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

Percentage Accurate: 89.5% → 99.8%

Time: 17.7s

Alternatives: 19

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

   1. fma-define 89.3%

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

   2. sub-neg 89.3%

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

   3. metadata-eval 89.3%

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

   4. sub-neg 89.3%

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

   5. metadata-eval 89.3%

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

   6. sub-neg 89.3%

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

   7. log1p-define 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 98.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + -1 \leq -20 \lor \neg \left(x + -1 \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - y \cdot \left(-1 + z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ x -1.0) -20.0) (not (<= (+ x -1.0) -0.5)))
   (- (- (* x (log y)) (* y (+ -1.0 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) <= -20.0) || !((x + -1.0) <= -0.5)) {
		tmp = ((x * log(y)) - (y * (-1.0 + 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)) <= (-20.0d0)) .or. (.not. ((x + (-1.0d0)) <= (-0.5d0)))) then
        tmp = ((x * log(y)) - (y * ((-1.0d0) + 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) <= -20.0) || !((x + -1.0) <= -0.5)) {
		tmp = ((x * Math.log(y)) - (y * (-1.0 + 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) <= -20.0) or not ((x + -1.0) <= -0.5):
		tmp = ((x * math.log(y)) - (y * (-1.0 + 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) <= -20.0) || !(Float64(x + -1.0) <= -0.5))
		tmp = Float64(Float64(Float64(x * log(y)) - Float64(y * Float64(-1.0 + 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) <= -20.0) || ~(((x + -1.0) <= -0.5)))
		tmp = ((x * log(y)) - (y * (-1.0 + 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], -20.0], N[Not[LessEqual[N[(x + -1.0), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y * N[(-1.0 + z), $MachinePrecision]), $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)) < -20 or -0.5 < (-.f64 x #s(literal 1 binary64))

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. fma-define 99.6%

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

      5. mul-1-neg 99.6%

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

      6. fmm-def 99.6%

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

      7. +-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

      10. +-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf 99.0%

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

      1. *-commutative 99.0%

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

   8. Simplified 99.0%

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

   if -20 < (-.f64 x #s(literal 1 binary64)) < -0.5

   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. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. fma-define 100.0%

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

      5. +-commutative 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. +-commutative 100.0%

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

      11. distribute-neg-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 98.0%

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

      1. +-commutative 98.0%

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

      2. mul-1-neg 98.0%

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

      3. unsub-neg 98.0%

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

   8. Simplified 98.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + -1 \leq -20 \lor \neg \left(x + -1 \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - y \cdot \left(-1 + z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(\left(-1 + y \cdot -0.5\right) \cdot \left(-1 + z\right)\right) - t\\ \mathbf{elif}\;x \leq 0.0195:\\ \;\;\;\;-\log y\\ \mathbf{elif}\;x \leq 75000000000000:\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.5e+61)
     t_1
     (if (<= x 2.25e-20)
       (- (* y (* (+ -1.0 (* y -0.5)) (+ -1.0 z))) t)
       (if (<= x 0.0195)
         (- (log y))
         (if (<= x 75000000000000.0) (- t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.5e+61) {
		tmp = t_1;
	} else if (x <= 2.25e-20) {
		tmp = (y * ((-1.0 + (y * -0.5)) * (-1.0 + z))) - t;
	} else if (x <= 0.0195) {
		tmp = -log(y);
	} else if (x <= 75000000000000.0) {
		tmp = -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-2.5d+61)) then
        tmp = t_1
    else if (x <= 2.25d-20) then
        tmp = (y * (((-1.0d0) + (y * (-0.5d0))) * ((-1.0d0) + z))) - t
    else if (x <= 0.0195d0) then
        tmp = -log(y)
    else if (x <= 75000000000000.0d0) then
        tmp = -t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -2.5e+61) {
		tmp = t_1;
	} else if (x <= 2.25e-20) {
		tmp = (y * ((-1.0 + (y * -0.5)) * (-1.0 + z))) - t;
	} else if (x <= 0.0195) {
		tmp = -Math.log(y);
	} else if (x <= 75000000000000.0) {
		tmp = -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -2.5e+61:
		tmp = t_1
	elif x <= 2.25e-20:
		tmp = (y * ((-1.0 + (y * -0.5)) * (-1.0 + z))) - t
	elif x <= 0.0195:
		tmp = -math.log(y)
	elif x <= 75000000000000.0:
		tmp = -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.5e+61)
		tmp = t_1;
	elseif (x <= 2.25e-20)
		tmp = Float64(Float64(y * Float64(Float64(-1.0 + Float64(y * -0.5)) * Float64(-1.0 + z))) - t);
	elseif (x <= 0.0195)
		tmp = Float64(-log(y));
	elseif (x <= 75000000000000.0)
		tmp = Float64(-t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -2.5e+61)
		tmp = t_1;
	elseif (x <= 2.25e-20)
		tmp = (y * ((-1.0 + (y * -0.5)) * (-1.0 + z))) - t;
	elseif (x <= 0.0195)
		tmp = -log(y);
	elseif (x <= 75000000000000.0)
		tmp = -t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+61], t$95$1, If[LessEqual[x, 2.25e-20], N[(N[(y * N[(N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision] * N[(-1.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[x, 0.0195], (-N[Log[y], $MachinePrecision]), If[LessEqual[x, 75000000000000.0], (-t), t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.50000000000000009e61 or 7.5e13 < x

