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

Percentage Accurate: 99.8% → 99.8%

Time: 8.6s

Alternatives: 14

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: 99.8% 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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.8

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

   5. lift--.f64 N/A

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

   6. lift-*.f64 N/A

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

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

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

   8. +-commutative N/A

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

   9. lower-fma.f64 N/A

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

   10. lower-neg.f64 99.9

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

   11. lift-+.f64 N/A

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

   12. +-commutative N/A

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

   13. lower-+.f64 99.9

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

   14. lift-+.f64 N/A

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

   15. +-commutative N/A

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

   16. lower-+.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-10}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -5e-10)
     (- (+ z (+ y x)) (* (- b) (- a 0.5)))
     (if (<= t_1 5e-15)
       (fma (- 1.0 (log t)) z (+ x y))
       (fma (- a 0.5) b (+ y x))))))

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-10) {
		tmp = (z + (y + x)) - (-b * (a - 0.5));
	} else if (t_1 <= 5e-15) {
		tmp = fma((1.0 - log(t)), z, (x + y));
	} else {
		tmp = fma((a - 0.5), b, (y + x));
	}
	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-10)
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(-b) * Float64(a - 0.5)));
	elseif (t_1 <= 5e-15)
		tmp = fma(Float64(1.0 - log(t)), z, Float64(x + y));
	else
		tmp = fma(Float64(a - 0.5), b, Float64(y + x));
	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-10], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[((-b) * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-15], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(a - 0.5), $MachinePrecision] * b + N[(y + x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.00000000000000031e-10

   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
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 89.2

         \[\leadsto \left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \color{blue}{\left(a - 0.5\right)} \]

   7. Applied rewrites 89.2%

      \[\leadsto \left(z + \left(y + x\right)\right) - \color{blue}{\left(-b\right) \cdot \left(a - 0.5\right)} \]

   if -5.00000000000000031e-10 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.99999999999999999e-15

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} \]

      2. lower-*.f64 3.4

         \[\leadsto \color{blue}{b \cdot a} \]

   5. Applied rewrites 3.4%

      \[\leadsto \color{blue}{b \cdot a} \]

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 96.1%

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

   if 4.99999999999999999e-15 < (*.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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 91.3

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

   5. Applied rewrites 91.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -5 \cdot 10^{-10}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;\left(a - 0.5\right) \cdot b \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+109} \lor \neg \left(z \leq 1.35 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(-0.5 + a, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.2e+109) (not (<= z 1.35e+71)))
   (fma (- 1.0 (log t)) z (fma (+ -0.5 a) b x))
   (- (+ z (+ y x)) (* (- b) (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e+109) || !(z <= 1.35e+71)) {
		tmp = fma((1.0 - log(t)), z, fma((-0.5 + a), b, x));
	} else {
		tmp = (z + (y + x)) - (-b * (a - 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.2e+109) || !(z <= 1.35e+71))
		tmp = fma(Float64(1.0 - log(t)), z, fma(Float64(-0.5 + a), b, x));
	else
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(-b) * Float64(a - 0.5)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.2e+109], N[Not[LessEqual[z, 1.35e+71]], $MachinePrecision]], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(N[(-0.5 + a), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[((-b) * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000001e109 or 1.34999999999999998e71 < 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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. associate-+r+ N/A

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

   5. Applied rewrites 86.1%

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

   if -3.2000000000000001e109 < z < 1.34999999999999998e71

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 96.8

         \[\leadsto \left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \color{blue}{\left(a - 0.5\right)} \]

   7. Applied rewrites 96.8%

      \[\leadsto \left(z + \left(y + x\right)\right) - \color{blue}{\left(-b\right) \cdot \left(a - 0.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+109} \lor \neg \left(z \leq 1.35 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(-0.5 + a, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \log t\\ \mathbf{if}\;x + y \leq -4 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, \mathsf{fma}\left(-0.5 + a, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, \mathsf{fma}\left(a - 0.5, b, y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (log t))))
   (if (<= (+ x y) -4e-59)
     (fma t_1 z (fma (+ -0.5 a) b x))
     (fma t_1 z (fma (- a 0.5) b y)))))

