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

Percentage Accurate: 89.5% → 99.8%

Time: 16.0s

Alternatives: 17

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: 89.5% 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: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\mathsf{log1p}\left(0 - y\right) \cdot \left(z + -1\right) + \log y \cdot \left(x + -1\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (log1p (- 0.0 y)) (+ z -1.0)) (* (log y) (+ x -1.0))) t))

C

double code(double x, double y, double z, double t) {
	return ((log1p((0.0 - y)) * (z + -1.0)) + (log(y) * (x + -1.0))) - t;
}

Java

public static double code(double x, double y, double z, double t) {
	return ((Math.log1p((0.0 - y)) * (z + -1.0)) + (Math.log(y) * (x + -1.0))) - t;
}

Python

def code(x, y, z, t):
	return ((math.log1p((0.0 - y)) * (z + -1.0)) + (math.log(y) * (x + -1.0))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(log1p(Float64(0.0 - y)) * Float64(z + -1.0)) + Float64(log(y) * Float64(x + -1.0))) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[Log[1 + N[(0.0 - y), $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 89.6%

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

   1. sub-neg N/A

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

   2. log1p-define N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \left(\mathsf{log1p}\left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), t\right) \]

   3. log1p-lowering-log1p.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{log1p.f64}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), t\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{log1p.f64}\left(\left(0 - y\right)\right)\right)\right), t\right) \]

   5. --lowering--.f64 99.9%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \mathsf{log1p.f64}\left(\mathsf{\_.f64}\left(0, y\right)\right)\right)\right), t\right) \]

4. Applied egg-rr 99.9%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\mathsf{log1p}\left(0 - y\right)}\right) - t \]

5. Final simplification 99.9%

   \[\leadsto \left(\mathsf{log1p}\left(0 - y\right) \cdot \left(z + -1\right) + \log y \cdot \left(x + -1\right)\right) - t \]
6. Add Preprocessing

Alternative 2: 99.5% accurate, 1.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (+
   (* y (- (* (+ z -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 * (((z + -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 * (((z + (-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 * (((z + -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 * (((z + -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(y * Float64(Float64(Float64(z + -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 * (((z + -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[(y * N[(N[(N[(z + -1.0), $MachinePrecision] * N[(y * N[(-0.5 + N[(y * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 89.6%

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

3. Taylor expanded in y around 0

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

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

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

   2. +-commutative N/A

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

   3. mul-1-neg N/A

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

   4. unsub-neg N/A

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

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

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

5. Simplified 99.2%

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

6. Final simplification 99.2%

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

Alternative 3: 99.5% accurate, 1.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (+
   (* (+ z -1.0) (* y (+ -1.0 (* y (+ -0.5 (* y -0.3333333333333333))))))
   (* (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 + (y * -0.3333333333333333)))))) + (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) + (y * (-0.3333333333333333d0))))))) + (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 + (y * -0.3333333333333333)))))) + (Math.log(y) * (x + -1.0))) - t;
}

Python

def code(x, y, z, t):
	return (((z + -1.0) * (y * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) + (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 * Float64(-0.5 + Float64(y * -0.3333333333333333)))))) + 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 + (y * -0.3333333333333333)))))) + (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 * N[(-0.5 + N[(y * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 89.6%

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

3. Taylor expanded in y around 0

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

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

Alternative 4: 95.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot \left(x + -1\right) - t\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-8}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* (log y) (+ x -1.0)) t)))
   (if (<= x -2.6e-8)
     t_1
     (if (<= x 3e-8) (- (- (* 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 <= -2.6e-8) {
		tmp = t_1;
	} else if (x <= 3e-8) {
		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 <= (-2.6d-8)) then
        tmp = t_1
    else if (x <= 3d-8) 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 <= -2.6e-8) {
		tmp = t_1;
	} else if (x <= 3e-8) {
		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 <= -2.6e-8:
		tmp = t_1
	elif x <= 3e-8:
		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 <= -2.6e-8)
		tmp = t_1;
	elseif (x <= 3e-8)
		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 <= -2.6e-8)
		tmp = t_1;
	elseif (x <= 3e-8)
		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, -2.6e-8], t$95$1, If[LessEqual[x, 3e-8], 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 < -2.6000000000000001e-8 or 2.99999999999999973e-8 < x

