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

Percentage Accurate: 89.2% → 99.8%

Time: 29.8s

Alternatives: 18

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% 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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(z + -1.0), $MachinePrecision] * N[Log[1 + (-y)], $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 90.2%

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

   1. +-commutative 90.2%

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

   2. fma-def 90.2%

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

   3. sub-neg 90.2%

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

   4. metadata-eval 90.2%

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

   5. sub-neg 90.2%

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

   6. log1p-def 99.9%

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

   7. sub-neg 99.9%

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

   8. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 98.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-1 + x \leq -2000 \lor \neg \left(-1 + x \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - z \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\log y\right) - y \cdot \left(z + -1\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ -1.0 x) -2000.0) (not (<= (+ -1.0 x) -0.5)))
   (- (- (* x (log y)) (* z y)) t)
   (- (- (- (log y)) (* y (+ z -1.0))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((-1.0 + x) <= -2000.0) || !((-1.0 + x) <= -0.5)) {
		tmp = ((x * log(y)) - (z * y)) - t;
	} else {
		tmp = (-log(y) - (y * (z + -1.0))) - 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 ((((-1.0d0) + x) <= (-2000.0d0)) .or. (.not. (((-1.0d0) + x) <= (-0.5d0)))) then
        tmp = ((x * log(y)) - (z * y)) - t
    else
        tmp = (-log(y) - (y * (z + (-1.0d0)))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((-1.0 + x) <= -2000.0) || !((-1.0 + x) <= -0.5)) {
		tmp = ((x * Math.log(y)) - (z * y)) - t;
	} else {
		tmp = (-Math.log(y) - (y * (z + -1.0))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((-1.0 + x) <= -2000.0) or not ((-1.0 + x) <= -0.5):
		tmp = ((x * math.log(y)) - (z * y)) - t
	else:
		tmp = (-math.log(y) - (y * (z + -1.0))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(-1.0 + x) <= -2000.0) || !(Float64(-1.0 + x) <= -0.5))
		tmp = Float64(Float64(Float64(x * log(y)) - Float64(z * y)) - t);
	else
		tmp = Float64(Float64(Float64(-log(y)) - Float64(y * Float64(z + -1.0))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((-1.0 + x) <= -2000.0) || ~(((-1.0 + x) <= -0.5)))
		tmp = ((x * log(y)) - (z * y)) - t;
	else
		tmp = (-log(y) - (y * (z + -1.0))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(-1.0 + x), $MachinePrecision], -2000.0], N[Not[LessEqual[N[(-1.0 + x), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[((-N[Log[y], $MachinePrecision]) - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x 1) < -2e3 or -0.5 < (-.f64 x 1)

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 98.9%

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

      1. +-commutative 98.9%

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

      2. sub-neg 98.9%

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

      3. metadata-eval 98.9%

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

      4. mul-1-neg 98.9%

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

      5. unsub-neg 98.9%

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

      6. *-commutative 98.9%

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

      7. +-commutative 98.9%

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

      8. *-commutative 98.9%

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

      9. sub-neg 98.9%

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

      10. metadata-eval 98.9%

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

      11. +-commutative 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in z around inf 98.9%

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

   6. Taylor expanded in x around inf 97.9%

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

   if -2e3 < (-.f64 x 1) < -0.5

   1. Initial program 88.7%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. mul-1-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. *-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 98.0%

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

      1. mul-1-neg 98.0%

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

   7. Simplified 98.0%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -2000 \lor \neg \left(-1 + x \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - z \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\log y\right) - y \cdot \left(z + -1\right)\right) - t\\ \end{array} \]

