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

Percentage Accurate: 89.3% → 99.4%

Time: 19.3s

Alternatives: 13

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: 89.3% 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: 99.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

3. Taylor expanded in y around 0 99.8%

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

4. Taylor expanded in z around inf 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 86.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\log y\right) - t\\ t_2 := x \cdot \log y - t\\ \mathbf{if}\;x \leq -280000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (log y)) t)) (t_2 (- (* x (log y)) t)))
   (if (<= x -280000.0)
     t_2
     (if (<= x 6.8e-218)
       t_1
       (if (<= x 2.1e-171) (- (* y (- 1.0 z)) t) (if (<= x 1.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -log(y) - t;
	double t_2 = (x * log(y)) - t;
	double tmp;
	if (x <= -280000.0) {
		tmp = t_2;
	} else if (x <= 6.8e-218) {
		tmp = t_1;
	} else if (x <= 2.1e-171) {
		tmp = (y * (1.0 - z)) - t;
	} else if (x <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = -log(y) - t
    t_2 = (x * log(y)) - t
    if (x <= (-280000.0d0)) then
        tmp = t_2
    else if (x <= 6.8d-218) then
        tmp = t_1
    else if (x <= 2.1d-171) then
        tmp = (y * (1.0d0 - z)) - t
    else if (x <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_2
    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) - t;
	double t_2 = (x * Math.log(y)) - t;
	double tmp;
	if (x <= -280000.0) {
		tmp = t_2;
	} else if (x <= 6.8e-218) {
		tmp = t_1;
	} else if (x <= 2.1e-171) {
		tmp = (y * (1.0 - z)) - t;
	} else if (x <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -math.log(y) - t
	t_2 = (x * math.log(y)) - t
	tmp = 0
	if x <= -280000.0:
		tmp = t_2
	elif x <= 6.8e-218:
		tmp = t_1
	elif x <= 2.1e-171:
		tmp = (y * (1.0 - z)) - t
	elif x <= 1.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-log(y)) - t)
	t_2 = Float64(Float64(x * log(y)) - t)
	tmp = 0.0
	if (x <= -280000.0)
		tmp = t_2;
	elseif (x <= 6.8e-218)
		tmp = t_1;
	elseif (x <= 2.1e-171)
		tmp = Float64(Float64(y * Float64(1.0 - z)) - t);
	elseif (x <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -log(y) - t;
	t_2 = (x * log(y)) - t;
	tmp = 0.0;
	if (x <= -280000.0)
		tmp = t_2;
	elseif (x <= 6.8e-218)
		tmp = t_1;
	elseif (x <= 2.1e-171)
		tmp = (y * (1.0 - z)) - t;
	elseif (x <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[x, -280000.0], t$95$2, If[LessEqual[x, 6.8e-218], t$95$1, If[LessEqual[x, 2.1e-171], N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[x, 1.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8e5 or 1 < x

   1. Initial program 92.7%

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

      1. +-commutative 92.7%

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

      2. fma-define 92.7%

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

      3. sub-neg 92.7%

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

      4. metadata-eval 92.7%

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

      5. sub-neg 92.7%

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

      6. log1p-define 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 74.5%

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

      1. sub-neg 74.5%

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

      2. log1p-define 81.5%

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

      3. +-commutative 81.5%

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

      4. mul-1-neg 81.5%

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

      5. unsub-neg 81.5%

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

      6. sub-neg 81.5%

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

      7. metadata-eval 81.5%

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

      8. *-commutative 81.5%

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

      9. div-sub 81.5%

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

      10. *-commutative 81.5%

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

      11. +-commutative 81.5%

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

      12. sub-neg 81.5%

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

      13. log1p-define 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in x around inf 91.3%