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 ((x + y) <= -4e-59) {
		tmp = fma(t_1, z, fma((-0.5 + a), b, x));
	} else {
		tmp = fma(t_1, z, fma((a - 0.5), b, y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - log(t))
	tmp = 0.0
	if (Float64(x + y) <= -4e-59)
		tmp = fma(t_1, z, fma(Float64(-0.5 + a), b, x));
	else
		tmp = fma(t_1, z, fma(Float64(a - 0.5), b, y));
	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[N[(x + y), $MachinePrecision], -4e-59], N[(t$95$1 * z + N[(N[(-0.5 + a), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * z + N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.0000000000000001e-59

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. associate-+r+ N/A

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

   5. Applied rewrites 71.7%

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

   if -4.0000000000000001e-59 < (+.f64 x y)

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

   5. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(-0.5 + a, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+239} \lor \neg \left(z \leq 9.5 \cdot 10^{+202}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.6e+239) (not (<= z 9.5e+202)))
   (fma (- 1.0 (log t)) z y)
   (- (+ z (+ y x)) (* (- b) (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.6e+239) || !(z <= 9.5e+202)) {
		tmp = fma((1.0 - log(t)), z, y);
	} else {
		tmp = (z + (y + x)) - (-b * (a - 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.6e+239) || !(z <= 9.5e+202))
		tmp = fma(Float64(1.0 - log(t)), z, y);
	else
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(-b) * Float64(a - 0.5)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.6e+239], N[Not[LessEqual[z, 9.5e+202]], $MachinePrecision]], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[((-b) * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e239 or 9.50000000000000059e202 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 89.6%

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

   if -3.6e239 < z < 9.50000000000000059e202

   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
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 90.6

         \[\leadsto \left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \color{blue}{\left(a - 0.5\right)} \]

   7. Applied rewrites 90.6%

      \[\leadsto \left(z + \left(y + x\right)\right) - \color{blue}{\left(-b\right) \cdot \left(a - 0.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+239} \lor \neg \left(z \leq 9.5 \cdot 10^{+202}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+239} \lor \neg \left(z \leq 9.5 \cdot 10^{+202}\right):\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.6e+239) (not (<= z 9.5e+202)))
   (* (- 1.0 (log t)) z)
   (- (+ z (+ y x)) (* (- b) (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.6e+239) || !(z <= 9.5e+202)) {
		tmp = (1.0 - log(t)) * z;
	} else {
		tmp = (z + (y + x)) - (-b * (a - 0.5));
	}
	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 ((z <= (-3.6d+239)) .or. (.not. (z <= 9.5d+202))) then
        tmp = (1.0d0 - log(t)) * z
    else
        tmp = (z + (y + x)) - (-b * (a - 0.5d0))
    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 ((z <= -3.6e+239) || !(z <= 9.5e+202)) {
		tmp = (1.0 - Math.log(t)) * z;
	} else {
		tmp = (z + (y + x)) - (-b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.6e+239) or not (z <= 9.5e+202):
		tmp = (1.0 - math.log(t)) * z
	else:
		tmp = (z + (y + x)) - (-b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.6e+239) || !(z <= 9.5e+202))
		tmp = Float64(Float64(1.0 - log(t)) * z);
	else
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(-b) * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.6e+239) || ~((z <= 9.5e+202)))
		tmp = (1.0 - log(t)) * z;
	else
		tmp = (z + (y + x)) - (-b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.6e+239], N[Not[LessEqual[z, 9.5e+202]], $MachinePrecision]], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[((-b) * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e239 or 9.50000000000000059e202 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 75.5

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

   5. Applied rewrites 75.5%

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

   if -3.6e239 < z < 9.50000000000000059e202

   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
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 90.6

         \[\leadsto \left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \color{blue}{\left(a - 0.5\right)} \]

