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

Percentage Accurate: 88.8% → 99.8%

Time: 19.8s

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: 88.8% 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, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. sub-neg 87.9%

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

   2. +-commutative 87.9%

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

   3. associate-+l+ 87.9%

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

   4. fma-define 87.9%

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

   5. sub-neg 87.9%

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

   6. metadata-eval 87.9%

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

   7. sub-neg 87.9%

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

   8. log1p-define 99.8%

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

   9. fma-define 99.8%

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

   10. sub-neg 99.8%

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

   11. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. +-commutative 87.9%

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

   2. fma-define 87.9%

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

   3. sub-neg 87.9%

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

   4. metadata-eval 87.9%

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

   5. sub-neg 87.9%

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

   6. log1p-define 99.8%

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

   7. sub-neg 99.8%

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

   8. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 3: 74.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(\frac{y}{z} - y\right) - t\\ t_2 := x \cdot \log y\\ t_3 := \left(-\log y\right) - t\\ \mathbf{if}\;x \leq -1950000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-297}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-32}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z (- (/ y z) y)) t))
        (t_2 (* x (log y)))
        (t_3 (- (- (log y)) t)))
   (if (<= x -1950000000.0)
     t_2
     (if (<= x 3.05e-297)
       t_3
       (if (<= x 1e-187)
         t_1
         (if (<= x 3.6e-32) t_3 (if (<= x 1.2e+20) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * ((y / z) - y)) - t;
	double t_2 = x * log(y);
	double t_3 = -log(y) - t;
	double tmp;
	if (x <= -1950000000.0) {
		tmp = t_2;
	} else if (x <= 3.05e-297) {
		tmp = t_3;
	} else if (x <= 1e-187) {
		tmp = t_1;
	} else if (x <= 3.6e-32) {
		tmp = t_3;
	} else if (x <= 1.2e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * ((y / z) - y)) - t
    t_2 = x * log(y)
    t_3 = -log(y) - t
    if (x <= (-1950000000.0d0)) then
        tmp = t_2
    else if (x <= 3.05d-297) then
        tmp = t_3
    else if (x <= 1d-187) then
        tmp = t_1
    else if (x <= 3.6d-32) then
        tmp = t_3
    else if (x <= 1.2d+20) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * ((y / z) - y)) - t;
	double t_2 = x * Math.log(y);
	double t_3 = -Math.log(y) - t;
	double tmp;
	if (x <= -1950000000.0) {
		tmp = t_2;
	} else if (x <= 3.05e-297) {
		tmp = t_3;
	} else if (x <= 1e-187) {
		tmp = t_1;
	} else if (x <= 3.6e-32) {
		tmp = t_3;
	} else if (x <= 1.2e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * ((y / z) - y)) - t
	t_2 = x * math.log(y)
	t_3 = -math.log(y) - t
	tmp = 0
	if x <= -1950000000.0:
		tmp = t_2
	elif x <= 3.05e-297:
		tmp = t_3
	elif x <= 1e-187:
		tmp = t_1
	elif x <= 3.6e-32:
		tmp = t_3
	elif x <= 1.2e+20:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * Float64(Float64(y / z) - y)) - t)
	t_2 = Float64(x * log(y))
	t_3 = Float64(Float64(-log(y)) - t)
	tmp = 0.0
	if (x <= -1950000000.0)
		tmp = t_2;
	elseif (x <= 3.05e-297)
		tmp = t_3;
	elseif (x <= 1e-187)
		tmp = t_1;
	elseif (x <= 3.6e-32)
		tmp = t_3;
	elseif (x <= 1.2e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * ((y / z) - y)) - t;
	t_2 = x * log(y);
	t_3 = -log(y) - t;
	tmp = 0.0;
	if (x <= -1950000000.0)
		tmp = t_2;
	elseif (x <= 3.05e-297)
		tmp = t_3;
	elseif (x <= 1e-187)
		tmp = t_1;
	elseif (x <= 3.6e-32)
		tmp = t_3;
	elseif (x <= 1.2e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]}, If[LessEqual[x, -1950000000.0], t$95$2, If[LessEqual[x, 3.05e-297], t$95$3, If[LessEqual[x, 1e-187], t$95$1, If[LessEqual[x, 3.6e-32], t$95$3, If[LessEqual[x, 1.2e+20], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.95e9 or 1.2e20 < x

