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

Percentage Accurate: 99.8% → 99.9%

Time: 13.5s

Alternatives: 19

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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left({t}^{-0.5}\right)\\ z \cdot \left(\left(t\_1 + t\_1\right) + 1\right) + \left(\left(x + y\right) + \left(-0.5 + a\right) \cdot b\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (log (pow t -0.5))))
   (+ (* z (+ (+ t_1 t_1) 1.0)) (+ (+ x y) (* (+ -0.5 a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(pow(t, -0.5));
	return (z * ((t_1 + t_1) + 1.0)) + ((x + y) + ((-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
    real(8) :: t_1
    t_1 = log((t ** (-0.5d0)))
    code = (z * ((t_1 + t_1) + 1.0d0)) + ((x + y) + (((-0.5d0) + a) * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.log(Math.pow(t, -0.5));
	return (z * ((t_1 + t_1) + 1.0)) + ((x + y) + ((-0.5 + a) * b));
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(math.pow(t, -0.5))
	return (z * ((t_1 + t_1) + 1.0)) + ((x + y) + ((-0.5 + a) * b))

Julia

function code(x, y, z, t, a, b)
	t_1 = log((t ^ -0.5))
	return Float64(Float64(z * Float64(Float64(t_1 + t_1) + 1.0)) + Float64(Float64(x + y) + Float64(Float64(-0.5 + a) * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	t_1 = log((t ^ -0.5));
	tmp = (z * ((t_1 + t_1) + 1.0)) + ((x + y) + ((-0.5 + a) * b));
end

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   8. distribute-rgt1-in N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   12. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   13. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   14. log-lowering-log.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

   16. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

   17. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

   18. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

   19. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

   20. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

   21. metadata-eval 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

3. Simplified 99.9%

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

   1. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{y}\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{y}\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\log t\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{y}\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   4. neg-log N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\log \left(\frac{1}{t}\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   5. log-lowering-log.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\left(\frac{1}{t}\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   6. /-lowering-/.f64 99.9%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(1, t\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

6. Applied egg-rr 99.9%

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

   1. inv-pow N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\log \left({t}^{-1}\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   2. sqr-pow N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\log \left({t}^{\left(\frac{-1}{2}\right)} \cdot {t}^{\left(\frac{-1}{2}\right)}\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. log-prod N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\log \left({t}^{\left(\frac{-1}{2}\right)}\right) + \log \left({t}^{\left(\frac{-1}{2}\right)}\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\log \left({t}^{\left(\frac{-1}{2}\right)}\right), \log \left({t}^{\left(\frac{-1}{2}\right)}\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   5. log-lowering-log.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(\left({t}^{\left(\frac{-1}{2}\right)}\right)\right), \log \left({t}^{\left(\frac{-1}{2}\right)}\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(\left({t}^{\frac{-1}{2}}\right)\right), \log \left({t}^{\left(\frac{-1}{2}\right)}\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   7. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{pow.f64}\left(t, \frac{-1}{2}\right)\right), \log \left({t}^{\left(\frac{-1}{2}\right)}\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   8. log-lowering-log.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{pow.f64}\left(t, \frac{-1}{2}\right)\right), \mathsf{log.f64}\left(\left({t}^{\left(\frac{-1}{2}\right)}\right)\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{pow.f64}\left(t, \frac{-1}{2}\right)\right), \mathsf{log.f64}\left(\left({t}^{\frac{-1}{2}}\right)\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   10. pow-lowering-pow.f64 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{pow.f64}\left(t, \frac{-1}{2}\right)\right), \mathsf{log.f64}\left(\mathsf{pow.f64}\left(t, \frac{-1}{2}\right)\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

8. Applied egg-rr 99.9%

   \[\leadsto z \cdot \left(\color{blue}{\left(\log \left({t}^{-0.5}\right) + \log \left({t}^{-0.5}\right)\right)} + 1\right) + \left(\left(x + y\right) + \left(a + -0.5\right) \cdot b\right) \]

9. Final simplification 99.9%

   \[\leadsto z \cdot \left(\left(\log \left({t}^{-0.5}\right) + \log \left({t}^{-0.5}\right)\right) + 1\right) + \left(\left(x + y\right) + \left(-0.5 + a\right) \cdot b\right) \]
10. Add Preprocessing

