Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 12.0s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (((x + y) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (((x + y) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (((x + y) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing

Alternative 2: 92.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(b, a - 0.5, y\right)\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (log t)) z (fma b (- a 0.5) y))))
   (if (<= z -1.8e+120)
     t_1
     (if (<= z 2.35e+51) (fma b (- a 0.5) (+ y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - log(t)), z, fma(b, (a - 0.5), y));
	double tmp;
	if (z <= -1.8e+120) {
		tmp = t_1;
	} else if (z <= 2.35e+51) {
		tmp = fma(b, (a - 0.5), (y + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - log(t)), z, fma(b, Float64(a - 0.5), y))
	tmp = 0.0
	if (z <= -1.8e+120)
		tmp = t_1;
	elseif (z <= 2.35e+51)
		tmp = fma(b, Float64(a - 0.5), Float64(y + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(b * N[(a - 0.5), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+120], t$95$1, If[LessEqual[z, 2.35e+51], N[(b * N[(a - 0.5), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000008e120 or 2.3500000000000001e51 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate--l+ N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

   4. Applied rewrites 87.5%

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

   if -1.80000000000000008e120 < z < 2.3500000000000001e51

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 94.8

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 94.8%

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

Alternative 3: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \log t\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, \mathsf{fma}\left(b, a, y\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, t\_1 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (log t))))
   (if (<= z -2.4e+120)
     (fma t_1 z (fma b a y))
     (if (<= z 1.55e+99)
       (fma b (- a 0.5) (+ y x))
       (fma (- a 0.5) b (* t_1 z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - log(t);
	double tmp;
	if (z <= -2.4e+120) {
		tmp = fma(t_1, z, fma(b, a, y));
	} else if (z <= 1.55e+99) {
		tmp = fma(b, (a - 0.5), (y + x));
	} else {
		tmp = fma((a - 0.5), b, (t_1 * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - log(t))
	tmp = 0.0
	if (z <= -2.4e+120)
		tmp = fma(t_1, z, fma(b, a, y));
	elseif (z <= 1.55e+99)
		tmp = fma(b, Float64(a - 0.5), Float64(y + x));
	else
		tmp = fma(Float64(a - 0.5), b, Float64(t_1 * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+120], N[(t$95$1 * z + N[(b * a + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+99], N[(b * N[(a - 0.5), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(N[(a - 0.5), $MachinePrecision] * b + N[(t$95$1 * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000001e120

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate--l+ N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

   4. Applied rewrites 90.3%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 84.0%

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

   if -2.40000000000000001e120 < z < 1.55e99

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 94.1

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 94.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   if 1.55e99 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-log.f64 77.1

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

   4. Applied rewrites 77.1%

      \[\leadsto \color{blue}{\left(1 - \log t\right) \cdot z} + \left(a - 0.5\right) \cdot b \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. *-rgt-identity N/A

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

      8. metadata-eval N/A

         \[\leadsto \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right) \cdot b + \left(1 - \log t\right) \cdot z \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right) \cdot -1\right)\right)} \cdot b + \left(1 - \log t\right) \cdot z \]

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

          \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right)\right)\right) \cdot -1\right)} \cdot b + \left(1 - \log t\right) \cdot z \]

      11. *-rgt-identity N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right)\right)\right) \cdot -1\right) \cdot \color{blue}{\left(b \cdot 1\right)} + \left(1 - \log t\right) \cdot z \]

      12. lower-fma.f64 N/A

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

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

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

      14. distribute-rgt-neg-in N/A

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

      15. metadata-eval N/A

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

      16. *-rgt-identity N/A

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

      17. lift--.f64 N/A

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

      18. *-rgt-identity 77.1

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

   6. Applied rewrites 77.1%

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

Alternative 4: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(b, a, y\right)\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (log t)) z (fma b a y))))
   (if (<= z -2.4e+120)
     t_1
     (if (<= z 1.3e+52) (fma b (- a 0.5) (+ y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - log(t)), z, fma(b, a, y));
	double tmp;
	if (z <= -2.4e+120) {
		tmp = t_1;
	} else if (z <= 1.3e+52) {
		tmp = fma(b, (a - 0.5), (y + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - log(t)), z, fma(b, a, y))
	tmp = 0.0
	if (z <= -2.4e+120)
		tmp = t_1;
	elseif (z <= 1.3e+52)
		tmp = fma(b, Float64(a - 0.5), Float64(y + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(b * a + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+120], t$95$1, If[LessEqual[z, 1.3e+52], N[(b * N[(a - 0.5), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000001e120 or 1.3e52 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate--l+ N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 79.9%