   1. Initial program 96.1%

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

   3. 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 94.4%

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

   5. Simplified 94.4%

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

   if -2.6000000000000001e-8 < x < 2.99999999999999973e-8

   1. Initial program 82.8%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   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 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. neg-sub0 N/A

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

      11. associate-+l- N/A

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

      12. neg-sub0 N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

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

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

      16. log-lowering-log.f64 99.0%

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

   8. Simplified 99.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-8}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-8}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.4% 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 89.6%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
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 99.1%

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

6. Final simplification 99.1%

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

Alternative 6: 90.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+271}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+248}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.5e+271)
   (- (* y (- 1.0 z)) t)
   (if (<= z 1.3e+248)
     (- (* (log y) (+ x -1.0)) t)
     (- (* y (* z (+ -1.0 (* y (+ -0.5 (* y -0.3333333333333333)))))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+271) {
		tmp = (y * (1.0 - z)) - t;
	} else if (z <= 1.3e+248) {
		tmp = (log(y) * (x + -1.0)) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - 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 <= (-6.5d+271)) then
        tmp = (y * (1.0d0 - z)) - t
    else if (z <= 1.3d+248) then
        tmp = (log(y) * (x + (-1.0d0))) - t
    else
        tmp = (y * (z * ((-1.0d0) + (y * ((-0.5d0) + (y * (-0.3333333333333333d0))))))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+271) {
		tmp = (y * (1.0 - z)) - t;
	} else if (z <= 1.3e+248) {
		tmp = (Math.log(y) * (x + -1.0)) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e+271:
		tmp = (y * (1.0 - z)) - t
	elif z <= 1.3e+248:
		tmp = (math.log(y) * (x + -1.0)) - t
	else:
		tmp = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.5e+271)
		tmp = Float64(Float64(y * Float64(1.0 - z)) - t);
	elseif (z <= 1.3e+248)
		tmp = Float64(Float64(log(y) * Float64(x + -1.0)) - t);
	else
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * Float64(-0.5 + Float64(y * -0.3333333333333333)))))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.5e+271)
		tmp = (y * (1.0 - z)) - t;
	elseif (z <= 1.3e+248)
		tmp = (log(y) * (x + -1.0)) - t;
	else
		tmp = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.5e+271], N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[z, 1.3e+248], N[(N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y * N[(z * N[(-1.0 + N[(y * N[(-0.5 + N[(y * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.49999999999999998e271

   1. Initial program 22.7%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   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 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(y \cdot \left(0 - \left(z - 1\right)\right)\right), t\right) \]

      5. neg-sub0 N/A

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

      6. mul-1-neg N/A

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

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

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

      8. mul-1-neg N/A

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

      9. neg-sub0 N/A

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

      10. associate-+l- N/A

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

      11. neg-sub0 N/A

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

      12. +-commutative N/A

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

      13. sub-neg N/A

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

      14. --lowering--.f64 90.3%

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

   8. Simplified 90.3%

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

   if -6.49999999999999998e271 < z < 1.30000000000000005e248

   1. Initial program 93.4%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   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 92.2%

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

   5. Simplified 92.2%

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

   if 1.30000000000000005e248 < z

   1. Initial program 61.3%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) - 1\right)\right)}\right)\right), t\right) \]
   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 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in z around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 88.4%