Alternative 2: 88.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := \left(x + y\right) + t\_1\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+178}:\\ \;\;\;\;x + \left(y + z \cdot \left(1 + \log \left(\frac{1}{t}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (+ (+ x y) t_1)))
   (if (<= t_1 -1e+110)
     t_2
     (if (<= t_1 5e+178) (+ x (+ y (* z (+ 1.0 (log (/ 1.0 t)))))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = (x + y) + t_1;
	double tmp;
	if (t_1 <= -1e+110) {
		tmp = t_2;
	} else if (t_1 <= 5e+178) {
		tmp = x + (y + (z * (1.0 + log((1.0 / t)))));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    t_2 = (x + y) + t_1
    if (t_1 <= (-1d+110)) then
        tmp = t_2
    else if (t_1 <= 5d+178) then
        tmp = x + (y + (z * (1.0d0 + log((1.0d0 / t)))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = (x + y) + t_1;
	double tmp;
	if (t_1 <= -1e+110) {
		tmp = t_2;
	} else if (t_1 <= 5e+178) {
		tmp = x + (y + (z * (1.0 + Math.log((1.0 / t)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	t_2 = (x + y) + t_1
	tmp = 0
	if t_1 <= -1e+110:
		tmp = t_2
	elif t_1 <= 5e+178:
		tmp = x + (y + (z * (1.0 + math.log((1.0 / t)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(Float64(x + y) + t_1)
	tmp = 0.0
	if (t_1 <= -1e+110)
		tmp = t_2;
	elseif (t_1 <= 5e+178)
		tmp = Float64(x + Float64(y + Float64(z * Float64(1.0 + log(Float64(1.0 / t))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	t_2 = (x + y) + t_1;
	tmp = 0.0;
	if (t_1 <= -1e+110)
		tmp = t_2;
	elseif (t_1 <= 5e+178)
		tmp = x + (y + (z * (1.0 + log((1.0 / t)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+110], t$95$2, If[LessEqual[t$95$1, 5e+178], N[(x + N[(y + N[(z * N[(1.0 + N[Log[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1e110 or 4.9999999999999999e178 < (*.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

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x + y\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 95.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(a, \frac{1}{2}\right)}, b\right)\right) \]

   5. Simplified 95.4%

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

   if -1e110 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.9999999999999999e178

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 94.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right)\right) \]

   7. Simplified 94.5%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \left(1 + \color{blue}{\left(\mathsf{neg}\left(\log t\right)\right)}\right)\right)\right)\right) \]

      2. log-rec N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \left(1 + \log \left(\frac{1}{t}\right)\right)\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \left(\log \left(\frac{1}{t}\right) + \color{blue}{1}\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\log \left(\frac{1}{t}\right), \color{blue}{1}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\left(\frac{1}{t}\right)\right), 1\right)\right)\right)\right) \]

      6. /-lowering-/.f64 94.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(1, t\right)\right), 1\right)\right)\right)\right) \]

   9. Applied egg-rr 94.5%

      \[\leadsto x + \left(y + z \cdot \color{blue}{\left(\log \left(\frac{1}{t}\right) + 1\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+110}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+178}:\\ \;\;\;\;x + \left(y + z \cdot \left(1 + \log \left(\frac{1}{t}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := \left(x + y\right) + t\_1\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+178}:\\ \;\;\;\;x + \left(y + z \cdot \left(1 - \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (+ (+ x y) t_1)))
   (if (<= t_1 -1e+110)
     t_2
     (if (<= t_1 5e+178) (+ x (+ y (* z (- 1.0 (log t))))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = (x + y) + t_1;
	double tmp;
	if (t_1 <= -1e+110) {
		tmp = t_2;
	} else if (t_1 <= 5e+178) {
		tmp = x + (y + (z * (1.0 - log(t))));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    t_2 = (x + y) + t_1
    if (t_1 <= (-1d+110)) then
        tmp = t_2
    else if (t_1 <= 5d+178) then
        tmp = x + (y + (z * (1.0d0 - log(t))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = (x + y) + t_1;
	double tmp;
	if (t_1 <= -1e+110) {
		tmp = t_2;
	} else if (t_1 <= 5e+178) {
		tmp = x + (y + (z * (1.0 - Math.log(t))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	t_2 = (x + y) + t_1
	tmp = 0
	if t_1 <= -1e+110:
		tmp = t_2
	elif t_1 <= 5e+178:
		tmp = x + (y + (z * (1.0 - math.log(t))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(Float64(x + y) + t_1)
	tmp = 0.0
	if (t_1 <= -1e+110)
		tmp = t_2;
	elseif (t_1 <= 5e+178)
		tmp = Float64(x + Float64(y + Float64(z * Float64(1.0 - log(t)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	t_2 = (x + y) + t_1;
	tmp = 0.0;
	if (t_1 <= -1e+110)
		tmp = t_2;
	elseif (t_1 <= 5e+178)
		tmp = x + (y + (z * (1.0 - log(t))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+110], t$95$2, If[LessEqual[t$95$1, 5e+178], N[(x + N[(y + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1e110 or 4.9999999999999999e178 < (*.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