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

   if -2.40000000000000001e120 < z < 1.3e52

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 94.8

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 94.8%

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

Alternative 5: 87.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \log t, z, y + x\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (log t)) z (+ y x))))
   (if (<= z -1.6e+101)
     t_1
     (if (<= z 6.5e+116) (fma b (- a 0.5) (+ y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - log(t)), z, (y + x));
	double tmp;
	if (z <= -1.6e+101) {
		tmp = t_1;
	} else if (z <= 6.5e+116) {
		tmp = fma(b, (a - 0.5), (y + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - log(t)), z, Float64(y + x))
	tmp = 0.0
	if (z <= -1.6e+101)
		tmp = t_1;
	elseif (z <= 6.5e+116)
		tmp = fma(b, Float64(a - 0.5), Float64(y + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+101], t$95$1, If[LessEqual[z, 6.5e+116], N[(b * N[(a - 0.5), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000003e101 or 6.4999999999999998e116 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in b around 0

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

      1. associate-+l+ N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

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

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

      17. metadata-eval N/A

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

      18. *-lft-identity N/A

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

   4. Applied rewrites 73.5%

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

   if -1.60000000000000003e101 < z < 6.4999999999999998e116

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 94.1

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 94.1%

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

Alternative 6: 85.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+120}:\\ \;\;\;\;z - \left(\log t \cdot z - y\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.8e+120)
   (- z (- (* (log t) z) y))
   (if (<= z 2.8e+117) (fma b (- a 0.5) (+ y x)) (fma (- 1.0 (log t)) z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.8e+120) {
		tmp = z - ((log(t) * z) - y);
	} else if (z <= 2.8e+117) {
		tmp = fma(b, (a - 0.5), (y + x));
	} else {
		tmp = fma((1.0 - log(t)), z, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.8e+120)
		tmp = Float64(z - Float64(Float64(log(t) * z) - y));
	elseif (z <= 2.8e+117)
		tmp = fma(b, Float64(a - 0.5), Float64(y + x));
	else
		tmp = fma(Float64(1.0 - log(t)), z, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.8e+120], N[(z - N[(N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+117], N[(b * N[(a - 0.5), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000002e120

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate--l+ N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

   4. Applied rewrites 90.3%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 66.0%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. mul-1-neg N/A

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

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

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

      11. *-lft-identity N/A

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

      12. *-commutative N/A

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

      13. associate-+l- N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-log.f64 65.9

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

   9. Applied rewrites 65.9%

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

   if -4.80000000000000002e120 < z < 2.79999999999999997e117

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 93.6

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 93.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   if 2.79999999999999997e117 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate--l+ N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 61.0%

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

Alternative 7: 84.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \log t, z, y\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (log t)) z y)))
   (if (<= z -4.8e+120)
     t_1
     (if (<= z 2.8e+117) (fma b (- a 0.5) (+ y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - log(t)), z, y);
	double tmp;
	if (z <= -4.8e+120) {
		tmp = t_1;
	} else if (z <= 2.8e+117) {
		tmp = fma(b, (a - 0.5), (y + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - log(t)), z, y)
	tmp = 0.0
	if (z <= -4.8e+120)
		tmp = t_1;
	elseif (z <= 2.8e+117)
		tmp = fma(b, Float64(a - 0.5), Float64(y + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[z, -4.8e+120], t$95$1, If[LessEqual[z, 2.8e+117], N[(b * N[(a - 0.5), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000002e120 or 2.79999999999999997e117 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate--l+ N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

   4. Applied rewrites 89.0%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 63.4%

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

   if -4.80000000000000002e120 < z < 2.79999999999999997e117

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 93.6

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 93.6%

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

Alternative 8: 84.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \log t, z, x\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (log t)) z x)))
   (if (<= z -1.5e+198)
     t_1
     (if (<= z 9.5e+136) (fma b (- a 0.5) (+ y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - log(t)), z, x);
	double tmp;
	if (z <= -1.5e+198) {
		tmp = t_1;
	} else if (z <= 9.5e+136) {
		tmp = fma(b, (a - 0.5), (y + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - log(t)), z, x)
	tmp = 0.0
	if (z <= -1.5e+198)
		tmp = t_1;
	elseif (z <= 9.5e+136)
		tmp = fma(b, Float64(a - 0.5), Float64(y + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[z, -1.5e+198], t$95$1, If[LessEqual[z, 9.5e+136], N[(b * N[(a - 0.5), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000009e198 or 9.49999999999999907e136 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in b around 0

