

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

5. Applied rewrites 99.5%

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

6. Taylor expanded in x around 0

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

   1. lower--.f64 N/A

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

8. Applied rewrites 64.2%

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

9. Taylor expanded in z around inf

   \[\leadsto y \cdot \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right) - t \]
10. Step-by-step derivation

    1. *-commutative N/A

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

    2. lower-*.f64 N/A

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

    3. *-commutative N/A

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

    4. lower-*.f64 N/A

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

    5. lower--.f64 N/A

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

    6. lower-*.f64 45.7

       \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y - t \]

11. Applied rewrites 45.7%

    \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y - t \]
12. Add Preprocessing

Alternative 14: 42.0% accurate, 10.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1860000000:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;\left(1 - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1860000000.0) (- t) (if (<= t 1.1e+44) (* (- 1.0 z) y) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1860000000.0) {
		tmp = -t;
	} else if (t <= 1.1e+44) {
		tmp = (1.0 - z) * y;
	} 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 <= (-1860000000.0d0)) then
        tmp = -t
    else if (t <= 1.1d+44) then
        tmp = (1.0d0 - z) * y
    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 <= -1860000000.0) {
		tmp = -t;
	} else if (t <= 1.1e+44) {
		tmp = (1.0 - z) * y;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1860000000.0:
		tmp = -t
	elif t <= 1.1e+44:
		tmp = (1.0 - z) * y
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1860000000.0)
		tmp = Float64(-t);
	elseif (t <= 1.1e+44)
		tmp = Float64(Float64(1.0 - z) * y);
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1860000000.0)
		tmp = -t;
	elseif (t <= 1.1e+44)
		tmp = (1.0 - z) * y;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1860000000.0], (-t), If[LessEqual[t, 1.1e+44], N[(N[(1.0 - z), $MachinePrecision] * y), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -1.86e9 or 1.09999999999999998e44 < t

   1. Initial program 95.0%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 70.4

         \[\leadsto -t \]

   5. Applied rewrites 70.4%

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

   if -1.86e9 < t < 1.09999999999999998e44

   1. Initial program 83.9%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. div-sub N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 10.2

          \[\leadsto \mathsf{fma}\left(-0.5, z - 1, \frac{1 - z}{y}\right) \cdot \left(y \cdot y\right) \]

   8. Applied rewrites 10.2%

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

   9. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lift--.f64 18.4

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

   11. Applied rewrites 18.4%

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

Alternative 15: 41.8% accurate, 11.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1860000000:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1860000000.0) (- t) (if (<= t 1.1e+44) (* (- z) y) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1860000000.0) {
		tmp = -t;
	} else if (t <= 1.1e+44) {
		tmp = -z * y;
	} 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 <= (-1860000000.0d0)) then
        tmp = -t
    else if (t <= 1.1d+44) then
        tmp = -z * y
    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 <= -1860000000.0) {
		tmp = -t;
	} else if (t <= 1.1e+44) {
		tmp = -z * y;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1860000000.0:
		tmp = -t
	elif t <= 1.1e+44:
		tmp = -z * y
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1860000000.0)
		tmp = Float64(-t);
	elseif (t <= 1.1e+44)
		tmp = Float64(Float64(-z) * y);
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1860000000.0)
		tmp = -t;
	elseif (t <= 1.1e+44)
		tmp = -z * y;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1860000000.0], (-t), If[LessEqual[t, 1.1e+44], N[((-z) * y), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -1.86e9 or 1.09999999999999998e44 < t

   1. Initial program 95.0%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 70.4

         \[\leadsto -t \]

   5. Applied rewrites 70.4%

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

   if -1.86e9 < t < 1.09999999999999998e44

   1. Initial program 83.9%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift--.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift-*.f64 18.2

         \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y \]

   8. Applied rewrites 18.2%

      \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot \color{blue}{y} \]

   9. Taylor expanded in y around 0

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 17.9

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

   11. Applied rewrites 17.9%

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

Alternative 16: 45.6% accurate, 18.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

3. Taylor expanded in y around 0

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

   1. associate--l+ N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. +-commutative N/A

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

   5. associate-*r* N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lift--.f64 N/A

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

   9. mul-1-neg N/A

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

   10. lower-neg.f64 N/A

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

   11. lift--.f64 N/A

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

   12. lower--.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. lift-log.f64 N/A

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

   15. lift--.f64 99.5

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

5. Applied rewrites 99.5%

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

6. Taylor expanded in t around inf

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, t \cdot \left(\frac{\log y \cdot \left(x - 1\right)}{t} - 1\right)\right) \]
7. Step-by-step derivation

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. associate-/l* N/A

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

   5. lower-*.f64 N/A

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

   6. lift-log.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. lift--.f64 87.8

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

8. Applied rewrites 87.8%

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

9. Taylor expanded in y around 0

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

    1. lower--.f64 87.5

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

11. Applied rewrites 87.5%

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

12. Taylor expanded in t around inf

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

    1. mul-1-neg N/A

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

    2. lower-neg.f64 45.6

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

14. Applied rewrites 45.6%

    \[\leadsto \mathsf{fma}\left(1 - z, y, -t\right) \]
15. Add Preprocessing

Alternative 17: 45.5% accurate, 20.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (-y * z) - 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 = (-y * z) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

3. Taylor expanded in y around 0

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

   1. associate-*r* N/A

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

   2. mul-1-neg N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-neg.f64 N/A

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

   5. lift--.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lift-log.f64 N/A

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

   8. lift--.f64 99.1

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

5. Applied rewrites 99.1%

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

6. Taylor expanded in z around inf

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

   1. associate-*r* N/A

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

   2. mul-1-neg N/A

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

   3. lower-*.f64 N/A

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

   4. lift-neg.f64 45.5

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

8. Applied rewrites 45.5%

   \[\leadsto \left(-y\right) \cdot \color{blue}{z} - t \]
9. Add Preprocessing

Alternative 18: 34.9% accurate, 75.3× 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 88.9%

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

3. Taylor expanded in t around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 34.9

      \[\leadsto -t \]

5. Applied rewrites 34.9%

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

Reproduce

herbie shell --seed 2025089 
(FPCore (x y z t)
  :name "Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2"
  :precision binary64
  (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))