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

Percentage Accurate: 89.1% → 99.6%

Time: 15.2s

Alternatives: 18

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \left(\left(y \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot \left(-0.3333333333333333 + y \cdot -0.25\right)\right)\right)\right) \cdot \left(z + -1\right) + \log y \cdot \left(x + -1\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (+
   (*
    (* y (+ -1.0 (* y (+ -0.5 (* y (+ -0.3333333333333333 (* y -0.25)))))))
    (+ z -1.0))
   (* (log y) (+ x -1.0)))
  t))

C

double code(double x, double y, double z, double t) {
	return (((y * (-1.0 + (y * (-0.5 + (y * (-0.3333333333333333 + (y * -0.25))))))) * (z + -1.0)) + (log(y) * (x + -1.0))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((y * ((-1.0d0) + (y * ((-0.5d0) + (y * ((-0.3333333333333333d0) + (y * (-0.25d0)))))))) * (z + (-1.0d0))) + (log(y) * (x + (-1.0d0)))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((y * (-1.0 + (y * (-0.5 + (y * (-0.3333333333333333 + (y * -0.25))))))) * (z + -1.0)) + (Math.log(y) * (x + -1.0))) - t;
}

Python

def code(x, y, z, t):
	return (((y * (-1.0 + (y * (-0.5 + (y * (-0.3333333333333333 + (y * -0.25))))))) * (z + -1.0)) + (math.log(y) * (x + -1.0))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(y * Float64(-1.0 + Float64(y * Float64(-0.5 + Float64(y * Float64(-0.3333333333333333 + Float64(y * -0.25))))))) * Float64(z + -1.0)) + Float64(log(y) * Float64(x + -1.0))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((y * (-1.0 + (y * (-0.5 + (y * (-0.3333333333333333 + (y * -0.25))))))) * (z + -1.0)) + (log(y) * (x + -1.0))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(y * N[(-1.0 + N[(y * N[(-0.5 + N[(y * N[(-0.3333333333333333 + N[(y * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 92.0%

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

3. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(y \cdot \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right)\right)}\right)\right), t\right) \]
4. Step-by-step derivation

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right)\right)\right)\right), t\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), t\right) \]

   3. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) + -1\right)\right)\right)\right), t\right) \]

   4. +-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(-1 + y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right)\right)\right)\right)\right), t\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right)\right)\right)\right)\right)\right), t\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right)\right)\right)\right)\right)\right), t\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) + \frac{-1}{2}\right)\right)\right)\right)\right)\right), t\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(\frac{-1}{2} + y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right)\right)\right)\right)\right)\right)\right), t\right) \]

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

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

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

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

   12. sub-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \left(\frac{-1}{4} \cdot y + \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \left(\frac{-1}{4} \cdot y + \frac{-1}{3}\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \left(\frac{-1}{3} + \frac{-1}{4} \cdot y\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

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

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{3}, \left(\frac{-1}{4} \cdot y\right)\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{3}, \left(y \cdot \frac{-1}{4}\right)\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

   17. *-lowering-*.f64 99.2%

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{3}, \mathsf{*.f64}\left(y, \frac{-1}{4}\right)\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

5. Simplified 99.2%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot \left(-0.3333333333333333 + y \cdot -0.25\right)\right)\right)\right)}\right) - t \]

6. Final simplification 99.2%

   \[\leadsto \left(\left(y \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot \left(-0.3333333333333333 + y \cdot -0.25\right)\right)\right)\right) \cdot \left(z + -1\right) + \log y \cdot \left(x + -1\right)\right) - t \]
7. Add Preprocessing

Alternative 2: 99.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \left(\left(y \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right) \cdot \left(z + -1\right) + \log y \cdot \left(x + -1\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (+
   (* (* y (+ -1.0 (* y (+ -0.5 (* y -0.3333333333333333))))) (+ z -1.0))
   (* (log y) (+ x -1.0)))
  t))

C

double code(double x, double y, double z, double t) {
	return (((y * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333))))) * (z + -1.0)) + (log(y) * (x + -1.0))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((y * ((-1.0d0) + (y * ((-0.5d0) + (y * (-0.3333333333333333d0)))))) * (z + (-1.0d0))) + (log(y) * (x + (-1.0d0)))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((y * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333))))) * (z + -1.0)) + (Math.log(y) * (x + -1.0))) - t;
}