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

      1. associate-+l+ N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

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

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

      17. metadata-eval N/A

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

      18. *-lft-identity N/A

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 69.3%

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

   if -1.50000000000000009e198 < z < 9.49999999999999907e136

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 90.6

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 90.6%

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

Alternative 9: 83.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+198}:\\ \;\;\;\;z - \log t \cdot z\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.62e+198)
   (- z (* (log t) z))
   (if (<= z 1.32e+137) (fma b (- a 0.5) (+ y x)) (* (- 1.0 (log t)) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.62e+198) {
		tmp = z - (log(t) * z);
	} else if (z <= 1.32e+137) {
		tmp = fma(b, (a - 0.5), (y + x));
	} else {
		tmp = (1.0 - log(t)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.62e+198)
		tmp = Float64(z - Float64(log(t) * z));
	elseif (z <= 1.32e+137)
		tmp = fma(b, Float64(a - 0.5), Float64(y + x));
	else
		tmp = Float64(Float64(1.0 - log(t)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.62e+198], N[(z - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e+137], N[(b * N[(a - 0.5), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.61999999999999989e198

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate--l+ N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

   4. Applied rewrites 94.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 74.5%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. mul-1-neg N/A

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

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

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

      11. *-lft-identity N/A

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

      12. *-commutative N/A

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

      13. associate-+l- N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-log.f64 74.4

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

   9. Applied rewrites 74.4%

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

   10. Taylor expanded in z around inf

       \[\leadsto z - z \cdot \color{blue}{\log t} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto z - \log t \cdot z \]

       2. lift-log.f64 N/A

          \[\leadsto z - \log t \cdot z \]

       3. lift-*.f64 67.7

          \[\leadsto z - \log t \cdot z \]

   12. Applied rewrites 67.7%

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

   if -1.61999999999999989e198 < z < 1.31999999999999997e137

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 90.6

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   if 1.31999999999999997e137 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift-log.f64 56.5

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

   4. Applied rewrites 56.5%

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

Alternative 10: 83.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \log t\right) \cdot z\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (log t)) z)))
   (if (<= z -1.62e+198)
     t_1
     (if (<= z 1.32e+137) (fma b (- a 0.5) (+ y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - log(t)) * z;
	double tmp;
	if (z <= -1.62e+198) {
		tmp = t_1;
	} else if (z <= 1.32e+137) {
		tmp = fma(b, (a - 0.5), (y + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - log(t)) * z)
	tmp = 0.0
	if (z <= -1.62e+198)
		tmp = t_1;
	elseif (z <= 1.32e+137)
		tmp = fma(b, Float64(a - 0.5), Float64(y + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.62e+198], t$95$1, If[LessEqual[z, 1.32e+137], N[(b * N[(a - 0.5), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.61999999999999989e198 or 1.31999999999999997e137 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift-log.f64 60.8

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

   4. Applied rewrites 60.8%

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

   if -1.61999999999999989e198 < z < 1.31999999999999997e137

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 90.6

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 90.6%

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

Alternative 11: 78.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(b, a - 0.5, y + x\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (fma b (- a 0.5) (+ y x)))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. remove-double-neg N/A

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

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

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

   5. distribute-rgt-neg-out N/A

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

   6. mul-1-neg N/A

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

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

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

   8. distribute-rgt-neg-in N/A

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

   9. *-commutative N/A

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

   10. distribute-rgt-neg-in N/A

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

   11. metadata-eval N/A

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

   12. *-rgt-identity N/A

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

   13. *-rgt-identity N/A

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

   14. lower-fma.f64 N/A

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

   15. *-rgt-identity N/A

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

   16. lift--.f64 N/A

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

   17. +-commutative N/A

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

   18. lower-+.f64 78.7

       \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

4. Applied rewrites 78.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]
5. Add Preprocessing

Alternative 12: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(x + y\right) + z\right) - z \cdot \log t \leq -5 \cdot 10^{-152}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- (+ (+ x y) z) (* z (log t))) -5e-152)
   (fma b (- a 0.5) x)
   (fma b (- a 0.5) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((x + y) + z) - (z * log(t))) <= -5e-152) {
		tmp = fma(b, (a - 0.5), x);
	} else {
		tmp = fma(b, (a - 0.5), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) <= -5e-152)
		tmp = fma(b, Float64(a - 0.5), x);
	else
		tmp = fma(b, Float64(a - 0.5), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e-152], N[(b * N[(a - 0.5), $MachinePrecision] + x), $MachinePrecision], N[(b * N[(a - 0.5), $MachinePrecision] + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < -4.9999999999999997e-152