Alternative 3: 98.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-1 + x \leq -2000 \lor \neg \left(-1 + x \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - z \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\log y\right) - z \cdot y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ -1.0 x) -2000.0) (not (<= (+ -1.0 x) -0.5)))
   (- (- (* x (log y)) (* z y)) t)
   (- (- (- (log y)) (* z y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((-1.0 + x) <= -2000.0) || !((-1.0 + x) <= -0.5)) {
		tmp = ((x * log(y)) - (z * y)) - t;
	} else {
		tmp = (-log(y) - (z * y)) - 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 ((((-1.0d0) + x) <= (-2000.0d0)) .or. (.not. (((-1.0d0) + x) <= (-0.5d0)))) then
        tmp = ((x * log(y)) - (z * y)) - t
    else
        tmp = (-log(y) - (z * y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((-1.0 + x) <= -2000.0) || !((-1.0 + x) <= -0.5)) {
		tmp = ((x * Math.log(y)) - (z * y)) - t;
	} else {
		tmp = (-Math.log(y) - (z * y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((-1.0 + x) <= -2000.0) or not ((-1.0 + x) <= -0.5):
		tmp = ((x * math.log(y)) - (z * y)) - t
	else:
		tmp = (-math.log(y) - (z * y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(-1.0 + x) <= -2000.0) || !(Float64(-1.0 + x) <= -0.5))
		tmp = Float64(Float64(Float64(x * log(y)) - Float64(z * y)) - t);
	else
		tmp = Float64(Float64(Float64(-log(y)) - Float64(z * y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((-1.0 + x) <= -2000.0) || ~(((-1.0 + x) <= -0.5)))
		tmp = ((x * log(y)) - (z * y)) - t;
	else
		tmp = (-log(y) - (z * y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(-1.0 + x), $MachinePrecision], -2000.0], N[Not[LessEqual[N[(-1.0 + x), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[((-N[Log[y], $MachinePrecision]) - N[(z * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x 1) < -2e3 or -0.5 < (-.f64 x 1)

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 98.9%

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

      1. +-commutative 98.9%

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

      2. sub-neg 98.9%

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

      3. metadata-eval 98.9%

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

      4. mul-1-neg 98.9%

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

      5. unsub-neg 98.9%

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

      6. *-commutative 98.9%

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

      7. +-commutative 98.9%

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

      8. *-commutative 98.9%

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

      9. sub-neg 98.9%

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

      10. metadata-eval 98.9%

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

      11. +-commutative 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in z around inf 98.9%

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

   6. Taylor expanded in x around inf 97.9%

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

   if -2e3 < (-.f64 x 1) < -0.5

   1. Initial program 88.7%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. mul-1-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. *-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in x around 0 98.0%

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

      1. mul-1-neg 98.0%

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

      2. *-commutative 98.0%

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

   8. Simplified 98.0%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -2000 \lor \neg \left(-1 + x \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - z \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\log y\right) - z \cdot y\right) - t\\ \end{array} \]

Alternative 4: 94.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-1 + x \leq -2 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;-1 + x \leq -1:\\ \;\;\;\;\left(\left(-\log y\right) - z \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ -1.0 x) -2e+29)
   (- (* x (log y)) t)
   (if (<= (+ -1.0 x) -1.0)
     (- (- (- (log y)) (* z y)) t)
     (- (* (log y) (+ -1.0 x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((-1.0 + x) <= -2e+29) {
		tmp = (x * log(y)) - t;
	} else if ((-1.0 + x) <= -1.0) {
		tmp = (-log(y) - (z * y)) - t;
	} else {
		tmp = (log(y) * (-1.0 + x)) - 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 (((-1.0d0) + x) <= (-2d+29)) then
        tmp = (x * log(y)) - t
    else if (((-1.0d0) + x) <= (-1.0d0)) then
        tmp = (-log(y) - (z * y)) - t
    else
        tmp = (log(y) * ((-1.0d0) + x)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((-1.0 + x) <= -2e+29) {
		tmp = (x * Math.log(y)) - t;
	} else if ((-1.0 + x) <= -1.0) {
		tmp = (-Math.log(y) - (z * y)) - t;
	} else {
		tmp = (Math.log(y) * (-1.0 + x)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (-1.0 + x) <= -2e+29:
		tmp = (x * math.log(y)) - t
	elif (-1.0 + x) <= -1.0:
		tmp = (-math.log(y) - (z * y)) - t
	else:
		tmp = (math.log(y) * (-1.0 + x)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(-1.0 + x) <= -2e+29)
		tmp = Float64(Float64(x * log(y)) - t);
	elseif (Float64(-1.0 + x) <= -1.0)
		tmp = Float64(Float64(Float64(-log(y)) - Float64(z * y)) - t);
	else
		tmp = Float64(Float64(log(y) * Float64(-1.0 + x)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((-1.0 + x) <= -2e+29)
		tmp = (x * log(y)) - t;
	elseif ((-1.0 + x) <= -1.0)
		tmp = (-log(y) - (z * y)) - t;
	else
		tmp = (log(y) * (-1.0 + x)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(-1.0 + x), $MachinePrecision], -2e+29], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[N[(-1.0 + x), $MachinePrecision], -1.0], N[(N[((-N[Log[y], $MachinePrecision]) - N[(z * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x 1) < -1.99999999999999983e29