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 99.4%

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

   4. Taylor expanded in x around inf 74.6%

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

      1. *-commutative 74.6%

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

   6. Simplified 74.6%

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

   if -1.95e9 < x < 3.05e-297 or 1e-187 < x < 3.59999999999999993e-32

   1. Initial program 91.2%

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

   3. Taylor expanded in x around inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. +-commutative 69.7%

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

      3. mul-1-neg 69.7%

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

      4. unsub-neg 69.7%

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

      5. div-sub 69.7%

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

      6. unsub-neg 69.7%

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

      7. mul-1-neg 69.7%

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

      8. +-commutative 69.7%

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

      9. div-sub 69.7%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in y around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. distribute-neg-frac2 68.7%

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

      3. +-commutative 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in x around 0 89.8%

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

       1. mul-1-neg 89.8%

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

       2. distribute-neg-in 89.8%

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

       3. unsub-neg 89.8%

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

   11. Simplified 89.8%

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

   if 3.05e-297 < x < 1e-187 or 3.59999999999999993e-32 < x < 1.2e20

   1. Initial program 63.7%

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

   3. Taylor expanded in y around 0 96.9%

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

      1. mul-1-neg 96.9%

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

      2. distribute-rgt-neg-in 96.9%

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

      3. sub-neg 96.9%

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

      4. metadata-eval 96.9%

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

      5. +-commutative 96.9%

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

      6. distribute-neg-in 96.9%

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

      7. metadata-eval 96.9%

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

      8. unsub-neg 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in z around inf 96.9%

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

      1. +-commutative 96.9%

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

      2. mul-1-neg 96.9%

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

      3. unsub-neg 96.9%

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

      4. +-commutative 96.9%

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

      5. sub-neg 96.9%

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

      6. metadata-eval 96.9%

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

      7. associate-/l* 96.9%

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

      8. fma-define 96.9%

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

      9. +-commutative 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in y around inf 80.2%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1950000000:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-297}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{elif}\;x \leq 10^{-187}:\\ \;\;\;\;z \cdot \left(\frac{y}{z} - y\right) - t\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-32}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(\frac{y}{z} - y\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.6% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Taylor expanded in y around 0 99.4%

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

4. Final simplification 99.4%

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

Alternative 5: 97.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;-1 + x \leq -2000000000 \lor \neg \left(-1 + x \leq -0.5\right):\\ \;\;\;\;\left(t\_1 + x \cdot \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 - \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 z))))
   (if (or (<= (+ -1.0 x) -2000000000.0) (not (<= (+ -1.0 x) -0.5)))
     (- (+ t_1 (* x (log y))) t)
     (- (- t_1 (log y)) t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (1.0 - z);
	double tmp;
	if (((-1.0 + x) <= -2000000000.0) || !((-1.0 + x) <= -0.5)) {
		tmp = (t_1 + (x * log(y))) - t;
	} else {
		tmp = (t_1 - 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) :: t_1
    real(8) :: tmp
    t_1 = y * (1.0d0 - z)
    if ((((-1.0d0) + x) <= (-2000000000.0d0)) .or. (.not. (((-1.0d0) + x) <= (-0.5d0)))) then
        tmp = (t_1 + (x * log(y))) - t
    else
        tmp = (t_1 - log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (1.0 - z);
	double tmp;
	if (((-1.0 + x) <= -2000000000.0) || !((-1.0 + x) <= -0.5)) {
		tmp = (t_1 + (x * Math.log(y))) - t;
	} else {
		tmp = (t_1 - Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (1.0 - z)
	tmp = 0
	if ((-1.0 + x) <= -2000000000.0) or not ((-1.0 + x) <= -0.5):
		tmp = (t_1 + (x * math.log(y))) - t
	else:
		tmp = (t_1 - math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(1.0 - z))
	tmp = 0.0
	if ((Float64(-1.0 + x) <= -2000000000.0) || !(Float64(-1.0 + x) <= -0.5))
		tmp = Float64(Float64(t_1 + Float64(x * log(y))) - t);
	else
		tmp = Float64(Float64(t_1 - log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (1.0 - z);
	tmp = 0.0;
	if (((-1.0 + x) <= -2000000000.0) || ~(((-1.0 + x) <= -0.5)))
		tmp = (t_1 + (x * log(y))) - t;
	else
		tmp = (t_1 - log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(-1.0 + x), $MachinePrecision], -2000000000.0], N[Not[LessEqual[N[(-1.0 + x), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(t$95$1 + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(t$95$1 - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -2e9 or -0.5 < (-.f64 x #s(literal 1 binary64))