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 78.4

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(b, a - \frac{1}{2}, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 57.8%

      \[\leadsto \mathsf{fma}\left(b, a - 0.5, x\right) \]

   if -4.9999999999999997e-152 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 79.0

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(b, a - \frac{1}{2}, y\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 58.6%

      \[\leadsto \mathsf{fma}\left(b, a - 0.5, y\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 58.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq 10^{-146}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(b, -0.5, y\right)\\ \mathbf{else}:\\ \;\;\;\;z - \left(-a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b))))
   (if (<= t_1 1e-146)
     (fma b (- a 0.5) x)
     (if (<= t_1 2e+307) (fma b -0.5 y) (- z (* (- a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
	double tmp;
	if (t_1 <= 1e-146) {
		tmp = fma(b, (a - 0.5), x);
	} else if (t_1 <= 2e+307) {
		tmp = fma(b, -0.5, y);
	} else {
		tmp = z - (-a * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
	tmp = 0.0
	if (t_1 <= 1e-146)
		tmp = fma(b, Float64(a - 0.5), x);
	elseif (t_1 <= 2e+307)
		tmp = fma(b, -0.5, y);
	else
		tmp = Float64(z - Float64(Float64(-a) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-146], N[(b * N[(a - 0.5), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], N[(b * -0.5 + y), $MachinePrecision], N[(z - N[((-a) * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)) < 1.00000000000000003e-146

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 78.4

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(b, a - \frac{1}{2}, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 57.9%

      \[\leadsto \mathsf{fma}\left(b, a - 0.5, x\right) \]

   if 1.00000000000000003e-146 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)) < 1.99999999999999997e307

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 76.1

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 76.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b, \frac{-1}{2}, y + x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 61.6%

      \[\leadsto \mathsf{fma}\left(b, -0.5, y + x\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(b, \frac{-1}{2}, y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 38.3%

       \[\leadsto \mathsf{fma}\left(b, -0.5, y\right) \]

   if 1.99999999999999997e307 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b))

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate--l+ N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. distribute-lft-neg-in N/A

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

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

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

      13. *-commutative N/A

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

      14. distribute-lft-in N/A

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

      15. *-commutative N/A

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

   4. Applied rewrites 98.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 5.6%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. mul-1-neg N/A

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

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

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

      11. *-lft-identity N/A

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

      12. *-commutative N/A

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

      13. associate-+l- N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-log.f64 5.6

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

   9. Applied rewrites 5.6%

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

   10. Taylor expanded in a around inf

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

       1. mul-1-neg N/A

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

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

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

       3. lower-*.f64 N/A

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

       4. lower-neg.f64 96.0

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

   12. Applied rewrites 96.0%

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

Alternative 14: 58.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-152}:\\ \;\;\;\;\mathsf{fma}\left(b, -0.5, x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(b, -0.5, y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b))))
   (if (<= t_1 (- INFINITY))
     (* b a)
     (if (<= t_1 -5e-152)
       (fma b -0.5 x)
       (if (<= t_1 2e+307) (fma b -0.5 y) (* b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = b * a;
	} else if (t_1 <= -5e-152) {
		tmp = fma(b, -0.5, x);
	} else if (t_1 <= 2e+307) {
		tmp = fma(b, -0.5, y);
	} else {
		tmp = b * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(b * a);
	elseif (t_1 <= -5e-152)
		tmp = fma(b, -0.5, x);
	elseif (t_1 <= 2e+307)
		tmp = fma(b, -0.5, y);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, -5e-152], N[(b * -0.5 + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], N[(b * -0.5 + y), $MachinePrecision], N[(b * a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)) < -inf.0 or 1.99999999999999997e307 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b))

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf

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

      1. remove-double-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. metadata-eval N/A

          \[\leadsto \left(b \cdot 1\right) \cdot a \]