   1. Initial program 92.0%

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

   2. Taylor expanded in y around 0 92.0%

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

   3. Taylor expanded in x around inf 92.0%

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

   if -1.99999999999999983e29 < (-.f64 x 1) < -1

   1. Initial program 86.3%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. mul-1-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. *-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in x around 0 98.1%

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

      1. mul-1-neg 98.1%

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

      2. *-commutative 98.1%

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

   8. Simplified 98.1%

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

   if -1 < (-.f64 x 1)

   1. Initial program 95.8%

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

   2. Taylor expanded in y around 0 93.8%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -2 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;-1 + x \leq -1:\\ \;\;\;\;\left(\left(-\log y\right) - z \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \]

Alternative 5: 95.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot \left(-1 + x\right)\\ \mathbf{if}\;t \leq -29000000 \lor \neg \left(t \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;t_1 - t\\ \mathbf{else}:\\ \;\;\;\;t_1 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) (+ -1.0 x))))
   (if (or (<= t -29000000.0) (not (<= t 1.8e-5))) (- t_1 t) (- t_1 (* z y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * (-1.0 + x);
	double tmp;
	if ((t <= -29000000.0) || !(t <= 1.8e-5)) {
		tmp = t_1 - t;
	} else {
		tmp = t_1 - (z * y);
	}
	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) * ((-1.0d0) + x)
    if ((t <= (-29000000.0d0)) .or. (.not. (t <= 1.8d-5))) then
        tmp = t_1 - t
    else
        tmp = t_1 - (z * y)
    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) * (-1.0 + x);
	double tmp;
	if ((t <= -29000000.0) || !(t <= 1.8e-5)) {
		tmp = t_1 - t;
	} else {
		tmp = t_1 - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * (-1.0 + x)
	tmp = 0
	if (t <= -29000000.0) or not (t <= 1.8e-5):
		tmp = t_1 - t
	else:
		tmp = t_1 - (z * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * Float64(-1.0 + x))
	tmp = 0.0
	if ((t <= -29000000.0) || !(t <= 1.8e-5))
		tmp = Float64(t_1 - t);
	else
		tmp = Float64(t_1 - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * (-1.0 + x);
	tmp = 0.0;
	if ((t <= -29000000.0) || ~((t <= 1.8e-5)))
		tmp = t_1 - t;
	else
		tmp = t_1 - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -29000000.0], N[Not[LessEqual[t, 1.8e-5]], $MachinePrecision]], N[(t$95$1 - t), $MachinePrecision], N[(t$95$1 - N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9e7 or 1.80000000000000005e-5 < t

   1. Initial program 95.2%

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

   2. Taylor expanded in y around 0 94.6%

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

   if -2.9e7 < t < 1.80000000000000005e-5

   1. Initial program 85.5%

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

   2. Taylor expanded in y around 0 99.3%

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

      1. +-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. mul-1-neg 99.3%

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

      5. unsub-neg 99.3%

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

      6. *-commutative 99.3%

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

      7. +-commutative 99.3%

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

      8. *-commutative 99.3%

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

      9. sub-neg 99.3%

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

      10. metadata-eval 99.3%

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

      11. +-commutative 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in z around inf 99.3%

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

   6. Taylor expanded in t around 0 98.4%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -29000000 \lor \neg \left(t \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - z \cdot y\\ \end{array} \]