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. distribute-rgt-neg-in 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

      5. +-commutative 99.3%

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

      6. distribute-neg-in 99.3%

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

      7. metadata-eval 99.3%

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

      8. unsub-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around inf 98.1%

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

      1. *-commutative 98.1%

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

   8. Simplified 98.1%

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

   if -2e9 < (-.f64 x #s(literal 1 binary64)) < -0.5

   1. Initial program 83.1%

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

   3. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. distribute-rgt-neg-in 98.5%

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

      3. sub-neg 98.5%

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

      4. metadata-eval 98.5%

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

      5. +-commutative 98.5%

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

      6. distribute-neg-in 98.5%

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

      7. metadata-eval 98.5%

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

      8. unsub-neg 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. mul-1-neg 97.9%

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

      3. unsub-neg 97.9%

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

   8. Simplified 97.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -2000000000 \lor \neg \left(-1 + x \leq -0.5\right):\\ \;\;\;\;\left(y \cdot \left(1 - z\right) + x \cdot \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-1 + x \leq -1 \lor \neg \left(-1 + x \leq -0.1\right):\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ -1.0 x) -1.0) (not (<= (+ -1.0 x) -0.1)))
   (- (* (log y) (+ -1.0 x)) t)
   (- (- (* y (- 1.0 z)) (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((-1.0 + x) <= -1.0) || !((-1.0 + x) <= -0.1)) {
		tmp = (log(y) * (-1.0 + x)) - 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 ((((-1.0d0) + x) <= (-1.0d0)) .or. (.not. (((-1.0d0) + x) <= (-0.1d0)))) then
        tmp = (log(y) * ((-1.0d0) + x)) - 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 (((-1.0 + x) <= -1.0) || !((-1.0 + x) <= -0.1)) {
		tmp = (Math.log(y) * (-1.0 + x)) - t;
	} else {
		tmp = ((y * (1.0 - z)) - Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((-1.0 + x) <= -1.0) or not ((-1.0 + x) <= -0.1):
		tmp = (math.log(y) * (-1.0 + x)) - 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(-1.0 + x) <= -1.0) || !(Float64(-1.0 + x) <= -0.1))
		tmp = Float64(Float64(log(y) * Float64(-1.0 + x)) - 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 (((-1.0 + x) <= -1.0) || ~(((-1.0 + x) <= -0.1)))
		tmp = (log(y) * (-1.0 + x)) - 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[(-1.0 + x), $MachinePrecision], -1.0], N[Not[LessEqual[N[(-1.0 + x), $MachinePrecision], -0.1]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -1 or -0.10000000000000001 < (-.f64 x #s(literal 1 binary64))