   7. Applied rewrites 90.6%

      \[\leadsto \left(z + \left(y + x\right)\right) - \color{blue}{\left(-b\right) \cdot \left(a - 0.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+239} \lor \neg \left(z \leq 9.5 \cdot 10^{+202}\right):\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+239} \lor \neg \left(z \leq 9.5 \cdot 10^{+202}\right):\\ \;\;\;\;z - \log t \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.6e+239) (not (<= z 9.5e+202)))
   (- z (* (log t) z))
   (- (+ z (+ y x)) (* (- b) (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.6e+239) || !(z <= 9.5e+202)) {
		tmp = z - (log(t) * z);
	} else {
		tmp = (z + (y + x)) - (-b * (a - 0.5));
	}
	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 ((z <= (-3.6d+239)) .or. (.not. (z <= 9.5d+202))) then
        tmp = z - (log(t) * z)
    else
        tmp = (z + (y + x)) - (-b * (a - 0.5d0))
    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 ((z <= -3.6e+239) || !(z <= 9.5e+202)) {
		tmp = z - (Math.log(t) * z);
	} else {
		tmp = (z + (y + x)) - (-b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.6e+239) or not (z <= 9.5e+202):
		tmp = z - (math.log(t) * z)
	else:
		tmp = (z + (y + x)) - (-b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.6e+239) || !(z <= 9.5e+202))
		tmp = Float64(z - Float64(log(t) * z));
	else
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(-b) * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.6e+239) || ~((z <= 9.5e+202)))
		tmp = z - (log(t) * z);
	else
		tmp = (z + (y + x)) - (-b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.6e+239], N[Not[LessEqual[z, 9.5e+202]], $MachinePrecision]], N[(z - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[((-b) * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e239 or 9.50000000000000059e202 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 75.5

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

   5. Applied rewrites 75.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 75.3%

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

   if -3.6e239 < z < 9.50000000000000059e202

   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
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 90.6

         \[\leadsto \left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \color{blue}{\left(a - 0.5\right)} \]

   7. Applied rewrites 90.6%

      \[\leadsto \left(z + \left(y + x\right)\right) - \color{blue}{\left(-b\right) \cdot \left(a - 0.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+239} \lor \neg \left(z \leq 9.5 \cdot 10^{+202}\right):\\ \;\;\;\;z - \log t \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.7% accurate, 6.3× speedup

Math

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

FPCore

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

C

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

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 = (z + (y + x)) - (-b * (a - 0.5d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. associate-+l- N/A

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

   4. lower--.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-+.f64 N/A

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 N/A

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

   11. lift-*.f64 N/A

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

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

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-fma.f64 N/A

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

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

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

   17. *-commutative N/A

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

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

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

   19. lower-*.f64 N/A

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

   20. lower-neg.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Taylor expanded in z around 0

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

   1. associate-*r* N/A

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

   2. lower-*.f64 N/A

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

   3. mul-1-neg N/A

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

   4. lower-neg.f64 N/A

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

   5. lower--.f64 80.7

      \[\leadsto \left(z + \left(y + x\right)\right) - \left(-b\right) \cdot \color{blue}{\left(a - 0.5\right)} \]

7. Applied rewrites 80.7%

   \[\leadsto \left(z + \left(y + x\right)\right) - \color{blue}{\left(-b\right) \cdot \left(a - 0.5\right)} \]
8. Add Preprocessing

Alternative 9: 38.1% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.5 \lor \neg \left(a \leq 0.95\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -0.5) (not (<= a 0.95))) (* b a) (* -0.5 b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -0.5) || !(a <= 0.95)) {
		tmp = b * a;
	} else {
		tmp = -0.5 * b;
	}
	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 ((a <= (-0.5d0)) .or. (.not. (a <= 0.95d0))) then
        tmp = b * a
    else
        tmp = (-0.5d0) * b
    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 ((a <= -0.5) || !(a <= 0.95)) {
		tmp = b * a;
	} else {
		tmp = -0.5 * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -0.5) or not (a <= 0.95):
		tmp = b * a
	else:
		tmp = -0.5 * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -0.5) || !(a <= 0.95))
		tmp = Float64(b * a);
	else
		tmp = Float64(-0.5 * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -0.5) || ~((a <= 0.95)))
		tmp = b * a;
	else
		tmp = -0.5 * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -0.5], N[Not[LessEqual[a, 0.95]], $MachinePrecision]], N[(b * a), $MachinePrecision], N[(-0.5 * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.5 or 0.94999999999999996 < a

   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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{b \cdot a} \]

      2. lower-*.f64 48.9

         \[\leadsto \color{blue}{b \cdot a} \]

   5. Applied rewrites 48.9%

      \[\leadsto \color{blue}{b \cdot a} \]

   if -0.5 < a < 0.94999999999999996

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 25.0

         \[\leadsto \left(0.5 - a\right) \cdot \color{blue}{\left(-b\right)} \]