Alternative 6: 95.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot \left(-1 + x\right)\\ \mathbf{if}\;t \leq -29000000:\\ \;\;\;\;t_1 - t\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;t_1 - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(y + t_1\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) (+ -1.0 x))))
   (if (<= t -29000000.0)
     (- t_1 t)
     (if (<= t 1.7e-5) (- t_1 (* z y)) (- (+ y t_1) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * (-1.0 + x);
	double tmp;
	if (t <= -29000000.0) {
		tmp = t_1 - t;
	} else if (t <= 1.7e-5) {
		tmp = t_1 - (z * y);
	} else {
		tmp = (y + t_1) - 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) :: t_1
    real(8) :: tmp
    t_1 = log(y) * ((-1.0d0) + x)
    if (t <= (-29000000.0d0)) then
        tmp = t_1 - t
    else if (t <= 1.7d-5) then
        tmp = t_1 - (z * y)
    else
        tmp = (y + t_1) - t
    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) * (-1.0 + x);
	double tmp;
	if (t <= -29000000.0) {
		tmp = t_1 - t;
	} else if (t <= 1.7e-5) {
		tmp = t_1 - (z * y);
	} else {
		tmp = (y + t_1) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * (-1.0 + x)
	tmp = 0
	if t <= -29000000.0:
		tmp = t_1 - t
	elif t <= 1.7e-5:
		tmp = t_1 - (z * y)
	else:
		tmp = (y + t_1) - t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * Float64(-1.0 + x))
	tmp = 0.0
	if (t <= -29000000.0)
		tmp = Float64(t_1 - t);
	elseif (t <= 1.7e-5)
		tmp = Float64(t_1 - Float64(z * y));
	else
		tmp = Float64(Float64(y + t_1) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * (-1.0 + x);
	tmp = 0.0;
	if (t <= -29000000.0)
		tmp = t_1 - t;
	elseif (t <= 1.7e-5)
		tmp = t_1 - (z * y);
	else
		tmp = (y + t_1) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -29000000.0], N[(t$95$1 - t), $MachinePrecision], If[LessEqual[t, 1.7e-5], N[(t$95$1 - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(N[(y + t$95$1), $MachinePrecision] - t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9e7

   1. Initial program 97.0%

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

   2. Taylor expanded in y around 0 95.9%

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

   if -2.9e7 < t < 1.7e-5

   1. Initial program 85.5%

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

   2. Taylor expanded in y around 0 99.3%

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

      1. +-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. mul-1-neg 99.3%

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

      5. unsub-neg 99.3%

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

      6. *-commutative 99.3%

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

      7. +-commutative 99.3%

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

      8. *-commutative 99.3%

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

      9. sub-neg 99.3%

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

      10. metadata-eval 99.3%

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

      11. +-commutative 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in z around inf 99.3%

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

   6. Taylor expanded in t around 0 98.4%

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

   if 1.7e-5 < t

   1. Initial program 93.6%

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

      1. associate--l+ 93.6%

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

      2. fma-def 93.6%

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

      3. sub-neg 93.6%

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

      4. metadata-eval 93.6%

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

      5. fma-neg 93.6%

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

      6. sub-neg 93.6%

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

      7. metadata-eval 93.6%

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

      8. sub-neg 93.6%

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

      9. log1p-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

      4. mul-1-neg 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

      9. +-commutative 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in z around 0 93.6%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -29000000:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(y + \log y \cdot \left(-1 + x\right)\right) - t\\ \end{array} \]