      11. lower-*.f64 N/A

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

      12. *-rgt-identity 96.2

          \[\leadsto b \cdot a \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{b \cdot a} \]

   if -inf.0 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)) < -4.9999999999999997e-152

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 76.0

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b, \frac{-1}{2}, y + x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 61.9%

      \[\leadsto \mathsf{fma}\left(b, -0.5, y + x\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(b, \frac{-1}{2}, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 38.9%

       \[\leadsto \mathsf{fma}\left(b, -0.5, x\right) \]

   if -4.9999999999999997e-152 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)) < 1.99999999999999997e307

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 76.0

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b, \frac{-1}{2}, y + x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 61.5%

      \[\leadsto \mathsf{fma}\left(b, -0.5, y + x\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(b, \frac{-1}{2}, y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 38.3%

       \[\leadsto \mathsf{fma}\left(b, -0.5, y\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 57.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+215}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+67}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)) (t_2 (* b (- a 0.5))))
   (if (<= t_1 -1e+215) t_2 (if (<= t_1 2e+67) (+ y x) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+215) {
		tmp = t_2;
	} else if (t_1 <= 2e+67) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    t_2 = b * (a - 0.5d0)
    if (t_1 <= (-1d+215)) then
        tmp = t_2
    else if (t_1 <= 2d+67) then
        tmp = y + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+215) {
		tmp = t_2;
	} else if (t_1 <= 2e+67) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	t_2 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -1e+215:
		tmp = t_2
	elif t_1 <= 2e+67:
		tmp = y + x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -1e+215)
		tmp = t_2;
	elseif (t_1 <= 2e+67)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -1e+215)
		tmp = t_2;
	elseif (t_1 <= 2e+67)
		tmp = y + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+215], t$95$2, If[LessEqual[t$95$1, 2e+67], N[(y + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -9.99999999999999907e214 or 1.99999999999999997e67 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]
   3. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(a - \frac{1}{2}\right)\right) \]

      3. distribute-rgt-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(-1 \cdot \color{blue}{\left(a - \frac{1}{2}\right)}\right) \]

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

         \[\leadsto \mathsf{neg}\left(b \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right) \cdot -1\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right) \]

      9. metadata-eval N/A

         \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) \]

      10. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot 1\right) \]

      11. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(a - \color{blue}{\frac{1}{2}}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \color{blue}{\left(a - \frac{1}{2}\right)} \]

      13. *-rgt-identity N/A

          \[\leadsto b \cdot \left(\color{blue}{a} - \frac{1}{2}\right) \]

      14. lift--.f64 73.1

          \[\leadsto b \cdot \left(a - \color{blue}{0.5}\right) \]

   4. Applied rewrites 73.1%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   if -9.99999999999999907e214 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.99999999999999997e67

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 70.6

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

         \[\leadsto y + x \]

      2. lift-+.f64 57.4

         \[\leadsto y + x \]

   7. Applied rewrites 57.4%

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

Alternative 16: 55.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+292}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(b, -0.5, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+43}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 10^{+306}:\\ \;\;\;\;\mathsf{fma}\left(b, -0.5, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -5e+292)
     (* b a)
     (if (<= t_1 -1e+215)
       (fma b -0.5 x)
       (if (<= t_1 1e+43)
         (+ y x)
         (if (<= t_1 1e+306) (fma b -0.5 x) (* b a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -5e+292) {
		tmp = b * a;
	} else if (t_1 <= -1e+215) {
		tmp = fma(b, -0.5, x);
	} else if (t_1 <= 1e+43) {
		tmp = y + x;
	} else if (t_1 <= 1e+306) {
		tmp = fma(b, -0.5, x);
	} else {
		tmp = b * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (t_1 <= -5e+292)
		tmp = Float64(b * a);
	elseif (t_1 <= -1e+215)
		tmp = fma(b, -0.5, x);
	elseif (t_1 <= 1e+43)
		tmp = Float64(y + x);
	elseif (t_1 <= 1e+306)
		tmp = fma(b, -0.5, x);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+292], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, -1e+215], N[(b * -0.5 + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+43], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+306], N[(b * -0.5 + x), $MachinePrecision], N[(b * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -4.9999999999999996e292 or 1.00000000000000002e306 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf

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

      1. remove-double-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. metadata-eval N/A

          \[\leadsto \left(b \cdot 1\right) \cdot a \]