   7. Applied rewrites 25.0%

      \[\leadsto \color{blue}{\left(0.5 - a\right) \cdot \left(-b\right)} \]

   8. Taylor expanded in a around 0

      \[\leadsto \frac{-1}{2} \cdot \color{blue}{b} \]
   9. Step-by-step derivation

   10. Applied rewrites 23.8%

       \[\leadsto -0.5 \cdot \color{blue}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.5 \lor \neg \left(a \leq 0.95\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.9% accurate, 7.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. associate-+l- N/A

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

   4. lower--.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-+.f64 N/A

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 N/A

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

   11. lift-*.f64 N/A

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

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

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-fma.f64 N/A

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

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

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

   17. *-commutative N/A

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

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

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

   19. lower-*.f64 N/A

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

   20. lower-neg.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Taylor expanded in a around 0

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

   1. lower--.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 N/A

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

   4. associate-+r+ N/A

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

   5. +-commutative N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-+.f64 N/A

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

   9. lower-fma.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lower-log.f64 99.9

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

7. Applied rewrites 99.9%

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

8. Taylor expanded in z around 0

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

10. Applied rewrites 79.8%

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

11. Final simplification 79.8%

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

Alternative 11: 78.9% accurate, 9.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. *-commutative N/A

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

   5. +-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lower--.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 79.7

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

5. Applied rewrites 79.7%

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

6. Final simplification 79.7%

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

Alternative 12: 59.1% accurate, 12.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

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

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

   3. mul-1-neg N/A

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

   4. *-commutative N/A

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

   5. mul-1-neg N/A

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

   6. log-rec N/A

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

   7. +-commutative N/A

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

   8. +-commutative N/A

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

   9. associate-+l+ N/A

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

   10. +-commutative N/A

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

   11. associate-+r+ N/A

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

5. Applied rewrites 77.7%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 64.0%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 58.1%

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

12. Final simplification 58.1%

    \[\leadsto \mathsf{fma}\left(a - 0.5, b, y\right) \]
13. Add Preprocessing

Alternative 13: 38.6% accurate, 14.0× speedup

Math

\[\begin{array}{l} \\ \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. associate-+l- N/A

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

   4. lower--.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-+.f64 N/A

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 N/A

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

   11. lift-*.f64 N/A

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

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

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-fma.f64 N/A

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

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

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

   17. *-commutative N/A

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

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

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

   19. lower-*.f64 N/A

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

   20. lower-neg.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Taylor expanded in a around 0

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

   1. lower--.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 N/A

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

   4. associate-+r+ N/A

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

   5. +-commutative N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-+.f64 N/A

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

   9. lower-fma.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lower-log.f64 99.9

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

7. Applied rewrites 99.9%

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

8. Taylor expanded in b around inf

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

10. Applied rewrites 37.6%

    \[\leadsto \left(a - 0.5\right) \cdot \color{blue}{b} \]

11. Final simplification 37.6%

    \[\leadsto \left(a - 0.5\right) \cdot b \]
12. Add Preprocessing

Alternative 14: 26.7% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ b \cdot a \end{array} \]

FPCore

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

C

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

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 = b * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Taylor expanded in a around inf

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

   1. *-commutative N/A

      \[\leadsto \color{blue}{b \cdot a} \]

   2. lower-*.f64 27.0

      \[\leadsto \color{blue}{b \cdot a} \]

5. Applied rewrites 27.0%

   \[\leadsto \color{blue}{b \cdot a} \]

6. Final simplification 27.0%

   \[\leadsto b \cdot a \]
7. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t))))
  (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - pow(log(t), 2.0)) * z) / (1.0 + 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) + (((1.0d0 - (log(t) ** 2.0d0)) * z) / (1.0d0 + 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) + (((1.0 - Math.pow(Math.log(t), 2.0)) * z) / (1.0 + Math.log(t)))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + y) + (((1.0 - math.pow(math.log(t), 2.0)) * z) / (1.0 + math.log(t)))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + y) + Float64(Float64(Float64(1.0 - (log(t) ^ 2.0)) * z) / Float64(1.0 + log(t)))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + y) + (((1.0 - (log(t) ^ 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(N[(N[(1.0 - N[Power[N[Log[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] / N[(1.0 + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024364 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 1/2) b)))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))