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

   8. Simplified 88.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right)} - t \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+271}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+248}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - t\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-43}:\\ \;\;\;\;0 - \left(\log y + t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) t)))
   (if (<= x -1.0) t_1 (if (<= x 1.02e-43) (- 0.0 (+ (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 <= -1.0) {
		tmp = t_1;
	} else if (x <= 1.02e-43) {
		tmp = 0.0 - (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 <= (-1.0d0)) then
        tmp = t_1
    else if (x <= 1.02d-43) then
        tmp = 0.0d0 - (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 <= -1.0) {
		tmp = t_1;
	} else if (x <= 1.02e-43) {
		tmp = 0.0 - (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 <= -1.0:
		tmp = t_1
	elif x <= 1.02e-43:
		tmp = 0.0 - (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 <= -1.0)
		tmp = t_1;
	elseif (x <= 1.02e-43)
		tmp = Float64(0.0 - Float64(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 <= -1.0)
		tmp = t_1;
	elseif (x <= 1.02e-43)
		tmp = 0.0 - (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, -1.0], t$95$1, If[LessEqual[x, 1.02e-43], N[(0.0 - N[(N[Log[y], $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.0200000000000001e-43 < x

   1. Initial program 95.5%

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

   3. Taylor expanded in 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 92.4%

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

   5. Simplified 92.4%

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

   if -1 < x < 1.0200000000000001e-43

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\log y \cdot \left(x - 1\right) - t} \]
   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 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in x around 0

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

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

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

      2. mul-1-neg N/A

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

      3. neg-sub0 N/A

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

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

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

      5. log-lowering-log.f64 80.3%

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

   8. Simplified 80.3%

      \[\leadsto \color{blue}{\left(0 - \log y\right) - t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-43}:\\ \;\;\;\;0 - \left(\log y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - t\\ \mathbf{if}\;t \leq -360:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-80}:\\ \;\;\;\;\log y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) t)))
   (if (<= t -360.0) t_1 (if (<= t 3.1e-80) (* (log y) (+ x -1.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - t;
	double tmp;
	if (t <= -360.0) {
		tmp = t_1;
	} else if (t <= 3.1e-80) {
		tmp = log(y) * (x + -1.0);
	} 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 (t <= (-360.0d0)) then
        tmp = t_1
    else if (t <= 3.1d-80) then
        tmp = log(y) * (x + (-1.0d0))
    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 (t <= -360.0) {
		tmp = t_1;
	} else if (t <= 3.1e-80) {
		tmp = Math.log(y) * (x + -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - t
	tmp = 0
	if t <= -360.0:
		tmp = t_1
	elif t <= 3.1e-80:
		tmp = math.log(y) * (x + -1.0)
	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 (t <= -360.0)
		tmp = t_1;
	elseif (t <= 3.1e-80)
		tmp = Float64(log(y) * Float64(x + -1.0));
	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 (t <= -360.0)
		tmp = t_1;
	elseif (t <= 3.1e-80)
		tmp = log(y) * (x + -1.0);
	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[t, -360.0], t$95$1, If[LessEqual[t, 3.1e-80], N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -360 or 3.10000000000000016e-80 < t

   1. Initial program 92.6%

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

   3. Taylor expanded in 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 89.3%

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

   5. Simplified 89.3%

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

   if -360 < t < 3.10000000000000016e-80

   1. Initial program 85.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\log y \cdot \left(x - 1\right) - t} \]
   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 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 83.4%

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

   8. Simplified 83.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -360:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-80}:\\ \;\;\;\;\log y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right) - t\\ \mathbf{if}\;t \leq -85000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10000000000000:\\ \;\;\;\;\log y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1
         (- (* y (* z (+ -1.0 (* y (+ -0.5 (* y -0.3333333333333333)))))) t)))
   (if (<= t -85000.0)
     t_1
     (if (<= t 10000000000000.0) (* (log y) (+ x -1.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - t;
	double tmp;
	if (t <= -85000.0) {
		tmp = t_1;
	} else if (t <= 10000000000000.0) {
		tmp = log(y) * (x + -1.0);
	} 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 = (y * (z * ((-1.0d0) + (y * ((-0.5d0) + (y * (-0.3333333333333333d0))))))) - t
    if (t <= (-85000.0d0)) then
        tmp = t_1
    else if (t <= 10000000000000.0d0) then
        tmp = log(y) * (x + (-1.0d0))
    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 = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - t;
	double tmp;
	if (t <= -85000.0) {
		tmp = t_1;
	} else if (t <= 10000000000000.0) {
		tmp = Math.log(y) * (x + -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - t
	tmp = 0
	if t <= -85000.0:
		tmp = t_1
	elif t <= 10000000000000.0:
		tmp = math.log(y) * (x + -1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * Float64(-0.5 + Float64(y * -0.3333333333333333)))))) - t)
	tmp = 0.0
	if (t <= -85000.0)
		tmp = t_1;
	elseif (t <= 10000000000000.0)
		tmp = Float64(log(y) * Float64(x + -1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - t;
	tmp = 0.0;
	if (t <= -85000.0)
		tmp = t_1;
	elseif (t <= 10000000000000.0)
		tmp = log(y) * (x + -1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * N[(z * N[(-1.0 + N[(y * N[(-0.5 + N[(y * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[t, -85000.0], t$95$1, If[LessEqual[t, 10000000000000.0], N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -85000 or 1e13 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) - 1\right)\right)}\right)\right), t\right) \]
   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 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in z around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 76.8%