Alternative 7: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.2%

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

2. Taylor expanded in y around 0 99.4%

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

   1. +-commutative 99.4%

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

   2. sub-neg 99.4%

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

   3. metadata-eval 99.4%

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

   4. mul-1-neg 99.4%

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

   5. unsub-neg 99.4%

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

   6. *-commutative 99.4%

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

   7. +-commutative 99.4%

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

   8. *-commutative 99.4%

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

   9. sub-neg 99.4%

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

   10. metadata-eval 99.4%

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

   11. +-commutative 99.4%

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

4. Simplified 99.4%

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

5. Final simplification 99.4%

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

Alternative 8: 99.0% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.2%

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

2. Taylor expanded in y around 0 99.4%

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

   1. +-commutative 99.4%

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

   2. sub-neg 99.4%

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

   3. metadata-eval 99.4%

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

   4. mul-1-neg 99.4%

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

   5. unsub-neg 99.4%

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

   6. *-commutative 99.4%

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

   7. +-commutative 99.4%

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

   8. *-commutative 99.4%

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

   9. sub-neg 99.4%

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

   10. metadata-eval 99.4%

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

   11. +-commutative 99.4%

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

4. Simplified 99.4%

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

5. Taylor expanded in z around inf 99.4%

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

6. Final simplification 99.4%

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

Alternative 9: 77.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+46} \lor \neg \left(t \leq 9.8 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.6e+46) (not (<= t 9.8e+54)))
   (- (* z (- y)) t)
   (* (log y) (+ -1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.6e+46) || !(t <= 9.8e+54)) {
		tmp = (z * -y) - t;
	} else {
		tmp = log(y) * (-1.0 + x);
	}
	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 <= (-3.6d+46)) .or. (.not. (t <= 9.8d+54))) then
        tmp = (z * -y) - t
    else
        tmp = log(y) * ((-1.0d0) + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.6e+46) || !(t <= 9.8e+54)) {
		tmp = (z * -y) - t;
	} else {
		tmp = Math.log(y) * (-1.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.6e+46) or not (t <= 9.8e+54):
		tmp = (z * -y) - t
	else:
		tmp = math.log(y) * (-1.0 + x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.6e+46) || !(t <= 9.8e+54))
		tmp = Float64(Float64(z * Float64(-y)) - t);
	else
		tmp = Float64(log(y) * Float64(-1.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.6e+46) || ~((t <= 9.8e+54)))
		tmp = (z * -y) - t;
	else
		tmp = log(y) * (-1.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.6e+46], N[Not[LessEqual[t, 9.8e+54]], $MachinePrecision]], N[(N[(z * (-y)), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5999999999999999e46 or 9.80000000000000002e54 < t

   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. Taylor expanded in y around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. mul-1-neg 99.4%

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

      5. unsub-neg 99.4%

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

      6. *-commutative 99.4%

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

      7. +-commutative 99.4%

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

      8. *-commutative 99.4%

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

      9. sub-neg 99.4%

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

      10. metadata-eval 99.4%

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

      11. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in z around inf 81.7%

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

      1. associate-*r* 81.7%

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

      2. neg-mul-1 81.7%

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

   7. Simplified 81.7%

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

   if -3.5999999999999999e46 < t < 9.80000000000000002e54

   1. Initial program 86.4%

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

   2. Taylor expanded in y around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. mul-1-neg 99.4%

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

      5. unsub-neg 99.4%

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

      6. *-commutative 99.4%

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

      7. +-commutative 99.4%

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

      8. *-commutative 99.4%

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

      9. sub-neg 99.4%

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

      10. metadata-eval 99.4%

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

      11. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in z around inf 99.4%

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

   6. Taylor expanded in t around 0 92.4%

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

   7. Taylor expanded in y around 0 79.1%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+46} \lor \neg \left(t \leq 9.8 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \end{array} \]

Alternative 10: 87.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -155000 \lor \neg \left(t \leq 330\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -155000.0) (not (<= t 330.0)))
   (- (* x (log y)) t)
   (* (log y) (+ -1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -155000.0) || !(t <= 330.0)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = log(y) * (-1.0 + x);
	}
	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 <= (-155000.0d0)) .or. (.not. (t <= 330.0d0))) then
        tmp = (x * log(y)) - t
    else
        tmp = log(y) * ((-1.0d0) + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -155000.0) || !(t <= 330.0)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = Math.log(y) * (-1.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -155000.0) or not (t <= 330.0):
		tmp = (x * math.log(y)) - t
	else:
		tmp = math.log(y) * (-1.0 + x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -155000.0) || !(t <= 330.0))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(log(y) * Float64(-1.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -155000.0) || ~((t <= 330.0)))
		tmp = (x * log(y)) - t;
	else
		tmp = log(y) * (-1.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -155000.0], N[Not[LessEqual[t, 330.0]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -155000 or 330 < t

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 94.6%

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

   3. Taylor expanded in x around inf 93.1%

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

   if -155000 < t < 330

   1. Initial program 85.5%

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

   2. Taylor expanded in y around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. mul-1-neg 99.4%

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

      5. unsub-neg 99.4%

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

      6. *-commutative 99.4%

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

      7. +-commutative 99.4%

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

      8. *-commutative 99.4%

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

      9. sub-neg 99.4%

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

      10. metadata-eval 99.4%

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

      11. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in z around inf 99.4%

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

   6. Taylor expanded in t around 0 98.2%

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

   7. Taylor expanded in y around 0 83.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -155000 \lor \neg \left(t \leq 330\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \end{array} \]