   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 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. +-commutative 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

      10. +-commutative 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. metadata-eval 99.7%

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

      13. unsub-neg 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. sub-neg 92.9%

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

      3. metadata-eval 92.9%

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

      4. fma-define 92.9%

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

      5. +-commutative 92.9%

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

   8. Simplified 92.9%

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

      1. fma-undefine 92.9%

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

   10. Applied egg-rr 92.9%

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

   11. Taylor expanded in x around inf 78.6%

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

       1. *-commutative 78.6%

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

   13. Simplified 78.6%

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

   if -2.50000000000000009e61 < x < 2.2500000000000001e-20

   1. Initial program 85.8%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around inf 74.1%

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

      1. *-commutative 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in x around 0 71.7%

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

   if 2.2500000000000001e-20 < x < 0.0195

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf 99.3%

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

   4. Taylor expanded in y around 0 96.6%

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

      1. sub-neg 96.6%

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

      2. metadata-eval 96.6%

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

      3. associate-*r/ 96.4%

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

      4. +-commutative 96.4%

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

   6. Simplified 96.4%

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

   7. Taylor expanded in x around 0 74.1%

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

      1. associate-*r/ 74.1%

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

      2. neg-mul-1 74.1%

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

   9. Simplified 74.1%

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

   10. Taylor expanded in t around 0 74.1%

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

       1. mul-1-neg 74.1%

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

   12. Simplified 74.1%

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

   if 0.0195 < x < 7.5e13

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{-t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(\left(-1 + y \cdot -0.5\right) \cdot \left(-1 + z\right)\right) - t\\ \mathbf{elif}\;x \leq 0.0195:\\ \;\;\;\;-\log y\\ \mathbf{elif}\;x \leq 75000000000000:\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + -1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;x + -1 \leq -1:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y + \log y \cdot \left(x + -1\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x -1.0) -5e+17)
   (- (* x (log y)) t)
   (if (<= (+ x -1.0) -1.0)
     (- (- (* y (- 1.0 z)) (log y)) t)
     (- (+ y (* (log y) (+ x -1.0))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + -1.0) <= -5e+17) {
		tmp = (x * log(y)) - t;
	} else if ((x + -1.0) <= -1.0) {
		tmp = ((y * (1.0 - z)) - log(y)) - t;
	} else {
		tmp = (y + (log(y) * (x + -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 ((x + (-1.0d0)) <= (-5d+17)) then
        tmp = (x * log(y)) - t
    else if ((x + (-1.0d0)) <= (-1.0d0)) then
        tmp = ((y * (1.0d0 - z)) - log(y)) - t
    else
        tmp = (y + (log(y) * (x + (-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 ((x + -1.0) <= -5e+17) {
		tmp = (x * Math.log(y)) - t;
	} else if ((x + -1.0) <= -1.0) {
		tmp = ((y * (1.0 - z)) - Math.log(y)) - t;
	} else {
		tmp = (y + (Math.log(y) * (x + -1.0))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + -1.0) <= -5e+17:
		tmp = (x * math.log(y)) - t
	elif (x + -1.0) <= -1.0:
		tmp = ((y * (1.0 - z)) - math.log(y)) - t
	else:
		tmp = (y + (math.log(y) * (x + -1.0))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + -1.0) <= -5e+17)
		tmp = Float64(Float64(x * log(y)) - t);
	elseif (Float64(x + -1.0) <= -1.0)
		tmp = Float64(Float64(Float64(y * Float64(1.0 - z)) - log(y)) - t);
	else
		tmp = Float64(Float64(y + Float64(log(y) * Float64(x + -1.0))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + -1.0) <= -5e+17)
		tmp = (x * log(y)) - t;
	elseif ((x + -1.0) <= -1.0)
		tmp = ((y * (1.0 - z)) - log(y)) - t;
	else
		tmp = (y + (log(y) * (x + -1.0))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + -1.0), $MachinePrecision], -5e+17], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[N[(x + -1.0), $MachinePrecision], -1.0], N[(N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y + N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -5e17