Python

def code(x, y, z, t):
	return (((y * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333))))) * (z + -1.0)) + (math.log(y) * (x + -1.0))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(y * Float64(-1.0 + Float64(y * Float64(-0.5 + Float64(y * -0.3333333333333333))))) * Float64(z + -1.0)) + Float64(log(y) * Float64(x + -1.0))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((y * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333))))) * (z + -1.0)) + (log(y) * (x + -1.0))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(y * N[(-1.0 + N[(y * N[(-0.5 + N[(y * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 92.0%

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

3. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) - 1\right)\right)}\right)\right), t\right) \]
4. Step-by-step derivation

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) - 1\right)\right)\right)\right), t\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), t\right) \]

   3. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) + -1\right)\right)\right)\right), t\right) \]

   4. +-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(-1 + y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right)\right)\right)\right)\right), t\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right)\right)\right)\right)\right)\right), t\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right)\right)\right)\right)\right)\right), t\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(\frac{-1}{3} \cdot y + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(\frac{-1}{3} \cdot y + \frac{-1}{2}\right)\right)\right)\right)\right)\right), t\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(\frac{-1}{2} + \frac{-1}{3} \cdot y\right)\right)\right)\right)\right)\right), t\right) \]

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

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(\frac{-1}{3} \cdot y\right)\right)\right)\right)\right)\right)\right), t\right) \]

   11. *-commutative N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(y \cdot \frac{-1}{3}\right)\right)\right)\right)\right)\right)\right), t\right) \]

   12. *-lowering-*.f64 99.2%

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \frac{-1}{3}\right)\right)\right)\right)\right)\right)\right), t\right) \]

5. Simplified 99.2%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right)}\right) - t \]

6. Final simplification 99.2%

   \[\leadsto \left(\left(y \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right) \cdot \left(z + -1\right) + \log y \cdot \left(x + -1\right)\right) - t \]
7. Add Preprocessing

Alternative 3: 95.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot \left(x + -1\right) - t\\ \mathbf{if}\;x \leq -1700000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10^{-49}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* (log y) (+ x -1.0)) t)))
   (if (<= x -1700000.0)
     t_1
     (if (<= x 1e-49) (- (- (* y (- 1.0 z)) (log y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (log(y) * (x + -1.0)) - t;
	double tmp;
	if (x <= -1700000.0) {
		tmp = t_1;
	} else if (x <= 1e-49) {
		tmp = ((y * (1.0 - z)) - log(y)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (log(y) * (x + (-1.0d0))) - t
    if (x <= (-1700000.0d0)) then
        tmp = t_1
    else if (x <= 1d-49) then
        tmp = ((y * (1.0d0 - z)) - log(y)) - t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (Math.log(y) * (x + -1.0)) - t;
	double tmp;
	if (x <= -1700000.0) {
		tmp = t_1;
	} else if (x <= 1e-49) {
		tmp = ((y * (1.0 - z)) - Math.log(y)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (math.log(y) * (x + -1.0)) - t
	tmp = 0
	if x <= -1700000.0:
		tmp = t_1
	elif x <= 1e-49:
		tmp = ((y * (1.0 - z)) - math.log(y)) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(log(y) * Float64(x + -1.0)) - t)
	tmp = 0.0
	if (x <= -1700000.0)
		tmp = t_1;
	elseif (x <= 1e-49)
		tmp = Float64(Float64(Float64(y * Float64(1.0 - z)) - log(y)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (log(y) * (x + -1.0)) - t;
	tmp = 0.0;
	if (x <= -1700000.0)
		tmp = t_1;
	elseif (x <= 1e-49)
		tmp = ((y * (1.0 - z)) - log(y)) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[x, -1700000.0], t$95$1, If[LessEqual[x, 1e-49], N[(N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e6 or 9.99999999999999936e-50 < x

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 96.2%

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

   5. Simplified 96.2%

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

   if -1.7e6 < x < 9.99999999999999936e-50

   1. Initial program 85.6%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. /-lowering-/.f64 N/A

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

      10. sub-neg N/A

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

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

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

      12. metadata-eval 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(-1 \cdot y\right)}\right)\right), t\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \left(0 - y\right)\right)\right), t\right) \]

      3. --lowering--.f64 98.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{\_.f64}\left(0, y\right)\right)\right), t\right) \]

   7. Simplified 98.4%

      \[\leadsto \left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \color{blue}{\left(0 - y\right)}\right) - t \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \left(0 - y\right)\right), \color{blue}{t}\right) \]