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x + y\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 95.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(a, \frac{1}{2}\right)}, b\right)\right) \]

   5. Simplified 95.4%

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

   if -1e110 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.9999999999999999e178

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 94.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right)\right) \]

   7. Simplified 94.5%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+110}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+178}:\\ \;\;\;\;x + \left(y + z \cdot \left(1 - \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+179}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+172}:\\ \;\;\;\;\left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= b -8e+179)
     (+ (+ x y) t_1)
     (if (<= b 2.2e+172)
       (+ (- (+ z (+ x y)) (* z (log t))) (* a b))
       (+ 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 (b <= -8e+179) {
		tmp = (x + y) + t_1;
	} else if (b <= 2.2e+172) {
		tmp = ((z + (x + y)) - (z * log(t))) + (a * b);
	} else {
		tmp = x + 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 = b * (a - 0.5d0)
    if (b <= (-8d+179)) then
        tmp = (x + y) + t_1
    else if (b <= 2.2d+172) then
        tmp = ((z + (x + y)) - (z * log(t))) + (a * b)
    else
        tmp = x + 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 = b * (a - 0.5);
	double tmp;
	if (b <= -8e+179) {
		tmp = (x + y) + t_1;
	} else if (b <= 2.2e+172) {
		tmp = ((z + (x + y)) - (z * Math.log(t))) + (a * b);
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if b <= -8e+179:
		tmp = (x + y) + t_1
	elif b <= 2.2e+172:
		tmp = ((z + (x + y)) - (z * math.log(t))) + (a * b)
	else:
		tmp = x + 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 (b <= -8e+179)
		tmp = Float64(Float64(x + y) + t_1);
	elseif (b <= 2.2e+172)
		tmp = Float64(Float64(Float64(z + Float64(x + y)) - Float64(z * log(t))) + Float64(a * b));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (b <= -8e+179)
		tmp = (x + y) + t_1;
	elseif (b <= 2.2e+172)
		tmp = ((z + (x + y)) - (z * log(t))) + (a * b);
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+179], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 2.2e+172], N[(N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.99999999999999984e179

   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

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x + y\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(a, \frac{1}{2}\right)}, b\right)\right) \]

   5. Simplified 99.9%

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

   if -7.99999999999999984e179 < b < 2.2000000000000001e172

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \mathsf{*.f64}\left(z, \mathsf{log.f64}\left(t\right)\right)\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \mathsf{*.f64}\left(z, \mathsf{log.f64}\left(t\right)\right)\right), \left(b \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 96.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \mathsf{*.f64}\left(z, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 96.3%

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

   if 2.2000000000000001e172 < 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 x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 92.4%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+179}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+172}:\\ \;\;\;\;\left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+156}:\\ \;\;\;\;y + t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+150}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -1.1e+156)
     (+ y t_1)
     (if (<= z 1.1e+150) (+ (+ x y) (* b (- a 0.5))) (+ x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -1.1e+156) {
		tmp = y + t_1;
	} else if (z <= 1.1e+150) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = x + 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 = z * (1.0d0 - log(t))
    if (z <= (-1.1d+156)) then
        tmp = y + t_1
    else if (z <= 1.1d+150) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = x + 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 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -1.1e+156) {
		tmp = y + t_1;
	} else if (z <= 1.1e+150) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -1.1e+156:
		tmp = y + t_1
	elif z <= 1.1e+150:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -1.1e+156)
		tmp = Float64(y + t_1);
	elseif (z <= 1.1e+150)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -1.1e+156)
		tmp = y + t_1;
	elseif (z <= 1.1e+150)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+156], N[(y + t$95$1), $MachinePrecision], If[LessEqual[z, 1.1e+150], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000002e156