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 99.8%

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

   4. Taylor expanded in x around inf 95.2%

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

      1. *-commutative 95.2%

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

   6. Simplified 95.2%

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

   if -5e17 < (-.f64 x #s(literal 1 binary64)) < -1

   1. Initial program 85.4%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. fma-define 100.0%

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

      5. +-commutative 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. +-commutative 100.0%

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

      11. distribute-neg-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 98.8%

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

      1. +-commutative 98.8%

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

      2. mul-1-neg 98.8%

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

      3. unsub-neg 98.8%

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

   8. Simplified 98.8%

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

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

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. +-commutative 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

      10. +-commutative 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. metadata-eval 99.7%

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

      13. unsub-neg 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 91.1%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + -1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;x + -1 \leq -1:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y + \log y \cdot \left(x + -1\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + -1 \leq -2 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x + -1 \leq -1:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x -1.0) -2e+66)
   (* x (log y))
   (if (<= (+ x -1.0) -1.0) (- (- (log y)) t) (* (log y) (+ x -1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + -1.0) <= -2e+66) {
		tmp = x * log(y);
	} else if ((x + -1.0) <= -1.0) {
		tmp = -log(y) - t;
	} else {
		tmp = log(y) * (x + -1.0);
	}
	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)) <= (-2d+66)) then
        tmp = x * log(y)
    else if ((x + (-1.0d0)) <= (-1.0d0)) then
        tmp = -log(y) - t
    else
        tmp = log(y) * (x + (-1.0d0))
    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) <= -2e+66) {
		tmp = x * Math.log(y);
	} else if ((x + -1.0) <= -1.0) {
		tmp = -Math.log(y) - t;
	} else {
		tmp = Math.log(y) * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + -1.0) <= -2e+66:
		tmp = x * math.log(y)
	elif (x + -1.0) <= -1.0:
		tmp = -math.log(y) - t
	else:
		tmp = math.log(y) * (x + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + -1.0) <= -2e+66)
		tmp = Float64(x * log(y));
	elseif (Float64(x + -1.0) <= -1.0)
		tmp = Float64(Float64(-log(y)) - t);
	else
		tmp = Float64(log(y) * Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + -1.0) <= -2e+66)
		tmp = x * log(y);
	elseif ((x + -1.0) <= -1.0)
		tmp = -log(y) - t;
	else
		tmp = log(y) * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + -1.0), $MachinePrecision], -2e+66], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + -1.0), $MachinePrecision], -1.0], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -1.99999999999999989e66

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. +-commutative 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

      10. +-commutative 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. metadata-eval 99.7%

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

      13. unsub-neg 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. sub-neg 96.0%

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

      3. metadata-eval 96.0%

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

      4. fma-define 96.0%

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

      5. +-commutative 96.0%

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

   8. Simplified 96.0%

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

      1. fma-undefine 96.0%

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

   10. Applied egg-rr 96.0%

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

   11. Taylor expanded in x around inf 85.6%

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

       1. *-commutative 85.6%

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

   13. Simplified 85.6%

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

   if -1.99999999999999989e66 < (-.f64 x #s(literal 1 binary64)) < -1

   1. Initial program 86.0%

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

   3. Taylor expanded in y around 0 85.8%

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

   4. Taylor expanded in x around 0 82.6%

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

      1. mul-1-neg 82.6%

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

   6. Simplified 82.6%

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

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

   1. Initial program 91.1%

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

   3. Taylor expanded in t around inf 74.2%

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

   4. Taylor expanded in y around 0 74.0%

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

      1. sub-neg 74.0%

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

      2. metadata-eval 74.0%

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

      3. associate-*r/ 73.8%

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

      4. +-commutative 73.8%

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

   6. Simplified 73.8%

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

      1. clear-num 73.8%

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

      2. un-div-inv 73.8%

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

   8. Applied egg-rr 73.8%

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

   9. Taylor expanded in t around 0 73.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + -1 \leq -2 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x + -1 \leq -1:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.9%