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

      1. *-commutative 91.3%

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

   10. Simplified 91.3%

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

   if -2.8e5 < x < 6.79999999999999971e-218 or 2.1e-171 < x < 1

   1. Initial program 89.8%

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

   3. Taylor expanded in y around 0 88.7%

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

   4. Taylor expanded in x around 0 88.2%

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

      1. mul-1-neg 88.2%

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

   6. Simplified 88.2%

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

   if 6.79999999999999971e-218 < x < 2.1e-171

   1. Initial program 46.7%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -280000:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-218}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + -1 \leq -1.002 \lor \neg \left(x + -1 \leq -1\right):\\ \;\;\;\;\left(x + -1\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ x -1.0) -1.002) (not (<= (+ x -1.0) -1.0)))
   (- (* (+ x -1.0) (log y)) t)
   (- (- (* y (- 1.0 z)) (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + -1.0) <= -1.002) || !((x + -1.0) <= -1.0)) {
		tmp = ((x + -1.0) * log(y)) - t;
	} else {
		tmp = ((y * (1.0 - z)) - 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 + (-1.0d0)) <= (-1.002d0)) .or. (.not. ((x + (-1.0d0)) <= (-1.0d0)))) then
        tmp = ((x + (-1.0d0)) * log(y)) - t
    else
        tmp = ((y * (1.0d0 - z)) - 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 + -1.0) <= -1.002) || !((x + -1.0) <= -1.0)) {
		tmp = ((x + -1.0) * Math.log(y)) - t;
	} else {
		tmp = ((y * (1.0 - z)) - Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x + -1.0) <= -1.002) or not ((x + -1.0) <= -1.0):
		tmp = ((x + -1.0) * math.log(y)) - t
	else:
		tmp = ((y * (1.0 - z)) - math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x + -1.0) <= -1.002) || !(Float64(x + -1.0) <= -1.0))
		tmp = Float64(Float64(Float64(x + -1.0) * log(y)) - t);
	else
		tmp = Float64(Float64(Float64(y * Float64(1.0 - z)) - log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x + -1.0) <= -1.002) || ~(((x + -1.0) <= -1.0)))
		tmp = ((x + -1.0) * log(y)) - t;
	else
		tmp = ((y * (1.0 - z)) - log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x + -1.0), $MachinePrecision], -1.002], N[Not[LessEqual[N[(x + -1.0), $MachinePrecision], -1.0]], $MachinePrecision]], N[(N[(N[(x + -1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -1.002 or -1 < (-.f64 x #s(literal 1 binary64))

   1. Initial program 92.9%

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

   3. Taylor expanded in y around 0 92.5%

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

   if -1.002 < (-.f64 x #s(literal 1 binary64)) < -1

   1. Initial program 86.1%

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

   3. Taylor expanded in y around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. distribute-rgt-neg-in 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

      5. +-commutative 99.3%

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

      6. distribute-neg-in 99.3%

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

      7. metadata-eval 99.3%

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

      8. unsub-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around 0 99.2%

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

      1. mul-1-neg 99.2%

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

   8. Simplified 99.2%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + -1 \leq -1.002 \lor \neg \left(x + -1 \leq -1\right):\\ \;\;\;\;\left(x + -1\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + -1 \leq -20000000 \lor \neg \left(x + -1 \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - y \cdot z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ x -1.0) -20000000.0) (not (<= (+ x -1.0) -0.5)))
   (- (- (* x (log y)) (* y z)) t)
   (- (- (* y (- 1.0 z)) (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + -1.0) <= -20000000.0) || !((x + -1.0) <= -0.5)) {
		tmp = ((x * log(y)) - (y * z)) - t;
	} else {
		tmp = ((y * (1.0 - z)) - 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 + (-1.0d0)) <= (-20000000.0d0)) .or. (.not. ((x + (-1.0d0)) <= (-0.5d0)))) then
        tmp = ((x * log(y)) - (y * z)) - t
    else
        tmp = ((y * (1.0d0 - z)) - 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 + -1.0) <= -20000000.0) || !((x + -1.0) <= -0.5)) {
		tmp = ((x * Math.log(y)) - (y * z)) - t;
	} else {
		tmp = ((y * (1.0 - z)) - Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x + -1.0) <= -20000000.0) or not ((x + -1.0) <= -0.5):
		tmp = ((x * math.log(y)) - (y * z)) - t
	else:
		tmp = ((y * (1.0 - z)) - math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x + -1.0) <= -20000000.0) || !(Float64(x + -1.0) <= -0.5))
		tmp = Float64(Float64(Float64(x * log(y)) - Float64(y * z)) - t);
	else
		tmp = Float64(Float64(Float64(y * Float64(1.0 - z)) - log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x + -1.0) <= -20000000.0) || ~(((x + -1.0) <= -0.5)))
		tmp = ((x * log(y)) - (y * z)) - t;
	else
		tmp = ((y * (1.0 - z)) - log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x + -1.0), $MachinePrecision], -20000000.0], N[Not[LessEqual[N[(x + -1.0), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -2e7 or -0.5 < (-.f64 x #s(literal 1 binary64))