   1. Initial program 99.5%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.5%

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

   5. Taylor expanded in b around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 80.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right)\right) \]

   7. Simplified 80.3%

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

   8. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right) \]

      4. log-lowering-log.f64 77.6%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right) \]

   10. Simplified 77.6%

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

   if -1.10000000000000002e156 < z < 1.1e150

   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

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x + y\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 92.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(a, \frac{1}{2}\right)}, b\right)\right) \]

   5. Simplified 92.0%

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

   if 1.1e150 < 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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 82.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right)\right) \]

   7. Simplified 82.9%

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

   8. Taylor expanded in y around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right) \]

      4. log-lowering-log.f64 78.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right) \]

   10. Simplified 78.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+156}:\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+150}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -1.66 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+142}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 (log t))))))
   (if (<= z -1.66e+155)
     t_1
     (if (<= z 1.1e+142) (+ (+ x y) (* b (- a 0.5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - log(t)));
	double tmp;
	if (z <= -1.66e+155) {
		tmp = t_1;
	} else if (z <= 1.1e+142) {
		tmp = (x + y) + (b * (a - 0.5));
	} 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 = x + (z * (1.0d0 - log(t)))
    if (z <= (-1.66d+155)) then
        tmp = t_1
    else if (z <= 1.1d+142) then
        tmp = (x + y) + (b * (a - 0.5d0))
    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 = x + (z * (1.0 - Math.log(t)));
	double tmp;
	if (z <= -1.66e+155) {
		tmp = t_1;
	} else if (z <= 1.1e+142) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - math.log(t)))
	tmp = 0
	if z <= -1.66e+155:
		tmp = t_1
	elif z <= 1.1e+142:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - log(t))))
	tmp = 0.0
	if (z <= -1.66e+155)
		tmp = t_1;
	elseif (z <= 1.1e+142)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - log(t)));
	tmp = 0.0;
	if (z <= -1.66e+155)
		tmp = t_1;
	elseif (z <= 1.1e+142)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.66e+155], t$95$1, If[LessEqual[z, 1.1e+142], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6600000000000001e155 or 1.09999999999999993e142 < z

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in b around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 81.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right)\right) \]

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right) \]

      4. log-lowering-log.f64 75.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right) \]

   10. Simplified 75.9%

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

   if -1.6600000000000001e155 < z < 1.09999999999999993e142

   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

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x + y\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 92.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(a, \frac{1}{2}\right)}, b\right)\right) \]

   5. Simplified 92.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{+155}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+142}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (((-0.5d0) + a) * b)) + (z * (1.0d0 + log((1.0d0 / t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   8. distribute-rgt1-in N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   12. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   13. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   14. log-lowering-log.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

   16. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

   17. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

   18. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

   19. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

   20. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

   21. metadata-eval 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

3. Simplified 99.9%

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

   1. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{y}\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{y}\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\log t\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{y}\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   4. neg-log N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\log \left(\frac{1}{t}\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   5. log-lowering-log.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\left(\frac{1}{t}\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   6. /-lowering-/.f64 99.9%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(1, t\right)\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

   \[\leadsto \left(\left(x + y\right) + \left(-0.5 + a\right) \cdot b\right) + z \cdot \left(1 + \log \left(\frac{1}{t}\right)\right) \]
8. Add Preprocessing

Alternative 8: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+150}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -4.6e+153)
     t_1
     (if (<= z 1.25e+150) (+ (+ x y) (* b (- a 0.5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -4.6e+153) {
		tmp = t_1;
	} else if (z <= 1.25e+150) {
		tmp = (x + y) + (b * (a - 0.5));
	} 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 = z * (1.0d0 - log(t))
    if (z <= (-4.6d+153)) then
        tmp = t_1
    else if (z <= 1.25d+150) then
        tmp = (x + y) + (b * (a - 0.5d0))
    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 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -4.6e+153) {
		tmp = t_1;
	} else if (z <= 1.25e+150) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -4.6e+153:
		tmp = t_1
	elif z <= 1.25e+150:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -4.6e+153)
		tmp = t_1;
	elseif (z <= 1.25e+150)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -4.6e+153)
		tmp = t_1;
	elseif (z <= 1.25e+150)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+153], t$95$1, If[LessEqual[z, 1.25e+150], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6000000000000003e153 or 1.25000000000000002e150 < z

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right) \]

      3. log-lowering-log.f64 68.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right) \]