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

Alternative 7: 87.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1650 \lor \neg \left(t \leq 35\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y + \log y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1650.0) (not (<= t 35.0)))
   (- (* x (log y)) t)
   (+ y (* (log y) (+ x -1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1650.0) || !(t <= 35.0)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = y + (log(y) * (x + -1.0));
	}
	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 <= (-1650.0d0)) .or. (.not. (t <= 35.0d0))) then
        tmp = (x * log(y)) - t
    else
        tmp = y + (log(y) * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1650.0) || !(t <= 35.0)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = y + (Math.log(y) * (x + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1650.0) or not (t <= 35.0):
		tmp = (x * math.log(y)) - t
	else:
		tmp = y + (math.log(y) * (x + -1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1650.0) || !(t <= 35.0))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(y + Float64(log(y) * Float64(x + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1650.0) || ~((t <= 35.0)))
		tmp = (x * log(y)) - t;
	else
		tmp = y + (log(y) * (x + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1650.0], N[Not[LessEqual[t, 35.0]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(y + N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1650 or 35 < t

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around inf 95.7%

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

      1. *-commutative 95.7%

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

   6. Simplified 95.7%

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

   if -1650 < t < 35

   1. Initial program 82.0%

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

   3. Taylor expanded in y around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. fma-define 99.7%

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

      5. +-commutative 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

      10. +-commutative 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. metadata-eval 99.7%

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

      13. unsub-neg 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. sub-neg 81.8%

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

      3. metadata-eval 81.8%

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

      4. fma-define 81.8%

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

      5. +-commutative 81.8%

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

   8. Simplified 81.8%

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

      1. fma-undefine 81.8%

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

   10. Applied egg-rr 81.8%

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

   11. Taylor expanded in t around 0 81.1%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1650 \lor \neg \left(t \leq 35\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y + \log y \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1650 \lor \neg \left(t \leq 35\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1650.0) (not (<= t 35.0)))
   (- (* x (log y)) t)
   (* (log y) (+ x -1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1650.0) || !(t <= 35.0)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = log(y) * (x + -1.0);
	}
	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 <= (-1650.0d0)) .or. (.not. (t <= 35.0d0))) then
        tmp = (x * log(y)) - t
    else
        tmp = log(y) * (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1650.0) || !(t <= 35.0)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = Math.log(y) * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1650.0) or not (t <= 35.0):
		tmp = (x * math.log(y)) - t
	else:
		tmp = math.log(y) * (x + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1650.0) || !(t <= 35.0))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(log(y) * Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1650.0) || ~((t <= 35.0)))
		tmp = (x * log(y)) - t;
	else
		tmp = log(y) * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1650.0], N[Not[LessEqual[t, 35.0]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1650 or 35 < t

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around inf 95.7%

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

      1. *-commutative 95.7%

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

   6. Simplified 95.7%

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

   if -1650 < t < 35

   1. Initial program 82.0%

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

   3. Taylor expanded in t around inf 59.7%

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

   4. Taylor expanded in y around 0 59.3%

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

      1. sub-neg 59.3%

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

      2. metadata-eval 59.3%

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

      3. associate-*r/ 59.2%

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

      4. +-commutative 59.2%

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

   6. Simplified 59.2%

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

      1. clear-num 59.2%

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

      2. un-div-inv 59.2%

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

   8. Applied egg-rr 59.2%

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

   9. Taylor expanded in t around 0 81.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1650 \lor \neg \left(t \leq 35\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+58} \lor \neg \left(x \leq 6.2 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.85e+58) (not (<= x 6.2e+14)))
   (* x (log y))
   (- (- (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.85e+58) || !(x <= 6.2e+14)) {
		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 <= (-1.85d+58)) .or. (.not. (x <= 6.2d+14))) 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 <= -1.85e+58) || !(x <= 6.2e+14)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.85e+58) or not (x <= 6.2e+14):
		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 <= -1.85e+58) || !(x <= 6.2e+14))
		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 <= -1.85e+58) || ~((x <= 6.2e+14)))
		tmp = x * log(y);
	else
		tmp = -log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.85e+58], N[Not[LessEqual[x, 6.2e+14]], $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 < -1.8500000000000001e58 or 6.2e14 < x