      11. lower-*.f64 N/A

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

      12. *-rgt-identity 95.3

          \[\leadsto b \cdot a \]

   4. Applied rewrites 95.3%

      \[\leadsto \color{blue}{b \cdot a} \]

   if -4.9999999999999996e292 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -9.99999999999999907e214 or 1.00000000000000001e43 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.00000000000000002e306

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

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

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-rgt-identity N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. *-rgt-identity N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 85.4

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 85.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b, \frac{-1}{2}, y + x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 57.0%

      \[\leadsto \mathsf{fma}\left(b, -0.5, y + x\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(b, \frac{-1}{2}, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 42.4%

       \[\leadsto \mathsf{fma}\left(b, -0.5, x\right) \]

   if -9.99999999999999907e214 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.00000000000000001e43

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

         \[\leadsto \left(x + y\right) + \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{\left(x + y\right)} \]

      3. remove-double-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot \left(a - \frac{1}{2}\right)\right)\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(a - \frac{1}{2}\right)\right)\right) + \left(x + y\right) \]

      5. distribute-rgt-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right) + \left(x + y\right) \]

      7. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      9. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right) \cdot -1\right)\right) + \left(x + y\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + y\right) \]

      11. metadata-eval N/A

          \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) + \left(x + y\right) \]

      12. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) + \left(x + y\right) \]

      13. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(a - \frac{1}{2}\right) + \left(x + y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 1, \color{blue}{a - \frac{1}{2}}, x + y\right) \]

      15. *-rgt-identity N/A

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{a} - \frac{1}{2}, x + y\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, a - \color{blue}{\frac{1}{2}}, x + y\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, a - \frac{1}{2}, y + x\right) \]

      18. lower-+.f64 70.5

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 70.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + x \]

      2. lift-+.f64 57.6

         \[\leadsto y + x \]

   7. Applied rewrites 57.6%

      \[\leadsto y + \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 52.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+216}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+67}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 10^{+306}:\\ \;\;\;\;b \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -1e+216)
     (* b a)
     (if (<= t_1 2e+67) (+ y x) (if (<= t_1 1e+306) (* b -0.5) (* b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -1e+216) {
		tmp = b * a;
	} else if (t_1 <= 2e+67) {
		tmp = y + x;
	} else if (t_1 <= 1e+306) {
		tmp = b * -0.5;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if (t_1 <= (-1d+216)) then
        tmp = b * a
    else if (t_1 <= 2d+67) then
        tmp = y + x
    else if (t_1 <= 1d+306) then
        tmp = b * (-0.5d0)
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -1e+216) {
		tmp = b * a;
	} else if (t_1 <= 2e+67) {
		tmp = y + x;
	} else if (t_1 <= 1e+306) {
		tmp = b * -0.5;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -1e+216:
		tmp = b * a
	elif t_1 <= 2e+67:
		tmp = y + x
	elif t_1 <= 1e+306:
		tmp = b * -0.5
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (t_1 <= -1e+216)
		tmp = Float64(b * a);
	elseif (t_1 <= 2e+67)
		tmp = Float64(y + x);
	elseif (t_1 <= 1e+306)
		tmp = Float64(b * -0.5);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (t_1 <= -1e+216)
		tmp = b * a;
	elseif (t_1 <= 2e+67)
		tmp = y + x;
	elseif (t_1 <= 1e+306)
		tmp = b * -0.5;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+216], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, 2e+67], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+306], N[(b * -0.5), $MachinePrecision], N[(b * a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1e216 or 1.00000000000000002e306 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   3. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot a\right)\right)\right) \]

      3. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot a\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot b\right) \cdot a\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot a\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \color{blue}{a} \]

      7. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(-1 \cdot b\right)\right) \cdot a \]

      8. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot -1\right)\right) \cdot a \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \left(b \cdot \left(\mathsf{neg}\left(-1\right)\right)\right) \cdot a \]

      10. metadata-eval N/A

          \[\leadsto \left(b \cdot 1\right) \cdot a \]

      11. lower-*.f64 N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \color{blue}{a} \]

      12. *-rgt-identity 77.4

          \[\leadsto b \cdot a \]

   4. Applied rewrites 77.4%

      \[\leadsto \color{blue}{b \cdot a} \]

   if -1e216 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.99999999999999997e67