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0 99.7%

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

   4. Taylor expanded in z around inf 99.7%

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

   5. Taylor expanded in x around inf 98.4%

      \[\leadsto \left(\color{blue}{x \cdot \log y} + y \cdot \left(z \cdot \left(y \cdot \left(-0.3333333333333333 \cdot y - 0.5\right) - 1\right)\right)\right) - t \]
   6. Step-by-step derivation

      1. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in y around 0 98.1%

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

      1. associate-*r* 98.1%

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

      2. neg-mul-1 98.1%

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

   10. Simplified 98.1%

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

   if -2e7 < (-.f64 x #s(literal 1 binary64)) < -0.5

   1. Initial program 86.7%

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

   3. Taylor expanded in y around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. distribute-rgt-neg-in 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

      5. +-commutative 99.3%

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

      6. distribute-neg-in 99.3%

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

      7. metadata-eval 99.3%

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

      8. unsub-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around 0 98.7%

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

      1. mul-1-neg 98.7%

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

   8. Simplified 98.7%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + -1 \leq -20000000 \lor \neg \left(x + -1 \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - y \cdot z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x + -1.0) * log(y)) + ((z + -1.0) * (y * ((y * -0.5) + -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 = (((x + (-1.0d0)) * log(y)) + ((z + (-1.0d0)) * (y * ((y * (-0.5d0)) + (-1.0d0))))) - 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) * (y * ((y * -0.5) + -1.0)))) - t;
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x + -1.0) * log(y)) + ((z + -1.0) * (y * ((y * -0.5) + -1.0)))) - 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[(y * N[(N[(y * -0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 89.8%

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

3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 99.7%

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

Alternative 6: 99.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

3. Taylor expanded in y around 0 99.8%

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

4. Taylor expanded in z around inf 99.8%

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

5. Taylor expanded in y around 0 99.7%

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

   1. associate-*r* 99.7%

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

   2. distribute-rgt-out 99.7%

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

7. Simplified 99.7%

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

8. Final simplification 99.7%

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

Alternative 7: 60.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+103} \lor \neg \left(z \leq 2.7 \cdot 10^{+126}\right):\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02e+103) (not (<= z 2.7e+126)))
   (- (* y (- 1.0 z)) t)
   (- (- (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e+103) || !(z <= 2.7e+126)) {
		tmp = (y * (1.0 - z)) - t;
	} 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 ((z <= (-1.02d+103)) .or. (.not. (z <= 2.7d+126))) then
        tmp = (y * (1.0d0 - z)) - t
    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 ((z <= -1.02e+103) || !(z <= 2.7e+126)) {
		tmp = (y * (1.0 - z)) - t;
	} else {
		tmp = -Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.02e+103) or not (z <= 2.7e+126):
		tmp = (y * (1.0 - z)) - t
	else:
		tmp = -math.log(y) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.02e+103) || !(z <= 2.7e+126))
		tmp = Float64(Float64(y * Float64(1.0 - z)) - t);
	else
		tmp = Float64(Float64(-log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.02e+103) || ~((z <= 2.7e+126)))
		tmp = (y * (1.0 - z)) - t;
	else
		tmp = -log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.02e+103], N[Not[LessEqual[z, 2.7e+126]], $MachinePrecision]], N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.01999999999999991e103 or 2.70000000000000002e126 < z

   1. Initial program 71.9%

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

   3. Taylor expanded in y around 0 98.3%

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

      1. mul-1-neg 98.3%

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

      2. distribute-rgt-neg-in 98.3%

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

      3. sub-neg 98.3%

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

      4. metadata-eval 98.3%

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

      5. +-commutative 98.3%

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

      6. distribute-neg-in 98.3%

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

      7. metadata-eval 98.3%

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

      8. unsub-neg 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in y around inf 66.4%

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

   if -1.01999999999999991e103 < z < 2.70000000000000002e126

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 98.5%

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

   4. Taylor expanded in x around 0 62.4%

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

      1. mul-1-neg 62.4%

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

   6. Simplified 62.4%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+103} \lor \neg \left(z \leq 2.7 \cdot 10^{+126}\right):\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.0% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