   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 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. +-commutative 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

      10. +-commutative 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. metadata-eval 99.7%

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

      13. unsub-neg 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. sub-neg 92.9%

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

      3. metadata-eval 92.9%

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

      4. fma-define 92.9%

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

      5. +-commutative 92.9%

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

   8. Simplified 92.9%

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

      1. fma-undefine 92.9%

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

   10. Applied egg-rr 92.9%

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

   11. Taylor expanded in x around inf 78.6%

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

       1. *-commutative 78.6%

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

   13. Simplified 78.6%

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

   if -1.8500000000000001e58 < x < 6.2e14

   1. Initial program 86.5%

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

   3. Taylor expanded in y around 0 86.2%

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

   4. Taylor expanded in x around 0 82.1%

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

      1. mul-1-neg 82.1%

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

   6. Simplified 82.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+58} \lor \neg \left(x \leq 6.2 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in y around 0 99.8%

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

   1. +-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. metadata-eval 99.8%

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

   4. fma-define 99.8%

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

   5. mul-1-neg 99.8%

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

   6. fmm-def 99.8%

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

   7. +-commutative 99.8%

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

   8. sub-neg 99.8%

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

   9. metadata-eval 99.8%

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

   10. +-commutative 99.8%

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

5. Simplified 99.8%

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

6. Final simplification 99.8%

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

Alternative 11: 50.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-275}:\\ \;\;\;\;-\log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.5e-15)
   (- (* y (* z (+ -1.0 (* y -0.5)))) t)
   (if (<= t -1.32e-275) (- (log y)) (- (* y (- 1.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e-15) {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	} else if (t <= -1.32e-275) {
		tmp = -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 (t <= (-3.5d-15)) then
        tmp = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
    else if (t <= (-1.32d-275)) then
        tmp = -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 (t <= -3.5e-15) {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	} else if (t <= -1.32e-275) {
		tmp = -Math.log(y);
	} else {
		tmp = (y * (1.0 - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.5e-15:
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t
	elif t <= -1.32e-275:
		tmp = -math.log(y)
	else:
		tmp = (y * (1.0 - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.5e-15)
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * -0.5)))) - t);
	elseif (t <= -1.32e-275)
		tmp = Float64(-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 (t <= -3.5e-15)
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	elseif (t <= -1.32e-275)
		tmp = -log(y);
	else
		tmp = (y * (1.0 - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.5e-15], N[(N[(y * N[(z * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[t, -1.32e-275], (-N[Log[y], $MachinePrecision]), N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5000000000000001e-15

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 99.9%

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

   4. Taylor expanded in z around inf 69.6%

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

   if -3.5000000000000001e-15 < t < -1.31999999999999996e-275

   1. Initial program 90.7%

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

   3. Taylor expanded in t around inf 66.6%

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

   4. Taylor expanded in y around 0 66.3%

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

      1. sub-neg 66.3%

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

      2. metadata-eval 66.3%

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

      3. associate-*r/ 66.2%

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

      4. +-commutative 66.2%

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

   6. Simplified 66.2%

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

   7. Taylor expanded in x around 0 39.0%

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

      1. associate-*r/ 39.0%

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

      2. neg-mul-1 39.0%

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

   9. Simplified 39.0%

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

   10. Taylor expanded in t around 0 39.0%

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

       1. mul-1-neg 39.0%

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

   12. Simplified 39.0%

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

   if -1.31999999999999996e-275 < t

   1. Initial program 85.2%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. fma-define 99.9%

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

      5. +-commutative 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

      10. +-commutative 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 55.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-275}:\\ \;\;\;\;-\log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in y around 0 99.8%

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

   1. +-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. metadata-eval 99.8%

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

   4. fma-define 99.8%

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

   5. +-commutative 99.8%

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

   6. mul-1-neg 99.8%

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

   7. distribute-rgt-neg-in 99.8%

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

   8. sub-neg 99.8%

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

   9. metadata-eval 99.8%

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

   10. +-commutative 99.8%

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

   11. distribute-neg-in 99.8%

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

   12. metadata-eval 99.8%

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

   13. unsub-neg 99.8%

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

5. Simplified 99.8%

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

6. Taylor expanded in z around 0 89.2%

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

7. Final simplification 89.2%

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

Alternative 13: 88.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in y around 0 89.1%