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

   8. Simplified 76.8%

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

   if -85000 < t < 1e13

   1. Initial program 86.7%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   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 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 83.7%

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

   8. Simplified 83.7%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -85000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right) - t\\ \mathbf{elif}\;t \leq 10000000000000:\\ \;\;\;\;\log y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.72 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -7.5e+34)
     t_1
     (if (<= x 1.72e+121)
       (- (* y (* z (+ -1.0 (* y (+ -0.5 (* y -0.3333333333333333)))))) t)
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -7.5e+34) {
		tmp = t_1;
	} else if (x <= 1.72e+121) {
		tmp = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - 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 <= (-7.5d+34)) then
        tmp = t_1
    else if (x <= 1.72d+121) then
        tmp = (y * (z * ((-1.0d0) + (y * ((-0.5d0) + (y * (-0.3333333333333333d0))))))) - 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 <= -7.5e+34) {
		tmp = t_1;
	} else if (x <= 1.72e+121) {
		tmp = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -7.5e+34:
		tmp = t_1
	elif x <= 1.72e+121:
		tmp = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - 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 <= -7.5e+34)
		tmp = t_1;
	elseif (x <= 1.72e+121)
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * Float64(-0.5 + Float64(y * -0.3333333333333333)))))) - 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 <= -7.5e+34)
		tmp = t_1;
	elseif (x <= 1.72e+121)
		tmp = (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - 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, -7.5e+34], t$95$1, If[LessEqual[x, 1.72e+121], N[(N[(y * N[(z * N[(-1.0 + N[(y * N[(-0.5 + N[(y * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.49999999999999976e34 or 1.7200000000000001e121 < x

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   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 78.0%

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

   5. Simplified 78.0%

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

   if -7.49999999999999976e34 < x < 1.7200000000000001e121

   1. Initial program 85.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 1\right), \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, 1\right), \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) - 1\right)\right)}\right)\right), t\right) \]
   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 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 64.4%

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

   8. Simplified 64.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right)} - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 1.72 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 89.6%

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

3. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)}, t\right) \]
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 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 12: 98.9% 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 89.6%

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

3. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)}, t\right) \]
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 98.7%

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

5. Simplified 98.7%

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

6. Taylor expanded in z around inf

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

   1. *-lowering-*.f64 98.5%

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

8. Simplified 98.5%

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

9. Final simplification 98.5%

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

Alternative 13: 43.9% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -25500000:\\ \;\;\;\;0 - t\\ \mathbf{elif}\;t \leq 54000000000000:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -25500000.0)
   (- 0.0 t)
   (if (<= t 54000000000000.0) (* y (- 1.0 z)) (- 0.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -25500000.0) {
		tmp = 0.0 - t;
	} else if (t <= 54000000000000.0) {
		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 <= (-25500000.0d0)) then
        tmp = 0.0d0 - t
    else if (t <= 54000000000000.0d0) 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 <= -25500000.0) {
		tmp = 0.0 - t;
	} else if (t <= 54000000000000.0) {
		tmp = y * (1.0 - z);
	} else {
		tmp = 0.0 - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -25500000.0:
		tmp = 0.0 - t
	elif t <= 54000000000000.0:
		tmp = y * (1.0 - z)
	else:
		tmp = 0.0 - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -25500000.0)
		tmp = Float64(0.0 - t);
	elseif (t <= 54000000000000.0)
		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 <= -25500000.0)
		tmp = 0.0 - t;
	elseif (t <= 54000000000000.0)
		tmp = y * (1.0 - z);
	else
		tmp = 0.0 - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -25500000.0], N[(0.0 - t), $MachinePrecision], If[LessEqual[t, 54000000000000.0], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(0.0 - t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.55e7 or 5.4e13 < t