Alternative 11: 89.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \log y - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.85e+213) (- (* x (log y)) (* z y)) (- (* (log y) (+ -1.0 x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+213) {
		tmp = (x * log(y)) - (z * y);
	} else {
		tmp = (log(y) * (-1.0 + x)) - 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 <= (-1.85d+213)) then
        tmp = (x * log(y)) - (z * y)
    else
        tmp = (log(y) * ((-1.0d0) + x)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+213) {
		tmp = (x * Math.log(y)) - (z * y);
	} else {
		tmp = (Math.log(y) * (-1.0 + x)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.85e+213:
		tmp = (x * math.log(y)) - (z * y)
	else:
		tmp = (math.log(y) * (-1.0 + x)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.85e+213)
		tmp = Float64(Float64(x * log(y)) - Float64(z * y));
	else
		tmp = Float64(Float64(log(y) * Float64(-1.0 + x)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.85e+213)
		tmp = (x * log(y)) - (z * y);
	else
		tmp = (log(y) * (-1.0 + x)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.85e+213], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999996e213

   1. Initial program 51.2%

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

   2. Taylor expanded in y around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. *-commutative 99.6%

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

      7. +-commutative 99.6%

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

      8. *-commutative 99.6%

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

      9. sub-neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. +-commutative 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in t around 0 84.3%

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

   7. Taylor expanded in x around inf 80.0%

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

   if -1.84999999999999996e213 < z

   1. Initial program 94.8%

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

   2. Taylor expanded in y around 0 94.1%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \log y - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \]

Alternative 12: 75.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2300 \lor \neg \left(x \leq 400000000000\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2300.0) (not (<= x 400000000000.0)))
   (* x (log y))
   (- (- (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2300.0) || !(x <= 400000000000.0)) {
		tmp = x * log(y);
	} else {
		tmp = -log(y) - 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 ((x <= (-2300.0d0)) .or. (.not. (x <= 400000000000.0d0))) then
        tmp = x * log(y)
    else
        tmp = -log(y) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2300.0) || !(x <= 400000000000.0)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2300.0) or not (x <= 400000000000.0):
		tmp = x * math.log(y)
	else:
		tmp = -math.log(y) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2300.0) || !(x <= 400000000000.0))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2300.0) || ~((x <= 400000000000.0)))
		tmp = x * log(y);
	else
		tmp = -log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2300.0], N[Not[LessEqual[x, 400000000000.0]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2300 or 4e11 < x

   1. Initial program 91.4%

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

      1. associate--l+ 91.4%

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

      2. fma-def 91.4%

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

      3. sub-neg 91.4%

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

      4. metadata-eval 91.4%

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

      5. fma-neg 91.4%

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

      6. sub-neg 91.4%

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

      7. metadata-eval 91.4%

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

      8. sub-neg 91.4%

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

      9. log1p-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. +-commutative 98.9%

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

      3. unsub-neg 98.9%

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

      4. mul-1-neg 98.9%

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

      5. *-commutative 98.9%

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

      6. distribute-lft-neg-in 98.9%

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

      7. sub-neg 98.9%

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

      8. metadata-eval 98.9%

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

      9. +-commutative 98.9%

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

   6. Simplified 98.9%

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

   7. Taylor expanded in x around inf 70.7%

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

   if -2300 < x < 4e11

   1. Initial program 89.1%

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

   2. Taylor expanded in y around 0 88.9%

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

   3. Taylor expanded in x around 0 86.7%

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

      1. mul-1-neg 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2300 \lor \neg \left(x \leq 400000000000\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \]

Alternative 13: 66.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+26} \lor \neg \left(x \leq 5.2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.3e+26) (not (<= x 5.2e+61)))
   (* x (log y))
   (- (* y (- 1.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e+26) || !(x <= 5.2e+61)) {
		tmp = x * log(y);
	} else {
		tmp = (y * (1.0 - z)) - 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 ((x <= (-4.3d+26)) .or. (.not. (x <= 5.2d+61))) then
        tmp = x * log(y)
    else
        tmp = (y * (1.0d0 - z)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e+26) || !(x <= 5.2e+61)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * (1.0 - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.3e+26) or not (x <= 5.2e+61):
		tmp = x * math.log(y)
	else:
		tmp = (y * (1.0 - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.3e+26) || !(x <= 5.2e+61))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * Float64(1.0 - z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.3e+26) || ~((x <= 5.2e+61)))
		tmp = x * log(y);
	else
		tmp = (y * (1.0 - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.3e+26], N[Not[LessEqual[x, 5.2e+61]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2999999999999998e26 or 5.19999999999999945e61 < x