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

4. Final simplification 89.1%

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

Alternative 14: 46.1% accurate, 16.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in y around 0 99.9%

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

4. Taylor expanded in x around inf 83.4%

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

   1. *-commutative 83.4%

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

6. Simplified 83.4%

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

7. Taylor expanded in x around 0 48.4%

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

8. Final simplification 48.4%

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

Alternative 15: 45.9% 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 89.3%

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

3. Taylor expanded in y around 0 99.8%

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

   1. +-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. metadata-eval 99.8%

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

   4. fma-define 99.8%

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

   5. +-commutative 99.8%

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

   6. mul-1-neg 99.8%

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

   7. distribute-rgt-neg-in 99.8%

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

   8. sub-neg 99.8%

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

   9. metadata-eval 99.8%

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

   10. +-commutative 99.8%

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

   11. distribute-neg-in 99.8%

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

   12. metadata-eval 99.8%

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

   13. unsub-neg 99.8%

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

5. Simplified 99.8%

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

6. Taylor expanded in y around inf 48.4%

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

7. Final simplification 48.4%

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

Alternative 16: 45.7% accurate, 35.8× speedup

Math

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

FPCore

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

C

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

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 - (y * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in y around 0 99.8%

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

   1. +-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. metadata-eval 99.8%

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

   4. fma-define 99.8%

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

   5. +-commutative 99.8%

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

   6. mul-1-neg 99.8%

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

   7. distribute-rgt-neg-in 99.8%

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

   8. sub-neg 99.8%

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

   9. metadata-eval 99.8%

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

   10. +-commutative 99.8%

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

   11. distribute-neg-in 99.8%

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

   12. metadata-eval 99.8%

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

   13. unsub-neg 99.8%

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

5. Simplified 99.8%

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

6. Taylor expanded in z around inf 48.3%

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

   1. associate-*r* 48.3%

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

   2. neg-mul-1 48.3%

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

8. Simplified 48.3%

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

9. Final simplification 48.3%

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

Alternative 17: 36.1% 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 89.3%

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

3. Taylor expanded in y around 0 99.8%

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

   1. +-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. metadata-eval 99.8%

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

   4. fma-define 99.8%

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

   5. +-commutative 99.8%

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

   6. mul-1-neg 99.8%

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

   7. distribute-rgt-neg-in 99.8%

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

   8. sub-neg 99.8%

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

   9. metadata-eval 99.8%

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

   10. +-commutative 99.8%

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

   11. distribute-neg-in 99.8%

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

   12. metadata-eval 99.8%

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

   13. unsub-neg 99.8%

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

5. Simplified 99.8%

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

6. Taylor expanded in z around 0 89.2%

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

   1. +-commutative 89.2%

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

   2. sub-neg 89.2%

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

   3. metadata-eval 89.2%

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

   4. fma-define 89.2%

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

   5. +-commutative 89.2%

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

8. Simplified 89.2%

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

9. Taylor expanded in y around inf 37.9%

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

10. Final simplification 37.9%

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

Alternative 18: 35.9% 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 89.3%

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

3. Taylor expanded in t around inf 37.8%

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

   1. neg-mul-1 37.8%

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

5. Simplified 37.8%

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

6. Final simplification 37.8%

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

Alternative 19: 2.9% accurate, 215.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in y around 0 99.8%

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

   1. +-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. metadata-eval 99.8%

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

   4. fma-define 99.8%

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

   5. +-commutative 99.8%

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

   6. mul-1-neg 99.8%

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

   7. distribute-rgt-neg-in 99.8%

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

   8. sub-neg 99.8%

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

   9. metadata-eval 99.8%

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

   10. +-commutative 99.8%

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

   11. distribute-neg-in 99.8%

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

   12. metadata-eval 99.8%

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

   13. unsub-neg 99.8%

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

5. Simplified 99.8%

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

6. Taylor expanded in z around 0 89.2%

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

   1. +-commutative 89.2%

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

   2. sub-neg 89.2%

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

   3. metadata-eval 89.2%

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

   4. fma-define 89.2%

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

   5. +-commutative 89.2%

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

8. Simplified 89.2%

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

   1. fma-undefine 89.2%

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

10. Applied egg-rr 89.2%

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

11. Taylor expanded in y around inf 2.7%

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

12. Final simplification 2.7%

    \[\leadsto y \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(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))