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

Percentage Accurate: 99.9% → 99.9%

Time: 9.6s

Alternatives: 13

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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 - 0.5d0)) + ((z + (y + x)) - (log(t) * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 93.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+61}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(-0.5, b, x\right)\right) + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+61)
     (- (+ z (+ y x)) (* (- 0.5 a) b))
     (if (<= t_1 5e+100)
       (+ (fma (- 1.0 (log t)) z (fma -0.5 b 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 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+61) {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	} else if (t_1 <= 5e+100) {
		tmp = fma((1.0 - log(t)), z, fma(-0.5, b, 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(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -2e+61)
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	elseif (t_1 <= 5e+100)
		tmp = Float64(fma(Float64(1.0 - log(t)), z, fma(-0.5, b, 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[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+61], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+100], N[(N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(-0.5 * b + x), $MachinePrecision]), $MachinePrecision] + y), $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) < -1.9999999999999999e61

   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. lower--.f64 99.9

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 99.9

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. neg-mul-1 N/A

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

      10. sub-neg N/A

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

      11. lower--.f64 88.0

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

   7. Applied rewrites 88.0%

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

   if -1.9999999999999999e61 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.9999999999999999e100

   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 0

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

      1. *-commutative N/A

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

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

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

      3. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+r+ N/A

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

      8. associate-+l+ N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. log-rec N/A

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

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

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

      14. *-commutative N/A

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

      15. lower-+.f64 N/A

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

   5. Applied rewrites 97.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - \log t, z, y\right) + \mathsf{fma}\left(-0.5, b, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 97.8%

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

   if 4.9999999999999999e100 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   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. 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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 91.5

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

   5. Applied rewrites 91.5%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+61}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(-0.5, b, x\right)\right) + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+20}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+20)
     (- (+ z (+ y x)) (* (- 0.5 a) b))
     (if (<= t_1 5e+100)
       (fma (- 1.0 (log t)) z (+ y x))
       (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 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+20) {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	} else if (t_1 <= 5e+100) {
		tmp = fma((1.0 - log(t)), z, (y + x));
	} else {
		tmp = fma((a - 0.5), b, (y + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -5e+20)
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	elseif (t_1 <= 5e+100)
		tmp = fma(Float64(1.0 - log(t)), z, Float64(y + x));
	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[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+20], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+100], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(y + x), $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) < -5e20

   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. lower--.f64 99.9

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 99.9

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. neg-mul-1 N/A

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

      10. sub-neg N/A

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

      11. lower--.f64 85.6

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

   7. Applied rewrites 85.6%

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

   if -5e20 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.9999999999999999e100

   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. lower--.f64 99.8

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 99.8

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

      3. unsub-neg N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. *-lft-identity N/A

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

      9. log-rec N/A

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

      10. distribute-rgt-in N/A

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

      11. log-rec N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower--.f64 N/A

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

      17. lower-log.f64 N/A

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

      18. lower-+.f64 96.5

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

   7. Applied rewrites 96.5%

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

   if 4.9999999999999999e100 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   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. 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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 91.5

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

   5. Applied rewrites 91.5%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+20}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -2 \cdot 10^{-221}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z + y\right) - \log t \cdot z\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ y x) -2e-221)
   (fma (- 1.0 (log t)) z (fma (- a 0.5) b x))
   (+ (- (+ z y) (* (log t) z)) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y + x) <= -2e-221) {
		tmp = fma((1.0 - log(t)), z, fma((a - 0.5), b, x));
	} else {
		tmp = ((z + y) - (log(t) * z)) + (b * (a - 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(y + x) <= -2e-221)
		tmp = fma(Float64(1.0 - log(t)), z, fma(Float64(a - 0.5), b, x));
	else
		tmp = Float64(Float64(Float64(z + y) - Float64(log(t) * z)) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(y + x), $MachinePrecision], -2e-221], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(N[(a - 0.5), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z + y), $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -2.00000000000000003e-221

   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 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. cancel-sign-sub-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. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-commutative N/A

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

      10. distribute-lft1-in N/A

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

      11. +-commutative N/A

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

      12. log-rec N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 83.5%

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

   if -2.00000000000000003e-221 < (+.f64 x y)

   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 x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 73.8