   1. Initial program 94.0%

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

      1. associate--l+ 94.0%

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

      2. fma-def 94.0%

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

      3. sub-neg 94.0%

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

      4. metadata-eval 94.0%

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

      5. fma-neg 94.0%

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

      6. sub-neg 94.0%

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

      7. metadata-eval 94.0%

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

      8. sub-neg 94.0%

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

      9. log1p-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. unsub-neg 99.2%

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

      4. mul-1-neg 99.2%

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

      5. *-commutative 99.2%

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

      6. distribute-lft-neg-in 99.2%

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

      7. sub-neg 99.2%

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

      8. metadata-eval 99.2%

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

      9. +-commutative 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in x around inf 75.0%

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

   if -4.2999999999999998e26 < x < 5.19999999999999945e61

   1. Initial program 87.3%

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

   2. Taylor expanded in y around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. *-commutative 99.6%

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

      7. +-commutative 99.6%

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

      8. *-commutative 99.6%

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

      9. sub-neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. +-commutative 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in y around inf 59.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+26} \lor \neg \left(x \leq 5.2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \]

Alternative 14: 42.7% accurate, 23.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -14200000000:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 16000:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -14200000000.0) (- t) (if (<= t 16000.0) (* y (- 1.0 z)) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -14200000000.0) {
		tmp = -t;
	} else if (t <= 16000.0) {
		tmp = y * (1.0 - z);
	} else {
		tmp = -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 <= (-14200000000.0d0)) then
        tmp = -t
    else if (t <= 16000.0d0) then
        tmp = y * (1.0d0 - z)
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -14200000000.0) {
		tmp = -t;
	} else if (t <= 16000.0) {
		tmp = y * (1.0 - z);
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -14200000000.0:
		tmp = -t
	elif t <= 16000.0:
		tmp = y * (1.0 - z)
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -14200000000.0)
		tmp = Float64(-t);
	elseif (t <= 16000.0)
		tmp = Float64(y * Float64(1.0 - z));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -14200000000.0)
		tmp = -t;
	elseif (t <= 16000.0)
		tmp = y * (1.0 - z);
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -14200000000.0], (-t), If[LessEqual[t, 16000.0], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -1.42e10 or 16000 < t

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. fma-def 95.8%

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

      3. sub-neg 95.8%

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

      4. metadata-eval 95.8%

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

      5. sub-neg 95.8%

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

      6. log1p-def 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 69.9%

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

      1. mul-1-neg 69.9%

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

   6. Simplified 69.9%

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

   if -1.42e10 < t < 16000

   1. Initial program 85.1%

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

      1. associate--l+ 85.1%

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

      2. fma-def 85.1%

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

      3. sub-neg 85.1%

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

      4. metadata-eval 85.1%

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

      5. fma-neg 85.1%

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

      6. sub-neg 85.1%

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

      7. metadata-eval 85.1%

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

      8. sub-neg 85.1%

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

      9. log1p-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.4%

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

      1. mul-1-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. unsub-neg 99.4%

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

      4. mul-1-neg 99.4%

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

      5. *-commutative 99.4%

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

      6. distribute-lft-neg-in 99.4%

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

      7. sub-neg 99.4%

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

      8. metadata-eval 99.4%

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

      9. +-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in z around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. mul-1-neg 99.4%