   1. Initial program 94.3%

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

   3. Taylor expanded in 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 70.0%

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

   5. Simplified 70.0%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 70.0%

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

   7. Applied egg-rr 70.0%

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

   if -2.55e7 < t < 5.4e13

   1. Initial program 84.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)}, t\right) \]
   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 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
   7. 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. neg-sub0 N/A

         \[\leadsto y \cdot \left(\left(0 - z\right) + 1\right) \]

      4. associate-+l- N/A

         \[\leadsto y \cdot \left(0 - \color{blue}{\left(z - 1\right)}\right) \]

      5. neg-sub0 N/A

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

      6. mul-1-neg N/A

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

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

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

      8. mul-1-neg N/A

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

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(0 - \color{blue}{\left(z - 1\right)}\right)\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\left(0 - z\right) + \color{blue}{1}\right)\right) \]

      11. neg-sub0 N/A

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

      12. +-commutative N/A

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

      13. sub-neg N/A

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

      14. --lowering--.f64 16.8%

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

   8. Simplified 16.8%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -25500000:\\ \;\;\;\;0 - t\\ \mathbf{elif}\;t \leq 54000000000000:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.9% accurate, 14.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y * (z * (-1.0 + (y * (-0.5 + (y * -0.3333333333333333)))))) - 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) + (y * (-0.3333333333333333d0))))))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.6%

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

3. Taylor expanded in y around 0

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

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

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

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

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

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

   3. sub-neg N/A

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

   4. metadata-eval N/A

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

   5. +-commutative N/A

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

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

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

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

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

   8. sub-neg N/A

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

   9. metadata-eval N/A

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

   10. +-commutative N/A

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

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

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

   12. *-commutative N/A

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

   13. *-lowering-*.f64 47.0%

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

8. Simplified 47.0%

   \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-1 + y \cdot \left(-0.5 + y \cdot -0.3333333333333333\right)\right)\right)} - t \]
9. Add Preprocessing

Alternative 15: 46.8% 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 89.6%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
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 99.1%

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

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. *-commutative N/A

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

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

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

   4. sub-neg N/A

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

   5. metadata-eval N/A

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

   6. +-commutative N/A

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

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

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

   8. *-commutative N/A

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

   9. *-lowering-*.f64 46.9%

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

8. Simplified 46.9%

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

9. Final simplification 46.9%

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

Alternative 16: 46.7% accurate, 30.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y * (1.0 - 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 = (y * (1.0d0 - z)) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.6%

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

3. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)}, t\right) \]
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 98.7%

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

5. Simplified 98.7%

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

6. Taylor expanded in y around inf

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. neg-sub0 N/A

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

   4. associate-+l- N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(y \cdot \left(0 - \left(z - 1\right)\right)\right), t\right) \]

   5. neg-sub0 N/A

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

   6. mul-1-neg N/A

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

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

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

   8. mul-1-neg N/A

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

   9. neg-sub0 N/A

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

   10. associate-+l- N/A

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

   11. neg-sub0 N/A

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

   12. +-commutative N/A

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

   13. sub-neg N/A

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

   14. --lowering--.f64 46.6%

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

8. Simplified 46.6%

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

Alternative 17: 36.3% 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 89.6%

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

3. Taylor expanded in 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 36.8%

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

5. Simplified 36.8%

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

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 36.8%

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

7. Applied egg-rr 36.8%

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

8. Final simplification 36.8%

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

Reproduce

herbie shell --seed 2024160 
(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))