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

   5. Applied rewrites 73.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -2 \cdot 10^{-221}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z + y\right) - \log t \cdot z\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 4.5e+84)
   (fma (- 1.0 (log t)) z (fma (- a 0.5) b x))
   (- (+ z (+ y x)) (* (- 0.5 a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 4.5e+84) {
		tmp = fma((1.0 - log(t)), z, fma((a - 0.5), b, x));
	} else {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 4.5e+84)
		tmp = fma(Float64(1.0 - log(t)), z, fma(Float64(a - 0.5), b, x));
	else
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 4.5e+84], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(N[(a - 0.5), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.4999999999999997e84

   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. cancel-sign-sub-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. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-commutative N/A

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

      10. distribute-lft1-in N/A

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

      11. +-commutative N/A

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

      12. log-rec N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 89.1%

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

   if 4.4999999999999997e84 < y

   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. lower--.f64 100.0

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 100.0

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 100.0

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

   4. Applied rewrites 100.0%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. neg-mul-1 N/A

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

      10. sub-neg N/A

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

      11. lower--.f64 96.6

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

   7. Applied rewrites 96.6%

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

Alternative 6: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \log t\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, y\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+279}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (log t))))
   (if (<= z -5.8e+154)
     (fma t_1 z y)
     (if (<= z 1.25e+279) (- (+ z (+ y x)) (* (- 0.5 a) b)) (* t_1 z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - log(t);
	double tmp;
	if (z <= -5.8e+154) {
		tmp = fma(t_1, z, y);
	} else if (z <= 1.25e+279) {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	} else {
		tmp = t_1 * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - log(t))
	tmp = 0.0
	if (z <= -5.8e+154)
		tmp = fma(t_1, z, y);
	elseif (z <= 1.25e+279)
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	else
		tmp = Float64(t_1 * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+154], N[(t$95$1 * z + y), $MachinePrecision], If[LessEqual[z, 1.25e+279], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.79999999999999959e154

   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. 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. lower--.f64 99.6

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 99.6

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

      3. unsub-neg N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. *-lft-identity N/A

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

      9. log-rec N/A

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

      10. distribute-rgt-in N/A

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

      11. log-rec N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower--.f64 N/A

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

      17. lower-log.f64 N/A

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

      18. lower-+.f64 85.8

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

   7. Applied rewrites 85.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 81.3%

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

   if -5.79999999999999959e154 < z < 1.25e279

   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. lower--.f64 99.9

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 99.9

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. neg-mul-1 N/A

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

      10. sub-neg N/A

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

      11. lower--.f64 86.6

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

   7. Applied rewrites 86.6%

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

   if 1.25e279 < z

   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 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. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 N/A

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

      8. lower-log.f64 77.7

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

   5. Applied rewrites 77.7%

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

Alternative 7: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \log t\right) \cdot z\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+279}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (log t)) z)))
   (if (<= z -4.8e+156)
     t_1
     (if (<= z 1.25e+279) (- (+ z (+ y x)) (* (- 0.5 a) b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - log(t)) * z;
	double tmp;
	if (z <= -4.8e+156) {
		tmp = t_1;
	} else if (z <= 1.25e+279) {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - log(t)) * z
    if (z <= (-4.8d+156)) then
        tmp = t_1
    else if (z <= 1.25d+279) then
        tmp = (z + (y + x)) - ((0.5d0 - a) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - Math.log(t)) * z;
	double tmp;
	if (z <= -4.8e+156) {
		tmp = t_1;
	} else if (z <= 1.25e+279) {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - math.log(t)) * z
	tmp = 0
	if z <= -4.8e+156:
		tmp = t_1
	elif z <= 1.25e+279:
		tmp = (z + (y + x)) - ((0.5 - a) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - log(t)) * z)
	tmp = 0.0
	if (z <= -4.8e+156)
		tmp = t_1;
	elseif (z <= 1.25e+279)
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - log(t)) * z;
	tmp = 0.0;
	if (z <= -4.8e+156)
		tmp = t_1;
	elseif (z <= 1.25e+279)
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.8e+156], t$95$1, If[LessEqual[z, 1.25e+279], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000002e156 or 1.25e279 < z

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. 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. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 N/A