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + y\right) + \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{\left(x + y\right)} \]

      3. remove-double-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot \left(a - \frac{1}{2}\right)\right)\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(a - \frac{1}{2}\right)\right)\right) + \left(x + y\right) \]

      5. distribute-rgt-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right) + \left(x + y\right) \]

      7. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      9. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right) \cdot -1\right)\right) + \left(x + y\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + y\right) \]

      11. metadata-eval N/A

          \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) + \left(x + y\right) \]

      12. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) + \left(x + y\right) \]

      13. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(a - \frac{1}{2}\right) + \left(x + y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 1, \color{blue}{a - \frac{1}{2}}, x + y\right) \]

      15. *-rgt-identity N/A

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{a} - \frac{1}{2}, x + y\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, a - \color{blue}{\frac{1}{2}}, x + y\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, a - \frac{1}{2}, y + x\right) \]

      18. lower-+.f64 70.7

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 70.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + x \]

      2. lift-+.f64 57.4

         \[\leadsto y + x \]

   7. Applied rewrites 57.4%

      \[\leadsto y + \color{blue}{x} \]

   if 1.99999999999999997e67 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.00000000000000002e306

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]
   3. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(a - \frac{1}{2}\right)\right) \]

      3. distribute-rgt-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(-1 \cdot \color{blue}{\left(a - \frac{1}{2}\right)}\right) \]

      5. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right) \cdot -1\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right) \]

      9. metadata-eval N/A

         \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) \]

      10. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot 1\right) \]

      11. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(a - \color{blue}{\frac{1}{2}}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \color{blue}{\left(a - \frac{1}{2}\right)} \]

      13. *-rgt-identity N/A

          \[\leadsto b \cdot \left(\color{blue}{a} - \frac{1}{2}\right) \]

      14. lift--.f64 54.7

          \[\leadsto b \cdot \left(a - \color{blue}{0.5}\right) \]

   4. Applied rewrites 54.7%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto b \cdot \frac{-1}{2} \]
   6. Step-by-step derivation

   7. Applied rewrites 28.1%

      \[\leadsto b \cdot -0.5 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 46.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+216}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+128}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -1e+216) (* b a) (if (<= t_1 2e+128) (+ y x) (* b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -1e+216) {
		tmp = b * a;
	} else if (t_1 <= 2e+128) {
		tmp = y + x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if (t_1 <= (-1d+216)) then
        tmp = b * a
    else if (t_1 <= 2d+128) then
        tmp = y + x
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -1e+216) {
		tmp = b * a;
	} else if (t_1 <= 2e+128) {
		tmp = y + x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -1e+216:
		tmp = b * a
	elif t_1 <= 2e+128:
		tmp = y + x
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (t_1 <= -1e+216)
		tmp = Float64(b * a);
	elseif (t_1 <= 2e+128)
		tmp = Float64(y + x);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (t_1 <= -1e+216)
		tmp = b * a;
	elseif (t_1 <= 2e+128)
		tmp = y + x;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+216], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, 2e+128], N[(y + x), $MachinePrecision], N[(b * a), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1e216 or 2.0000000000000002e128 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   3. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot a\right)\right)\right) \]

      3. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot a\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot b\right) \cdot a\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot a\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right) \cdot \color{blue}{a} \]

      7. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(-1 \cdot b\right)\right) \cdot a \]

      8. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot -1\right)\right) \cdot a \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \left(b \cdot \left(\mathsf{neg}\left(-1\right)\right)\right) \cdot a \]

      10. metadata-eval N/A

          \[\leadsto \left(b \cdot 1\right) \cdot a \]

      11. lower-*.f64 N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \color{blue}{a} \]

      12. *-rgt-identity 58.0

          \[\leadsto b \cdot a \]

   4. Applied rewrites 58.0%

      \[\leadsto \color{blue}{b \cdot a} \]

   if -1e216 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.0000000000000002e128

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + y\right) + \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{\left(x + y\right)} \]

      3. remove-double-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot \left(a - \frac{1}{2}\right)\right)\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(a - \frac{1}{2}\right)\right)\right) + \left(x + y\right) \]

      5. distribute-rgt-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right) + \left(x + y\right) \]

      7. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

      9. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right) \cdot -1\right)\right) + \left(x + y\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + y\right) \]

      11. metadata-eval N/A

          \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) + \left(x + y\right) \]