   7. Simplified 68.2%

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

   if -4.6000000000000003e153 < z < 1.25000000000000002e150

   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

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x + y\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 92.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(a, \frac{1}{2}\right)}, b\right)\right) \]

   5. Simplified 92.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+153}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+150}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (((-0.5d0) + a) * b)) + (z * (1.0d0 - log(t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   8. distribute-rgt1-in N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   12. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   13. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   14. log-lowering-log.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

   16. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

   17. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

   18. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

   19. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

   20. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

   21. metadata-eval 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

3. Simplified 99.9%

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

5. Final simplification 99.9%

   \[\leadsto \left(\left(x + y\right) + \left(-0.5 + a\right) \cdot b\right) + z \cdot \left(1 - \log t\right) \]
6. Add Preprocessing

Alternative 10: 67.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := x + t\_1\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+168}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (+ x t_1)))
   (if (<= t_1 -5e+169) t_2 (if (<= t_1 2e+168) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = x + t_1;
	double tmp;
	if (t_1 <= -5e+169) {
		tmp = t_2;
	} else if (t_1 <= 2e+168) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    t_2 = x + t_1
    if (t_1 <= (-5d+169)) then
        tmp = t_2
    else if (t_1 <= 2d+168) then
        tmp = x + y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = x + t_1;
	double tmp;
	if (t_1 <= -5e+169) {
		tmp = t_2;
	} else if (t_1 <= 2e+168) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	t_2 = x + t_1
	tmp = 0
	if t_1 <= -5e+169:
		tmp = t_2
	elif t_1 <= 2e+168:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(x + t_1)
	tmp = 0.0
	if (t_1 <= -5e+169)
		tmp = t_2;
	elseif (t_1 <= 2e+168)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	t_2 = x + t_1;
	tmp = 0.0;
	if (t_1 <= -5e+169)
		tmp = t_2;
	elseif (t_1 <= 2e+168)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+169], t$95$2, If[LessEqual[t$95$1, 2e+168], N[(x + y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.00000000000000017e169 or 1.9999999999999999e168 < (*.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 x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 85.2%

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

   if -5.00000000000000017e169 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.9999999999999999e168

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 93.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right)\right) \]

   7. Simplified 93.6%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 61.9%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{y}\right) \]

   10. Simplified 61.9%

       \[\leadsto \color{blue}{x + y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+169}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+168}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+39}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x + y \leq 10^{+25}:\\ \;\;\;\;\left(-0.5 + a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -4e+39)
   (+ x (* a b))
   (if (<= (+ x y) 1e+25) (* (+ -0.5 a) b) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -4e+39) {
		tmp = x + (a * b);
	} else if ((x + y) <= 1e+25) {
		tmp = (-0.5 + a) * b;
	} else {
		tmp = x + y;
	}
	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 ((x + y) <= (-4d+39)) then
        tmp = x + (a * b)
    else if ((x + y) <= 1d+25) then
        tmp = ((-0.5d0) + a) * b
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -4e+39) {
		tmp = x + (a * b);
	} else if ((x + y) <= 1e+25) {
		tmp = (-0.5 + a) * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -4e+39:
		tmp = x + (a * b)
	elif (x + y) <= 1e+25:
		tmp = (-0.5 + a) * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -4e+39)
		tmp = Float64(x + Float64(a * b));
	elseif (Float64(x + y) <= 1e+25)
		tmp = Float64(Float64(-0.5 + a) * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -4e+39)
		tmp = x + (a * b);
	elseif ((x + y) <= 1e+25)
		tmp = (-0.5 + a) * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -4e+39], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 1e+25], N[(N[(-0.5 + a), $MachinePrecision] * b), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -3.99999999999999976e39

   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 inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 53.4%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 47.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{a}\right)\right) \]

   8. Simplified 47.3%

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

   if -3.99999999999999976e39 < (+.f64 x y) < 1.00000000000000009e25

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a - \frac{1}{2}\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(a + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(a + \frac{-1}{2}\right)\right) \]

      4. +-lowering-+.f64 51.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\frac{-1}{2}}\right)\right) \]

   7. Simplified 51.2%

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

   if 1.00000000000000009e25 < (+.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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 81.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right)\right) \]

   7. Simplified 81.2%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 63.0%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{y}\right) \]