   9. Applied egg-rr 98.4%

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

   10. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. associate--r+ N/A

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

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

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

       4. sub-neg N/A

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

       5. +-commutative N/A

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

       6. mul-1-neg N/A

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

       7. unsub-neg N/A

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

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

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

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

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

       10. mul-1-neg N/A

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

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

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

       12. mul-1-neg N/A

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

       13. sub-neg N/A

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

       14. metadata-eval N/A

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

       15. distribute-neg-in N/A

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

       16. metadata-eval N/A

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

       17. +-commutative N/A

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

       18. sub-neg N/A

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

       19. --lowering--.f64 N/A

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

       20. log-lowering-log.f64 98.0%

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

   12. Simplified 98.0%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1700000:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \mathbf{elif}\;x \leq 10^{-49}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((z + (-1.0d0)) * (y * ((-1.0d0) + (y * (-0.5d0))))) + (log(y) * (x + (-1.0d0)))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

3. Taylor expanded in y around 0

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

5. Simplified 99.0%

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

6. Final simplification 99.0%

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

Alternative 5: 86.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - t\\ \mathbf{if}\;x \leq -900000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-23}:\\ \;\;\;\;\left(y - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) t)))
   (if (<= x -900000.0) t_1 (if (<= x 5.2e-23) (- (- y (log y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - t;
	double tmp;
	if (x <= -900000.0) {
		tmp = t_1;
	} else if (x <= 5.2e-23) {
		tmp = (y - log(y)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - t
    if (x <= (-900000.0d0)) then
        tmp = t_1
    else if (x <= 5.2d-23) then
        tmp = (y - log(y)) - t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - t;
	double tmp;
	if (x <= -900000.0) {
		tmp = t_1;
	} else if (x <= 5.2e-23) {
		tmp = (y - Math.log(y)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - t
	tmp = 0
	if x <= -900000.0:
		tmp = t_1
	elif x <= 5.2e-23:
		tmp = (y - math.log(y)) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - t)
	tmp = 0.0
	if (x <= -900000.0)
		tmp = t_1;
	elseif (x <= 5.2e-23)
		tmp = Float64(Float64(y - log(y)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - t;
	tmp = 0.0;
	if (x <= -900000.0)
		tmp = t_1;
	elseif (x <= 5.2e-23)
		tmp = (y - log(y)) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[x, -900000.0], t$95$1, If[LessEqual[x, 5.2e-23], N[(N[(y - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9e5 or 5.2e-23 < x

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log y \cdot x\right), t\right) \]

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

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

      3. log-lowering-log.f64 95.7%

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

   5. Simplified 95.7%

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

   if -9e5 < x < 5.2e-23

   1. Initial program 86.1%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. /-lowering-/.f64 N/A

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

      10. sub-neg N/A

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

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

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

      12. metadata-eval 86.1%

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(-1 \cdot y\right)}\right)\right), t\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \left(0 - y\right)\right)\right), t\right) \]

      3. --lowering--.f64 98.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{\_.f64}\left(0, y\right)\right)\right), t\right) \]

   7. Simplified 98.4%

      \[\leadsto \left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \color{blue}{\left(0 - y\right)}\right) - t \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y + \log y \cdot \left(x - 1\right)\right)}, t\right) \]
   9. Step-by-step derivation

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 84.1%

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

   10. Simplified 84.1%

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

   11. Taylor expanded in x around 0

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

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

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

       2. mul-1-neg N/A

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

       3. unsub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(y - \log y\right), t\right) \]

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

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

       5. log-lowering-log.f64 83.7%

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

   13. Simplified 83.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -900000:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-23}:\\ \;\;\;\;\left(y - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - t\\ \mathbf{if}\;x \leq -4600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10^{-49}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) t)))
   (if (<= x -4600000.0)
     t_1
     (if (<= x 1e-49) (- (* y (* z (+ -1.0 (* y -0.5)))) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - t;
	double tmp;
	if (x <= -4600000.0) {
		tmp = t_1;
	} else if (x <= 1e-49) {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - t
    if (x <= (-4600000.0d0)) then
        tmp = t_1
    else if (x <= 1d-49) then
        tmp = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - t;
	double tmp;
	if (x <= -4600000.0) {
		tmp = t_1;
	} else if (x <= 1e-49) {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - t
	tmp = 0
	if x <= -4600000.0:
		tmp = t_1
	elif x <= 1e-49:
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - t)
	tmp = 0.0
	if (x <= -4600000.0)
		tmp = t_1;
	elseif (x <= 1e-49)
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * -0.5)))) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - t;
	tmp = 0.0;
	if (x <= -4600000.0)
		tmp = t_1;
	elseif (x <= 1e-49)
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[x, -4600000.0], t$95$1, If[LessEqual[x, 1e-49], N[(N[(y * N[(z * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6e6 or 9.99999999999999936e-50 < x