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

      8. lower-log.f64 77.9

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

   5. Applied rewrites 77.9%

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

   if -4.8000000000000002e156 < z < 1.25e279

   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. lower--.f64 99.9

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 99.9

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. neg-mul-1 N/A

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

      10. sub-neg N/A

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

      11. lower--.f64 86.6

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

   7. Applied rewrites 86.6%

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

Alternative 8: 70.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, b, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+152) t_1 (if (<= t_1 2e+220) (fma -0.5 b (+ y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+152) {
		tmp = t_1;
	} else if (t_1 <= 2e+220) {
		tmp = fma(-0.5, b, (y + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -5e+152)
		tmp = t_1;
	elseif (t_1 <= 2e+220)
		tmp = fma(-0.5, b, Float64(y + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+152], t$95$1, If[LessEqual[t$95$1, 2e+220], N[(-0.5 * b + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5e152 or 2e220 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   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. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if -5e152 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2e220

   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 0

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

      1. *-commutative N/A

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

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

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

      3. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+r+ N/A

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

      8. associate-+l+ N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. log-rec N/A

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

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

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

      14. *-commutative N/A

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

      15. lower-+.f64 N/A

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

   5. Applied rewrites 92.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 63.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+152}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, b, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.5% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -126000:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-25}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -126000.0) (* b a) (if (<= a 2.85e-25) (* -0.5 b) (* b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -126000.0) {
		tmp = b * a;
	} else if (a <= 2.85e-25) {
		tmp = -0.5 * b;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 <= (-126000.0d0)) then
        tmp = b * a
    else if (a <= 2.85d-25) then
        tmp = (-0.5d0) * b
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -126000.0) {
		tmp = b * a;
	} else if (a <= 2.85e-25) {
		tmp = -0.5 * b;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -126000.0:
		tmp = b * a
	elif a <= 2.85e-25:
		tmp = -0.5 * b
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -126000.0)
		tmp = Float64(b * a);
	elseif (a <= 2.85e-25)
		tmp = Float64(-0.5 * b);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -126000.0)
		tmp = b * a;
	elseif (a <= 2.85e-25)
		tmp = -0.5 * b;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -126000.0], N[(b * a), $MachinePrecision], If[LessEqual[a, 2.85e-25], N[(-0.5 * b), $MachinePrecision], N[(b * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -126000 or 2.8500000000000002e-25 < 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 47.8

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

   5. Applied rewrites 47.8%

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

   if -126000 < a < 2.8500000000000002e-25

   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 0

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

      1. *-commutative N/A

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

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

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

      3. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+r+ N/A

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

      8. associate-+l+ N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. log-rec N/A

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

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

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

      14. *-commutative N/A

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

      15. lower-+.f64 N/A

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 22.3%

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

Alternative 10: 79.3% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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)) - ((0.5d0 - a) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing
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. lower--.f64 99.9

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

   12. lift-*.f64 N/A

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

   13. *-commutative N/A

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

   14. lower-*.f64 99.9

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

   15. lift-*.f64 N/A

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

   16. *-commutative N/A

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

   17. lower-*.f64 99.9

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

4. Applied rewrites 99.9%

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

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. *-commutative N/A

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

   2. associate-*r* N/A

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

   3. lower-*.f64 N/A

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

   4. sub-neg N/A

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

   5. metadata-eval N/A

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

   6. distribute-lft-in N/A

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

   7. metadata-eval N/A

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

   8. +-commutative N/A

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

   9. neg-mul-1 N/A

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

   10. sub-neg N/A

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

   11. lower--.f64 77.3

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

7. Applied rewrites 77.3%

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

Alternative 11: 78.5% 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 99.9%

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

3. Taylor expanded in z around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. lower--.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-+.f64 76.2

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

5. Applied rewrites 76.2%

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

Alternative 12: 37.3% accurate, 14.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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 - 0.5d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 35.7

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

5. Applied rewrites 35.7%

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

6. Final simplification 35.7%

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

Alternative 13: 14.1% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ -0.5 \cdot b \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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 = (-0.5d0) * b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around 0

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

   1. *-commutative N/A

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

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

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

   3. log-rec N/A

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

   4. *-commutative N/A

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

   5. +-commutative N/A

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

   6. +-commutative N/A

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

   7. associate-+r+ N/A

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

   8. associate-+l+ N/A

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

   9. associate-+r+ N/A

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

   10. +-commutative N/A

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

   11. *-commutative N/A

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

   12. log-rec N/A

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

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

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

   14. *-commutative N/A

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

   15. lower-+.f64 N/A

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

5. Applied rewrites 75.9%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 12.1%

   \[\leadsto -0.5 \cdot \color{blue}{b} \]
9. Add Preprocessing

Developer Target 1: 99.6% 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

real(8) function code(x, y, z, t, a, b)
    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 2024332 
(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)))