   10. Simplified 63.0%

       \[\leadsto \color{blue}{x + y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+39}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x + y \leq 10^{+25}:\\ \;\;\;\;\left(-0.5 + a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.5% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-92}:\\ \;\;\;\;x + \left(a \cdot b + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -1e-92) (+ x (+ (* a b) (* -0.5 b))) (+ y (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e-92) {
		tmp = x + ((a * b) + (-0.5 * b));
	} else {
		tmp = y + (b * (a - 0.5));
	}
	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 ((x + y) <= (-1d-92)) then
        tmp = x + ((a * b) + ((-0.5d0) * b))
    else
        tmp = y + (b * (a - 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e-92) {
		tmp = x + ((a * b) + (-0.5 * b));
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -1e-92:
		tmp = x + ((a * b) + (-0.5 * b))
	else:
		tmp = y + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -1e-92)
		tmp = Float64(x + Float64(Float64(a * b) + Float64(-0.5 * b)));
	else
		tmp = Float64(y + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -1e-92)
		tmp = x + ((a * b) + (-0.5 * b));
	else
		tmp = y + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-92], N[(x + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.99999999999999988e-93

   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 inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 57.8%

      \[\leadsto \color{blue}{x} + \left(a - 0.5\right) \cdot b \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \color{blue}{\left(a - \frac{1}{2}\right)}\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(a + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(a + \frac{-1}{2}\right)\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot a + \color{blue}{b \cdot \frac{-1}{2}}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot a\right), \color{blue}{\left(b \cdot \frac{-1}{2}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, a\right), \left(\color{blue}{b} \cdot \frac{-1}{2}\right)\right)\right) \]

      7. *-lowering-*.f64 57.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, a\right), \mathsf{*.f64}\left(b, \color{blue}{\frac{-1}{2}}\right)\right)\right) \]

   7. Applied egg-rr 57.8%

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

   if -9.99999999999999988e-93 < (+.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 50.0%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-92}:\\ \;\;\;\;x + \left(a \cdot b + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.7% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-0.5 + a\right) \cdot b\\ \mathbf{if}\;b \leq -2.25 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ -0.5 a) b)))
   (if (<= b -2.25e+168) t_1 (if (<= b 2.5e+47) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-0.5 + a) * b;
	double tmp;
	if (b <= -2.25e+168) {
		tmp = t_1;
	} else if (b <= 2.5e+47) {
		tmp = x + y;
	} 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 = ((-0.5d0) + a) * b
    if (b <= (-2.25d+168)) then
        tmp = t_1
    else if (b <= 2.5d+47) then
        tmp = x + y
    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 = (-0.5 + a) * b;
	double tmp;
	if (b <= -2.25e+168) {
		tmp = t_1;
	} else if (b <= 2.5e+47) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-0.5 + a) * b
	tmp = 0
	if b <= -2.25e+168:
		tmp = t_1
	elif b <= 2.5e+47:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-0.5 + a) * b)
	tmp = 0.0
	if (b <= -2.25e+168)
		tmp = t_1;
	elseif (b <= 2.5e+47)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-0.5 + a) * b;
	tmp = 0.0;
	if (b <= -2.25e+168)
		tmp = t_1;
	elseif (b <= 2.5e+47)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-0.5 + a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.25e+168], t$95$1, If[LessEqual[b, 2.5e+47], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.25000000000000006e168 or 2.50000000000000011e47 < b

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a - \frac{1}{2}\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(a + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(a + \frac{-1}{2}\right)\right) \]

      4. +-lowering-+.f64 68.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\frac{-1}{2}}\right)\right) \]

   7. Simplified 68.1%

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

   if -2.25000000000000006e168 < b < 2.50000000000000011e47

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 87.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right)\right) \]

   7. Simplified 87.1%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 58.7%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{y}\right) \]

   10. Simplified 58.7%

       \[\leadsto \color{blue}{x + y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+168}:\\ \;\;\;\;\left(-0.5 + a\right) \cdot b\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-0.5 + a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.5% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -1 \cdot 10^{-92}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) -1e-92) (+ x t_1) (+ y 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 ((x + y) <= -1e-92) {
		tmp = x + t_1;
	} else {
		tmp = y + 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 = b * (a - 0.5d0)
    if ((x + y) <= (-1d-92)) then
        tmp = x + t_1
    else
        tmp = y + 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 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -1e-92) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -1e-92:
		tmp = x + t_1
	else:
		tmp = y + 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 (Float64(x + y) <= -1e-92)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -1e-92)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -1e-92], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.99999999999999988e-93