   1. Initial program 88.1%

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

   3. Taylor expanded in y around 0 86.8%

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

   if -1 < (-.f64 x #s(literal 1 binary64)) < -0.10000000000000001

   1. Initial program 75.3%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 91.6%

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

      1. +-commutative 91.6%

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

      2. mul-1-neg 91.6%

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

      3. unsub-neg 91.6%

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

   8. Simplified 91.6%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -1 \lor \neg \left(-1 + x \leq -0.1\right):\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+14} \lor \neg \left(z \leq 4.2 \cdot 10^{+128}\right):\\ \;\;\;\;z \cdot \left(\log y \cdot \frac{-1 + x}{z} - y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e+14) (not (<= z 4.2e+128)))
   (- (* z (- (* (log y) (/ (+ -1.0 x) z)) y)) t)
   (- (* (log y) (+ -1.0 x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e+14) || !(z <= 4.2e+128)) {
		tmp = (z * ((log(y) * ((-1.0 + x) / z)) - y)) - t;
	} else {
		tmp = (log(y) * (-1.0 + x)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2d+14)) .or. (.not. (z <= 4.2d+128))) then
        tmp = (z * ((log(y) * (((-1.0d0) + x) / z)) - y)) - t
    else
        tmp = (log(y) * ((-1.0d0) + x)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e+14) || !(z <= 4.2e+128)) {
		tmp = (z * ((Math.log(y) * ((-1.0 + x) / z)) - y)) - t;
	} else {
		tmp = (Math.log(y) * (-1.0 + x)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e+14) or not (z <= 4.2e+128):
		tmp = (z * ((math.log(y) * ((-1.0 + x) / z)) - y)) - t
	else:
		tmp = (math.log(y) * (-1.0 + x)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e+14) || !(z <= 4.2e+128))
		tmp = Float64(Float64(z * Float64(Float64(log(y) * Float64(Float64(-1.0 + x) / z)) - y)) - t);
	else
		tmp = Float64(Float64(log(y) * Float64(-1.0 + x)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e+14) || ~((z <= 4.2e+128)))
		tmp = (z * ((log(y) * ((-1.0 + x) / z)) - y)) - t;
	else
		tmp = (log(y) * (-1.0 + x)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e+14], N[Not[LessEqual[z, 4.2e+128]], $MachinePrecision]], N[(N[(z * N[(N[(N[Log[y], $MachinePrecision] * N[(N[(-1.0 + x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e14 or 4.1999999999999999e128 < z

   1. Initial program 69.9%

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

   3. Taylor expanded in y around 0 98.2%

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

      1. mul-1-neg 98.2%

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

      2. distribute-rgt-neg-in 98.2%

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

      3. sub-neg 98.2%

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

      4. metadata-eval 98.2%

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

      5. +-commutative 98.2%

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

      6. distribute-neg-in 98.2%

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

      7. metadata-eval 98.2%

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

      8. unsub-neg 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in z around inf 98.2%

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

      1. +-commutative 98.2%

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

      2. mul-1-neg 98.2%

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

      3. unsub-neg 98.2%

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

      4. +-commutative 98.2%

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

      5. sub-neg 98.2%

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

      6. metadata-eval 98.2%

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

      7. associate-/l* 98.1%

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

      8. fma-define 98.1%

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

      9. +-commutative 98.1%

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

   8. Simplified 98.1%

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

   9. Taylor expanded in y around 0 98.2%

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

       1. sub-neg 98.2%

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

       2. metadata-eval 98.2%

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

       3. associate-*r/ 98.1%

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

       4. +-commutative 98.1%

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

   11. Simplified 98.1%

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

   if -2e14 < z < 4.1999999999999999e128

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.2%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+14} \lor \neg \left(z \leq 4.2 \cdot 10^{+128}\right):\\ \;\;\;\;z \cdot \left(\log y \cdot \frac{-1 + x}{z} - y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.5% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Taylor expanded in y around 0 99.4%