3. Taylor expanded in y around 0 99.8%

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

4. Taylor expanded in z around inf 99.8%

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

5. Taylor expanded in y around 0 99.7%

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

   1. associate-*r* 99.7%

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

   2. distribute-rgt-out 99.7%

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

7. Simplified 99.7%

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

8. Taylor expanded in y around 0 99.3%

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

   1. +-commutative 99.3%

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

   2. sub-neg 99.3%

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

   3. metadata-eval 99.3%

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

   4. +-commutative 99.3%

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

   5. *-commutative 99.3%

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

   6. mul-1-neg 99.3%

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

   7. *-commutative 99.3%

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

   8. unsub-neg 99.3%

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

   9. *-commutative 99.3%

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

10. Simplified 99.3%

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

11. Final simplification 99.3%

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

Alternative 9: 88.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

3. Taylor expanded in y around 0 89.1%

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

4. Final simplification 89.1%

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

Alternative 10: 42.6% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9600000000 \lor \neg \left(t \leq 2.9 \cdot 10^{+40}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9600000000.0) (not (<= t 2.9e+40))) (- t) (* y (- 1.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9600000000.0) || !(t <= 2.9e+40)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	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 <= (-9600000000.0d0)) .or. (.not. (t <= 2.9d+40))) then
        tmp = -t
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9600000000.0) || !(t <= 2.9e+40)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9600000000.0) or not (t <= 2.9e+40):
		tmp = -t
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9600000000.0) || !(t <= 2.9e+40))
		tmp = Float64(-t);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9600000000.0) || ~((t <= 2.9e+40)))
		tmp = -t;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9600000000.0], N[Not[LessEqual[t, 2.9e+40]], $MachinePrecision]], (-t), N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.6e9 or 2.90000000000000017e40 < t

   1. Initial program 95.4%

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

   3. Taylor expanded in t around inf 76.2%

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

      1. neg-mul-1 76.2%

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

   5. Simplified 76.2%

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

   if -9.6e9 < t < 2.90000000000000017e40

   1. Initial program 84.2%

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

   3. Taylor expanded in y around 0 99.1%

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

      1. mul-1-neg 99.1%

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

      2. distribute-rgt-neg-in 99.1%

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

      3. sub-neg 99.1%

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

      4. metadata-eval 99.1%

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

      5. +-commutative 99.1%

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

      6. distribute-neg-in 99.1%

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

      7. metadata-eval 99.1%

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

      8. unsub-neg 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in y around inf 19.1%

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

   7. Taylor expanded in y around inf 17.5%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9600000000 \lor \neg \left(t \leq 2.9 \cdot 10^{+40}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.2% accurate, 30.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

3. Taylor expanded in y around 0 99.3%

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

   1. mul-1-neg 99.3%

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

   2. distribute-rgt-neg-in 99.3%

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

   3. sub-neg 99.3%

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

   4. metadata-eval 99.3%

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

   5. +-commutative 99.3%

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

   6. distribute-neg-in 99.3%

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

   7. metadata-eval 99.3%

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

   8. unsub-neg 99.3%

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

5. Simplified 99.3%

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

6. Taylor expanded in y around inf 50.0%

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

7. Final simplification 50.0%

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

Alternative 12: 36.0% accurate, 71.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

3. Taylor expanded in y around 0 99.3%

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

   1. mul-1-neg 99.3%

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

   2. distribute-rgt-neg-in 99.3%

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

   3. sub-neg 99.3%

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

   4. metadata-eval 99.3%

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

   5. +-commutative 99.3%

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

   6. distribute-neg-in 99.3%

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

   7. metadata-eval 99.3%

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

   8. unsub-neg 99.3%

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

5. Simplified 99.3%

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

6. Taylor expanded in y around inf 50.0%

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

7. Taylor expanded in z around 0 40.5%

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

8. Final simplification 40.5%

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

Alternative 13: 35.7% 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 89.8%

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

3. Taylor expanded in t around inf 40.4%

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

   1. neg-mul-1 40.4%

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

5. Simplified 40.4%

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

6. Final simplification 40.4%

   \[\leadsto -t \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(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))