      12. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) + \left(x + y\right) \]

      13. *-rgt-identity N/A

          \[\leadsto \left(b \cdot 1\right) \cdot \left(a - \frac{1}{2}\right) + \left(x + y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot 1, \color{blue}{a - \frac{1}{2}}, x + y\right) \]

      15. *-rgt-identity N/A

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{a} - \frac{1}{2}, x + y\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, a - \color{blue}{\frac{1}{2}}, x + y\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, a - \frac{1}{2}, y + x\right) \]

      18. lower-+.f64 71.3

          \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

   4. Applied rewrites 71.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

   5. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + x \]

      2. lift-+.f64 56.7

         \[\leadsto y + x \]

   7. Applied rewrites 56.7%

      \[\leadsto y + \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 42.2% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ y + x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ y x))

C

double code(double x, double y, double z, double t, double a, double b) {
	return y + x;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = y + x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return y + x;
}

Python

def code(x, y, z, t, a, b):
	return y + x

Julia

function code(x, y, z, t, a, b)
	return Float64(y + x)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = y + x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

2. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
3. Step-by-step derivation

   1. associate-+r+ N/A

      \[\leadsto \left(x + y\right) + \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]

   2. +-commutative N/A

      \[\leadsto b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{\left(x + y\right)} \]

   3. remove-double-neg N/A

      \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b \cdot \left(a - \frac{1}{2}\right)\right)\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

   4. distribute-lft-neg-out N/A

      \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(b\right)\right) \cdot \left(a - \frac{1}{2}\right)\right)\right) + \left(x + y\right) \]

   5. distribute-rgt-neg-out N/A

      \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

   6. mul-1-neg N/A

      \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right) + \left(x + y\right) \]

   7. distribute-lft-neg-out N/A

      \[\leadsto \left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

   8. distribute-rgt-neg-in N/A

      \[\leadsto b \cdot \left(\mathsf{neg}\left(-1 \cdot \left(a - \frac{1}{2}\right)\right)\right) + \left(\color{blue}{x} + y\right) \]

   9. *-commutative N/A

      \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(a - \frac{1}{2}\right) \cdot -1\right)\right) + \left(x + y\right) \]

   10. distribute-rgt-neg-in N/A

       \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + y\right) \]

   11. metadata-eval N/A

       \[\leadsto b \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) + \left(x + y\right) \]

   12. *-rgt-identity N/A

       \[\leadsto \left(b \cdot 1\right) \cdot \left(\left(a - \frac{1}{2}\right) \cdot 1\right) + \left(x + y\right) \]

   13. *-rgt-identity N/A

       \[\leadsto \left(b \cdot 1\right) \cdot \left(a - \frac{1}{2}\right) + \left(x + y\right) \]

   14. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(b \cdot 1, \color{blue}{a - \frac{1}{2}}, x + y\right) \]

   15. *-rgt-identity N/A

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{a} - \frac{1}{2}, x + y\right) \]

   16. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(b, a - \color{blue}{\frac{1}{2}}, x + y\right) \]

   17. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(b, a - \frac{1}{2}, y + x\right) \]

   18. lower-+.f64 78.7

       \[\leadsto \mathsf{fma}\left(b, a - 0.5, y + x\right) \]

4. Applied rewrites 78.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, a - 0.5, y + x\right)} \]

5. Taylor expanded in b around 0

   \[\leadsto x + \color{blue}{y} \]
6. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto y + x \]

   2. lift-+.f64 42.2

      \[\leadsto y + x \]

7. Applied rewrites 42.2%

   \[\leadsto y + \color{blue}{x} \]
8. Add Preprocessing

Alternative 20: 22.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \leq -4 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)) -4e-220) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((((x + y) + z) - (z * log(t))) + ((a - 0.5) * b)) <= -4e-220) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((((x + y) + z) - (z * log(t))) + ((a - 0.5d0) * b)) <= (-4d-220)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b)) <= -4e-220) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)) <= -4e-220:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b)) <= -4e-220)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((((x + y) + z) - (z * log(t))) + ((a - 0.5) * b)) <= -4e-220)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], -4e-220], x, y]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)) < -3.99999999999999997e-220

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 22.9%

      \[\leadsto \color{blue}{x} \]

   if -3.99999999999999997e-220 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b))

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 21.2%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 22.0% accurate, 26.1× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 22.5%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))