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log y \cdot x\right), t\right) \]

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

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

      3. log-lowering-log.f64 95.3%

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

   5. Simplified 95.3%

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

   if -4.6e6 < x < 9.99999999999999936e-50

   1. Initial program 85.6%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right)\right)}, t\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 63.8%

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

   8. Simplified 63.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right)} - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4600000:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;x \leq 10^{-49}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.6 \cdot 10^{+214}:\\ \;\;\;\;\left(y + \log y \cdot \left(x + -1\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 7.6e+214)
   (- (+ y (* (log y) (+ x -1.0))) t)
   (- (* y (* z (+ -1.0 (* y -0.5)))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 7.6e+214) {
		tmp = (y + (log(y) * (x + -1.0))) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 7.6d+214) then
        tmp = (y + (log(y) * (x + (-1.0d0)))) - t
    else
        tmp = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 7.6e+214) {
		tmp = (y + (Math.log(y) * (x + -1.0))) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 7.6e+214:
		tmp = (y + (math.log(y) * (x + -1.0))) - t
	else:
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 7.6e+214)
		tmp = Float64(Float64(y + Float64(log(y) * Float64(x + -1.0))) - t);
	else
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * -0.5)))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 7.6e+214)
		tmp = (y + (log(y) * (x + -1.0))) - t;
	else
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 7.6e+214], N[(N[(y + N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y * N[(z * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.59999999999999994e214

   1. Initial program 94.5%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. /-lowering-/.f64 N/A

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

      10. sub-neg N/A

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

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

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

      12. metadata-eval 94.4%

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

   4. Applied egg-rr 94.4%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(-1 \cdot y\right)}\right)\right), t\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \left(0 - y\right)\right)\right), t\right) \]

      3. --lowering--.f64 99.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{\_.f64}\left(0, y\right)\right)\right), t\right) \]

   7. Simplified 99.0%

      \[\leadsto \left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \color{blue}{\left(0 - y\right)}\right) - t \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y + \log y \cdot \left(x - 1\right)\right)}, t\right) \]
   9. Step-by-step derivation

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 93.5%

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

   10. Simplified 93.5%

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

   if 7.59999999999999994e214 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 93.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right)\right)}, t\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 79.6%

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

   8. Simplified 79.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right)} - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.6 \cdot 10^{+214}:\\ \;\;\;\;\left(y + \log y \cdot \left(x + -1\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 64000000000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -3.4e+24)
     t_1
     (if (<= x 64000000000000.0) (- (* y (* z (+ -1.0 (* y -0.5)))) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -3.4e+24) {
		tmp = t_1;
	} else if (x <= 64000000000000.0) {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-3.4d+24)) then
        tmp = t_1
    else if (x <= 64000000000000.0d0) then
        tmp = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -3.4e+24) {
		tmp = t_1;
	} else if (x <= 64000000000000.0) {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -3.4e+24:
		tmp = t_1
	elif x <= 64000000000000.0:
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -3.4e+24)
		tmp = t_1;
	elseif (x <= 64000000000000.0)
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * -0.5)))) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -3.4e+24)
		tmp = t_1;
	elseif (x <= 64000000000000.0)
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+24], t$95$1, If[LessEqual[x, 64000000000000.0], N[(N[(y * N[(z * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4000000000000001e24 or 6.4e13 < x

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 71.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{log.f64}\left(y\right), x\right) \]

   5. Simplified 71.1%

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

   if -3.4000000000000001e24 < x < 6.4e13

   1. Initial program 86.9%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 99.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right)\right)}, t\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 65.9%

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

   8. Simplified 65.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right)} - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 64000000000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((log(y) * (x + (-1.0d0))) - (y * (z + (-1.0d0)))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. unsub-neg N/A