   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 inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 57.8%

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

   if -9.99999999999999988e-93 < (+.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 50.0%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-92}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.8% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+168}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+161}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e+168) (* a b) (if (<= b 1.1e+161) (+ x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+168) {
		tmp = a * b;
	} else if (b <= 1.1e+161) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	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 (b <= (-6.8d+168)) then
        tmp = a * b
    else if (b <= 1.1d+161) then
        tmp = x + y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+168) {
		tmp = a * b;
	} else if (b <= 1.1e+161) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e+168:
		tmp = a * b
	elif b <= 1.1e+161:
		tmp = x + y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e+168)
		tmp = Float64(a * b);
	elseif (b <= 1.1e+161)
		tmp = Float64(x + y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e+168)
		tmp = a * b;
	elseif (b <= 1.1e+161)
		tmp = x + y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e+168], N[(a * b), $MachinePrecision], If[LessEqual[b, 1.1e+161], N[(x + y), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.80000000000000005e168 or 1.1e161 < 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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 49.5%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{a}\right) \]

   7. Simplified 49.5%

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

   if -6.80000000000000005e168 < b < 1.1e161

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - \log t\right)}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right)\right) \]

      5. log-lowering-log.f64 83.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right)\right) \]

   7. Simplified 83.1%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 55.8%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{y}\right) \]

   10. Simplified 55.8%

       \[\leadsto \color{blue}{x + y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+168}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+161}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 28.1% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-32}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 7e-191) x (if (<= y 1.45e-32) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 7e-191) {
		tmp = x;
	} else if (y <= 1.45e-32) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	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 (y <= 7d-191) then
        tmp = x
    else if (y <= 1.45d-32) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 7e-191) {
		tmp = x;
	} else if (y <= 1.45e-32) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 7e-191:
		tmp = x
	elif y <= 1.45e-32:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 7e-191)
		tmp = x;
	elseif (y <= 1.45e-32)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 7e-191)
		tmp = x;
	elseif (y <= 1.45e-32)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 7e-191], x, If[LessEqual[y, 1.45e-32], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < 7.00000000000000013e-191

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 27.2%

      \[\leadsto \color{blue}{x} \]

   if 7.00000000000000013e-191 < y < 1.44999999999999998e-32

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 27.6%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{a}\right) \]

   7. Simplified 27.6%

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

   if 1.44999999999999998e-32 < 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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   6. Step-by-step derivation

   7. Simplified 47.7%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-32}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 78.9% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x + y\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
4. Step-by-step derivation

   1. +-lowering-+.f64 77.2%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(a, \frac{1}{2}\right)}, b\right)\right) \]

5. Simplified 77.2%

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

6. Final simplification 77.2%

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

Alternative 18: 26.3% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 5.5e-139) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.5e-139) {
		tmp = x;
	} else {
		tmp = y;
	}
	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 (y <= 5.5d-139) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.5e-139) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 5.5e-139:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 5.5e-139)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 5.5e-139)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 5.5e-139], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 5.4999999999999997e-139

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 28.2%

      \[\leadsto \color{blue}{x} \]

   if 5.4999999999999997e-139 < y

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      8. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

      21. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   6. Step-by-step derivation

   7. Simplified 38.2%

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

Alternative 19: 22.6% accurate, 115.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z - z \cdot \log t\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z - \log t \cdot z\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(\log t\right)\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   8. distribute-rgt1-in N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right) \cdot z\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right), \left(\color{blue}{\left(a - \frac{1}{2}\right) \cdot b} + \left(x + y\right)\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   12. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   13. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \log t\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot \color{blue}{b} + \left(x + y\right)\right)\right) \]

   14. log-lowering-log.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + y\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \left(\left(x + y\right) + \color{blue}{\left(a - \frac{1}{2}\right) \cdot b}\right)\right) \]

   16. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\left(a - \frac{1}{2}\right) \cdot b\right)}\right)\right) \]

   17. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{\left(a - \frac{1}{2}\right)} \cdot b\right)\right)\right) \]

   18. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a - \frac{1}{2}\right), \color{blue}{b}\right)\right)\right) \]

   19. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

   20. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), b\right)\right)\right) \]

   21. metadata-eval 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \frac{-1}{2}\right), b\right)\right)\right) \]

3. Simplified 99.9%

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

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 23.8%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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 2024158 
(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)))