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

4. Final simplification 99.4%

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

Alternative 9: 95.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+112} \lor \neg \left(z \leq 1.55 \cdot 10^{+133}\right):\\ \;\;\;\;z \cdot \left(x \cdot \frac{\log y}{z} - y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+112) (not (<= z 1.55e+133)))
   (- (* z (- (* x (/ (log y) z)) y)) t)
   (- (* (log y) (+ -1.0 x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+112) || !(z <= 1.55e+133)) {
		tmp = (z * ((x * (log(y) / z)) - y)) - t;
	} else {
		tmp = (log(y) * (-1.0 + x)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8d+112)) .or. (.not. (z <= 1.55d+133))) then
        tmp = (z * ((x * (log(y) / z)) - y)) - t
    else
        tmp = (log(y) * ((-1.0d0) + x)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+112) || !(z <= 1.55e+133)) {
		tmp = (z * ((x * (Math.log(y) / z)) - y)) - t;
	} else {
		tmp = (Math.log(y) * (-1.0 + x)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+112) or not (z <= 1.55e+133):
		tmp = (z * ((x * (math.log(y) / z)) - y)) - t
	else:
		tmp = (math.log(y) * (-1.0 + x)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+112) || !(z <= 1.55e+133))
		tmp = Float64(Float64(z * Float64(Float64(x * Float64(log(y) / z)) - y)) - t);
	else
		tmp = Float64(Float64(log(y) * Float64(-1.0 + x)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8e+112) || ~((z <= 1.55e+133)))
		tmp = (z * ((x * (log(y) / z)) - y)) - t;
	else
		tmp = (log(y) * (-1.0 + x)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e+112], N[Not[LessEqual[z, 1.55e+133]], $MachinePrecision]], N[(N[(z * N[(N[(x * N[(N[Log[y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999994e112 or 1.55e133 < z

   1. Initial program 60.4%

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

   3. Taylor expanded in y around 0 97.6%

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

      1. mul-1-neg 97.6%

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

      2. distribute-rgt-neg-in 97.6%

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

      3. sub-neg 97.6%

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

      4. metadata-eval 97.6%

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

      5. +-commutative 97.6%

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

      6. distribute-neg-in 97.6%

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

      7. metadata-eval 97.6%

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

      8. unsub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in z around inf 97.6%

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

      1. +-commutative 97.6%

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

      2. mul-1-neg 97.6%

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

      3. unsub-neg 97.6%

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

      4. +-commutative 97.6%

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

      5. sub-neg 97.6%

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

      6. metadata-eval 97.6%

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

      7. associate-/l* 97.5%

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

      8. fma-define 97.5%

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

      9. +-commutative 97.5%

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

   8. Simplified 97.5%

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

   9. Taylor expanded in x around inf 93.7%

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

       1. associate-/l* 93.6%

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

   11. Simplified 93.6%

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

   if -7.9999999999999994e112 < z < 1.55e133

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 98.3%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+112} \lor \neg \left(z \leq 1.55 \cdot 10^{+133}\right):\\ \;\;\;\;z \cdot \left(x \cdot \frac{\log y}{z} - y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Taylor expanded in y around 0 99.1%

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

4. Final simplification 99.1%

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

Alternative 11: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+242} \lor \neg \left(z \leq 1.65 \cdot 10^{+265}\right):\\ \;\;\;\;y \cdot \left(-z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e+242) (not (<= z 1.65e+265)))
   (- (* y (- z)) t)
   (- (* (log y) (+ -1.0 x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+242) || !(z <= 1.65e+265)) {
		tmp = (y * -z) - t;
	} else {
		tmp = (log(y) * (-1.0 + x)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.5d+242)) .or. (.not. (z <= 1.65d+265))) then
        tmp = (y * -z) - t
    else
        tmp = (log(y) * ((-1.0d0) + x)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+242) || !(z <= 1.65e+265)) {
		tmp = (y * -z) - t;
	} else {
		tmp = (Math.log(y) * (-1.0 + x)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e+242) or not (z <= 1.65e+265):
		tmp = (y * -z) - t
	else:
		tmp = (math.log(y) * (-1.0 + x)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e+242) || !(z <= 1.65e+265))
		tmp = Float64(Float64(y * Float64(-z)) - t);
	else
		tmp = Float64(Float64(log(y) * Float64(-1.0 + x)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e+242) || ~((z <= 1.65e+265)))
		tmp = (y * -z) - t;
	else
		tmp = (log(y) * (-1.0 + x)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e+242], N[Not[LessEqual[z, 1.65e+265]], $MachinePrecision]], N[(N[(y * (-z)), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000022e242 or 1.6499999999999999e265 < z