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

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

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

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

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

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

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

   7. sub-neg N/A

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

   8. metadata-eval N/A

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

   9. +-commutative N/A

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

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

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

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

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

   12. sub-neg N/A

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

   13. metadata-eval N/A

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

   14. +-commutative N/A

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

   15. +-lowering-+.f64 98.6%

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

5. Simplified 98.6%

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

6. Final simplification 98.6%

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

Alternative 10: 89.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.9 \cdot 10^{+217}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 2.9e+217)
   (- (* (log y) (+ x -1.0)) t)
   (- (* y (* z (+ -1.0 (* y -0.5)))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2.9e+217) {
		tmp = (log(y) * (x + -1.0)) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 2.9d+217) then
        tmp = (log(y) * (x + (-1.0d0))) - t
    else
        tmp = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2.9e+217) {
		tmp = (Math.log(y) * (x + -1.0)) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 2.9e+217:
		tmp = (math.log(y) * (x + -1.0)) - t
	else:
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2.9e+217)
		tmp = Float64(Float64(log(y) * Float64(x + -1.0)) - t);
	else
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * -0.5)))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 2.9e+217)
		tmp = (log(y) * (x + -1.0)) - t;
	else
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 2.9e+217], N[(N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y * N[(z * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.89999999999999985e217

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 93.5%

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

   5. Simplified 93.5%

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

   if 2.89999999999999985e217 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 93.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right)\right)}, t\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 79.6%

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

   8. Simplified 79.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right)} - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.9 \cdot 10^{+217}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.0% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((log(y) * (x + (-1.0d0))) - (y * z)) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

   1. *-commutative N/A

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

   2. flip-- N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

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

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

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

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

   7. clear-num N/A

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

   8. flip-- N/A

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

   9. /-lowering-/.f64 N/A

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

   10. sub-neg N/A

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

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

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

   12. metadata-eval 91.9%

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

4. Applied egg-rr 91.9%

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

5. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(-1 \cdot y\right)}\right)\right), t\right) \]
6. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \left(0 - y\right)\right)\right), t\right) \]

   3. --lowering--.f64 98.5%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{\_.f64}\left(0, y\right)\right)\right), t\right) \]

7. Simplified 98.5%

   \[\leadsto \left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \color{blue}{\left(0 - y\right)}\right) - t \]
8. Step-by-step derivation

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

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \left(0 - y\right)\right), \color{blue}{t}\right) \]

9. Applied egg-rr 98.6%

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

10. Taylor expanded in z around inf

    \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{+.f64}\left(x, -1\right)\right), \color{blue}{\left(y \cdot z\right)}\right), t\right) \]
11. Step-by-step derivation

    1. *-lowering-*.f64 98.6%

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

12. Simplified 98.6%

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

Alternative 12: 42.6% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-16}:\\ \;\;\;\;0 - t\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.25e-16) (- 0.0 t) (if (<= t 3.1e+43) (* y (- 1.0 z)) (- 0.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.25e-16) {
		tmp = 0.0 - t;
	} else if (t <= 3.1e+43) {
		tmp = y * (1.0 - z);
	} else {
		tmp = 0.0 - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.25d-16)) then
        tmp = 0.0d0 - t
    else if (t <= 3.1d+43) then
        tmp = y * (1.0d0 - z)
    else
        tmp = 0.0d0 - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.25e-16) {
		tmp = 0.0 - t;
	} else if (t <= 3.1e+43) {
		tmp = y * (1.0 - z);
	} else {
		tmp = 0.0 - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.25e-16:
		tmp = 0.0 - t
	elif t <= 3.1e+43:
		tmp = y * (1.0 - z)
	else:
		tmp = 0.0 - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.25e-16)
		tmp = Float64(0.0 - t);
	elseif (t <= 3.1e+43)
		tmp = Float64(y * Float64(1.0 - z));
	else
		tmp = Float64(0.0 - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.25e-16)
		tmp = 0.0 - t;
	elseif (t <= 3.1e+43)
		tmp = y * (1.0 - z);
	else
		tmp = 0.0 - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.25e-16], N[(0.0 - t), $MachinePrecision], If[LessEqual[t, 3.1e+43], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(0.0 - t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2500000000000001e-16 or 3.1000000000000002e43 < t

   1. Initial program 96.9%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{t} \]

      3. --lowering--.f64 69.9%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{t}\right) \]

   5. Simplified 69.9%

      \[\leadsto \color{blue}{0 - t} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 69.9%

         \[\leadsto \mathsf{neg.f64}\left(t\right) \]