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

      3. unsub-neg 99.4%

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

      4. *-commutative 99.4%

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

   9. Simplified 99.4%

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

   10. Taylor expanded in y around inf 17.8%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -14200000000:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 16000:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 15: 42.4% accurate, 26.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -68000000:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 4100:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -68000000.0) (- t) (if (<= t 4100.0) (* z (- y)) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -68000000.0) {
		tmp = -t;
	} else if (t <= 4100.0) {
		tmp = z * -y;
	} else {
		tmp = -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 <= (-68000000.0d0)) then
        tmp = -t
    else if (t <= 4100.0d0) then
        tmp = z * -y
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -68000000.0) {
		tmp = -t;
	} else if (t <= 4100.0) {
		tmp = z * -y;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -68000000.0:
		tmp = -t
	elif t <= 4100.0:
		tmp = z * -y
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -68000000.0)
		tmp = Float64(-t);
	elseif (t <= 4100.0)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -68000000.0)
		tmp = -t;
	elseif (t <= 4100.0)
		tmp = z * -y;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -68000000.0], (-t), If[LessEqual[t, 4100.0], N[(z * (-y)), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -6.8e7 or 4100 < t

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. fma-def 95.8%

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

      3. sub-neg 95.8%

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

      4. metadata-eval 95.8%

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

      5. sub-neg 95.8%

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

      6. log1p-def 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 69.9%

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

      1. mul-1-neg 69.9%

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

   6. Simplified 69.9%

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

   if -6.8e7 < t < 4100

   1. Initial program 85.1%

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

      1. associate--l+ 85.1%

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

      2. fma-def 85.1%

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

      3. sub-neg 85.1%

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

      4. metadata-eval 85.1%

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

      5. fma-neg 85.1%

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

      6. sub-neg 85.1%

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

      7. metadata-eval 85.1%

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

      8. sub-neg 85.1%

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

      9. log1p-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.4%

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

      1. mul-1-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. unsub-neg 99.4%

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

      4. mul-1-neg 99.4%

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

      5. *-commutative 99.4%

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

      6. distribute-lft-neg-in 99.4%

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

      7. sub-neg 99.4%

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

      8. metadata-eval 99.4%

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

      9. +-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in z around inf 17.2%

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

      1. mul-1-neg 17.2%

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

      2. *-commutative 17.2%

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

      3. distribute-rgt-neg-in 17.2%

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

   9. Simplified 17.2%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -68000000:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 4100:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 16: 45.6% 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 90.2%

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

2. Taylor expanded in y around 0 99.4%

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

   1. +-commutative 99.4%

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

   2. sub-neg 99.4%

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

   3. metadata-eval 99.4%

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

   4. mul-1-neg 99.4%

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

   5. unsub-neg 99.4%

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

   6. *-commutative 99.4%

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

   7. +-commutative 99.4%

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

   8. *-commutative 99.4%

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

   9. sub-neg 99.4%

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

   10. metadata-eval 99.4%

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

   11. +-commutative 99.4%

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

4. Simplified 99.4%

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

5. Taylor expanded in y around inf 44.1%

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

6. Final simplification 44.1%

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

Alternative 17: 45.4% accurate, 35.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.2%

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

2. Taylor expanded in y around 0 99.4%

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

   1. +-commutative 99.4%

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

   2. sub-neg 99.4%

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

   3. metadata-eval 99.4%

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

   4. mul-1-neg 99.4%

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

   5. unsub-neg 99.4%

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

   6. *-commutative 99.4%

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

   7. +-commutative 99.4%

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

   8. *-commutative 99.4%

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

   9. sub-neg 99.4%

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

   10. metadata-eval 99.4%

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

   11. +-commutative 99.4%

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

4. Simplified 99.4%

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

5. Taylor expanded in z around inf 43.9%

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

   1. associate-*r* 43.9%

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

   2. neg-mul-1 43.9%

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

7. Simplified 43.9%

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

8. Final simplification 43.9%

   \[\leadsto z \cdot \left(-y\right) - t \]

Alternative 18: 35.1% accurate, 107.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-t)

Derivation

1. Initial program 90.2%

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

   1. +-commutative 90.2%

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

   2. fma-def 90.2%

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

   3. sub-neg 90.2%

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

   4. metadata-eval 90.2%

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

   5. sub-neg 90.2%

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

   6. log1p-def 99.9%

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

   7. sub-neg 99.9%

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

   8. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in t around inf 34.7%

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

   1. mul-1-neg 34.7%

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

6. Simplified 34.7%

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

7. Final simplification 34.7%

   \[\leadsto -t \]

Reproduce

herbie shell --seed 2023274 
(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))