   7. Applied egg-rr 69.9%

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

   if -2.2500000000000001e-16 < t < 3.1000000000000002e43

   1. Initial program 86.3%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. /-lowering-/.f64 N/A

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

      10. sub-neg N/A

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

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

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

      12. metadata-eval 86.2%

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

   4. Applied egg-rr 86.2%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(-1 \cdot y\right)}\right)\right), t\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \left(0 - y\right)\right)\right), t\right) \]

      3. --lowering--.f64 97.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{\_.f64}\left(0, y\right)\right)\right), t\right) \]

   7. Simplified 97.5%

      \[\leadsto \left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \color{blue}{\left(0 - y\right)}\right) - t \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \left(0 - y\right)\right), \color{blue}{t}\right) \]

   9. Applied egg-rr 97.6%

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

   10. Taylor expanded in y around inf

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

       1. sub-neg N/A

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

       2. +-commutative N/A

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

       3. metadata-eval N/A

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

       4. distribute-neg-in N/A

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

       5. metadata-eval N/A

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

       6. sub-neg N/A

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

       7. mul-1-neg N/A

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

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

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

       9. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(z - 1\right)\right)\right)\right) \]

       10. sub-neg N/A

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

       11. metadata-eval N/A

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

       12. distribute-neg-in N/A

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

       13. metadata-eval N/A

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

       14. +-commutative N/A

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

       15. sub-neg N/A

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

       16. --lowering--.f64 17.0%

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

   12. Simplified 17.0%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-16}:\\ \;\;\;\;0 - t\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.4% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-15}:\\ \;\;\;\;0 - t\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+43}:\\ \;\;\;\;0 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;0 - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.26e-15) (- 0.0 t) (if (<= t 3.1e+43) (- 0.0 (* y z)) (- 0.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.26e-15) {
		tmp = 0.0 - t;
	} else if (t <= 3.1e+43) {
		tmp = 0.0 - (y * z);
	} else {
		tmp = 0.0 - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.26d-15)) then
        tmp = 0.0d0 - t
    else if (t <= 3.1d+43) then
        tmp = 0.0d0 - (y * z)
    else
        tmp = 0.0d0 - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.26e-15) {
		tmp = 0.0 - t;
	} else if (t <= 3.1e+43) {
		tmp = 0.0 - (y * z);
	} else {
		tmp = 0.0 - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.26e-15:
		tmp = 0.0 - t
	elif t <= 3.1e+43:
		tmp = 0.0 - (y * z)
	else:
		tmp = 0.0 - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.26e-15)
		tmp = Float64(0.0 - t);
	elseif (t <= 3.1e+43)
		tmp = Float64(0.0 - Float64(y * z));
	else
		tmp = Float64(0.0 - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.26e-15)
		tmp = 0.0 - t;
	elseif (t <= 3.1e+43)
		tmp = 0.0 - (y * z);
	else
		tmp = 0.0 - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.26e-15], N[(0.0 - t), $MachinePrecision], If[LessEqual[t, 3.1e+43], N[(0.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(0.0 - t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.26e-15 or 3.1000000000000002e43 < t

   1. Initial program 96.9%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{t} \]

      3. --lowering--.f64 69.9%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{t}\right) \]

   5. Simplified 69.9%

      \[\leadsto \color{blue}{0 - t} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 69.9%

         \[\leadsto \mathsf{neg.f64}\left(t\right) \]

   7. Applied egg-rr 69.9%

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

   if -1.26e-15 < t < 3.1000000000000002e43

   1. Initial program 86.3%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(y \cdot \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right)\right)}\right)\right), t\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right)\right)\right)\right), t\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), t\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) + -1\right)\right)\right)\right), t\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \left(-1 + y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right)\right)\right)\right)\right), t\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right)\right)\right)\right)\right)\right), t\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right)\right)\right)\right)\right)\right), t\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) + \frac{-1}{2}\right)\right)\right)\right)\right)\right), t\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(\frac{-1}{2} + y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right)\right)\right)\right)\right)\right)\right), t\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \left(\frac{-1}{4} \cdot y + \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \left(\frac{-1}{4} \cdot y + \frac{-1}{3}\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \left(\frac{-1}{3} + \frac{-1}{4} \cdot y\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{3}, \left(\frac{-1}{4} \cdot y\right)\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{3}, \left(y \cdot \frac{-1}{4}\right)\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

      17. *-lowering-*.f64 98.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{3}, \mathsf{*.f64}\left(y, \frac{-1}{4}\right)\right)\right)\right)\right)\right)\right)\right)\right), t\right) \]

   5. Simplified 98.5%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot \left(-0.3333333333333333 + y \cdot -0.25\right)\right)\right)\right)}\right) - t \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y \cdot z\right) \cdot \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right) \cdot \color{blue}{\left(y \cdot z\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right), \color{blue}{\left(y \cdot z\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) + \left(\mathsf{neg}\left(1\right)\right)\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) + -1\right), \left(y \cdot z\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 + y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right)\right), \left(\color{blue}{y} \cdot z\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right)\right)\right), \left(\color{blue}{y} \cdot z\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right)\right)\right), \left(y \cdot z\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right)\right), \left(y \cdot z\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) + \frac{-1}{2}\right)\right)\right), \left(y \cdot z\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right)\right), \frac{-1}{2}\right)\right)\right), \left(y \cdot z\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right)\right), \frac{-1}{2}\right)\right)\right), \left(y \cdot z\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-1}{4} \cdot y + \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)\right)\right), \frac{-1}{2}\right)\right)\right), \left(y \cdot z\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-1}{4} \cdot y + \frac{-1}{3}\right)\right), \frac{-1}{2}\right)\right)\right), \left(y \cdot z\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-1}{4} \cdot y\right), \frac{-1}{3}\right)\right), \frac{-1}{2}\right)\right)\right), \left(y \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(y \cdot \frac{-1}{4}\right), \frac{-1}{3}\right)\right), \frac{-1}{2}\right)\right)\right), \left(y \cdot z\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{4}\right), \frac{-1}{3}\right)\right), \frac{-1}{2}\right)\right)\right), \left(y \cdot z\right)\right) \]

   8. Simplified 17.5%

      \[\leadsto \color{blue}{\left(-1 + y \cdot \left(y \cdot \left(y \cdot -0.25 + -0.3333333333333333\right) + -0.5\right)\right) \cdot \left(y \cdot z\right)} \]

   9. Taylor expanded in y around 0

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

       1. mul-1-neg N/A

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

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{y \cdot z} \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y \cdot z\right)}\right) \]

       4. *-lowering-*.f64 16.5%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   11. Simplified 16.5%

       \[\leadsto \color{blue}{0 - y \cdot z} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

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

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

          \[\leadsto \mathsf{neg.f64}\left(\left(y \cdot z\right)\right) \]

       3. *-lowering-*.f64 16.5%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(y, z\right)\right) \]

   13. Applied egg-rr 16.5%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-15}:\\ \;\;\;\;0 - t\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+43}:\\ \;\;\;\;0 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;0 - t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.4% accurate, 19.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

3. Taylor expanded in y around 0

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

5. Simplified 99.0%

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

6. Taylor expanded in z around inf

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right)\right)}, t\right) \]
7. Step-by-step derivation

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

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

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

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

   3. sub-neg N/A

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

   4. metadata-eval N/A

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

   5. +-commutative N/A

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

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

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

   7. *-commutative N/A

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

   8. *-lowering-*.f64 47.9%

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

8. Simplified 47.9%

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

Alternative 15: 46.2% accurate, 30.7× speedup

Math

\[\begin{array}{l} \\ \left(0 - y \cdot z\right) - t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (- 0.0 (* y z)) t))

C

double code(double x, double y, double z, double t) {
	return (0.0 - (y * z)) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (0.0d0 - (y * z)) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (0.0 - (y * z)) - t;
}

Python

def code(x, y, z, t):
	return (0.0 - (y * z)) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(0.0 - Float64(y * z)) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (0.0 - (y * z)) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(0.0 - N[(y * z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 92.0%

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

   1. *-commutative N/A

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

   2. flip-- N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

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

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

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

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

   7. clear-num N/A

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

   8. flip-- N/A

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

   9. /-lowering-/.f64 N/A

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

   10. sub-neg N/A

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

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

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

   12. metadata-eval 91.9%

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

4. Applied egg-rr 91.9%

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

5. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(-1 \cdot y\right)}\right)\right), t\right) \]
6. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \left(0 - y\right)\right)\right), t\right) \]

   3. --lowering--.f64 98.5%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{\_.f64}\left(0, y\right)\right)\right), t\right) \]

7. Simplified 98.5%

   \[\leadsto \left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \color{blue}{\left(0 - y\right)}\right) - t \]

8. Taylor expanded in z around inf

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(y \cdot z\right)\right)}, t\right) \]
9. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(y \cdot z\right)\right), t\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(0 - y \cdot z\right), t\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot z\right)\right), t\right) \]

   4. *-lowering-*.f64 47.5%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, z\right)\right), t\right) \]

10. Simplified 47.5%

    \[\leadsto \color{blue}{\left(0 - y \cdot z\right)} - t \]
11. Add Preprocessing

Alternative 16: 36.0% accurate, 71.7× speedup

Math

\[\begin{array}{l} \\ y - t \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

   1. *-commutative N/A

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

   2. flip-- N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

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

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

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

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

   7. clear-num N/A

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

   8. flip-- N/A

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

   9. /-lowering-/.f64 N/A

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

   10. sub-neg N/A

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

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

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

   12. metadata-eval 91.9%

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

4. Applied egg-rr 91.9%

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

5. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(-1 \cdot y\right)}\right)\right), t\right) \]
6. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \left(0 - y\right)\right)\right), t\right) \]

   3. --lowering--.f64 98.5%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{\_.f64}\left(0, y\right)\right)\right), t\right) \]

7. Simplified 98.5%

   \[\leadsto \left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \color{blue}{\left(0 - y\right)}\right) - t \]

8. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y + \log y \cdot \left(x - 1\right)\right)}, t\right) \]
9. Step-by-step derivation

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

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

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

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

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

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

   4. sub-neg N/A

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

   5. metadata-eval N/A

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

   6. +-commutative N/A

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

   7. +-lowering-+.f64 90.3%

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

10. Simplified 90.3%

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

11. Taylor expanded in y around inf

    \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, t\right) \]
12. Step-by-step derivation

13. Simplified 39.6%

    \[\leadsto \color{blue}{y} - t \]
14. Add Preprocessing

Alternative 17: 35.7% accurate, 71.7× speedup

Math

\[\begin{array}{l} \\ 0 - t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- 0.0 t))

C

double code(double x, double y, double z, double t) {
	return 0.0 - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 0.0d0 - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.0 - t;
}

Python

def code(x, y, z, t):
	return 0.0 - t

Julia

function code(x, y, z, t)
	return Float64(0.0 - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.0 - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(0.0 - t), $MachinePrecision]

Derivation

1. Initial program 92.0%

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

3. Taylor expanded in t around inf

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{t} \]

   3. --lowering--.f64 39.4%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{t}\right) \]

5. Simplified 39.4%

   \[\leadsto \color{blue}{0 - t} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 39.4%

      \[\leadsto \mathsf{neg.f64}\left(t\right) \]

7. Applied egg-rr 39.4%

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

8. Final simplification 39.4%

   \[\leadsto 0 - t \]
9. Add Preprocessing

Alternative 18: 2.9% accurate, 215.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return y
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := y

Derivation

1. Initial program 92.0%

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

   1. *-commutative N/A

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

   2. flip-- N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

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

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

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

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

   7. clear-num N/A

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

   8. flip-- N/A

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

   9. /-lowering-/.f64 N/A

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

   10. sub-neg N/A

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

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

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

   12. metadata-eval 91.9%

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

4. Applied egg-rr 91.9%

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

5. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(-1 \cdot y\right)}\right)\right), t\right) \]
6. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \left(0 - y\right)\right)\right), t\right) \]

   3. --lowering--.f64 98.5%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{\_.f64}\left(0, y\right)\right)\right), t\right) \]

7. Simplified 98.5%

   \[\leadsto \left(\frac{\log y}{\frac{1}{x + -1}} + \left(z - 1\right) \cdot \color{blue}{\left(0 - y\right)}\right) - t \]

8. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y + \log y \cdot \left(x - 1\right)\right)}, t\right) \]
9. Step-by-step derivation

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

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

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

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

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

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

   4. sub-neg N/A

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

   5. metadata-eval N/A

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

   6. +-commutative N/A

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

   7. +-lowering-+.f64 90.3%

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

10. Simplified 90.3%

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

11. Taylor expanded in y around inf

    \[\leadsto \color{blue}{y} \]
12. Step-by-step derivation

13. Simplified 2.8%

    \[\leadsto \color{blue}{y} \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2024155 
(FPCore (x y z t)
  :name "Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2"
  :precision binary64
  (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))