   1. Initial program 33.9%

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

   3. Taylor expanded in y around 0 95.7%

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

      1. mul-1-neg 95.7%

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

      2. distribute-rgt-neg-in 95.7%

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

      3. sub-neg 95.7%

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

      4. metadata-eval 95.7%

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

      5. +-commutative 95.7%

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

      6. distribute-neg-in 95.7%

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

      7. metadata-eval 95.7%

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

      8. unsub-neg 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in z around inf 95.7%

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

      1. +-commutative 95.7%

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

      2. mul-1-neg 95.7%

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

      3. unsub-neg 95.7%

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

      4. +-commutative 95.7%

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

      5. sub-neg 95.7%

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

      6. metadata-eval 95.7%

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

      7. associate-/l* 95.7%

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

      8. fma-define 95.7%

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

      9. +-commutative 95.7%

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

   8. Simplified 95.7%

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

   9. Taylor expanded in z around inf 84.2%

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

       1. neg-mul-1 84.2%

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

   11. Simplified 84.2%

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

   if -5.50000000000000022e242 < z < 1.6499999999999999e265

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 93.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+242} \lor \neg \left(z \leq 1.65 \cdot 10^{+265}\right):\\ \;\;\;\;y \cdot \left(-z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+27} \lor \neg \left(t \leq 8 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(-z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.4e+27) (not (<= t 8e+46)))
   (- (* y (- z)) t)
   (* (log y) (+ -1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.4e+27) || !(t <= 8e+46)) {
		tmp = (y * -z) - t;
	} else {
		tmp = log(y) * (-1.0 + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.4d+27)) .or. (.not. (t <= 8d+46))) then
        tmp = (y * -z) - t
    else
        tmp = log(y) * ((-1.0d0) + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.4e+27) || !(t <= 8e+46)) {
		tmp = (y * -z) - t;
	} else {
		tmp = Math.log(y) * (-1.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.4e+27) or not (t <= 8e+46):
		tmp = (y * -z) - t
	else:
		tmp = math.log(y) * (-1.0 + x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.4e+27) || !(t <= 8e+46))
		tmp = Float64(Float64(y * Float64(-z)) - t);
	else
		tmp = Float64(log(y) * Float64(-1.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.4e+27) || ~((t <= 8e+46)))
		tmp = (y * -z) - t;
	else
		tmp = log(y) * (-1.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.4e+27], N[Not[LessEqual[t, 8e+46]], $MachinePrecision]], N[(N[(y * (-z)), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3999999999999997e27 or 7.9999999999999999e46 < t

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-rgt-neg-in 98.8%

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

      3. sub-neg 98.8%

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

      4. metadata-eval 98.8%

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

      5. +-commutative 98.8%

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

      6. distribute-neg-in 98.8%

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

      7. metadata-eval 98.8%

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

      8. unsub-neg 98.8%

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

   5. Simplified 98.8%

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

   6. Taylor expanded in z around inf 90.9%

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

      1. +-commutative 90.9%

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

      2. mul-1-neg 90.9%

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

      3. unsub-neg 90.9%

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

      4. +-commutative 90.9%

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

      5. sub-neg 90.9%

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

      6. metadata-eval 90.9%

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

      7. associate-/l* 90.8%

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

      8. fma-define 90.8%

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

      9. +-commutative 90.8%

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

   8. Simplified 90.8%

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

   9. Taylor expanded in z around inf 81.4%

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

       1. neg-mul-1 81.4%

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

   11. Simplified 81.4%

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

   if -4.3999999999999997e27 < t < 7.9999999999999999e46

   1. Initial program 84.5%

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

   3. Taylor expanded in y around 0 83.3%

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

   4. Taylor expanded in t around 0 82.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+27} \lor \neg \left(t \leq 8 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(-z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3300000000 \lor \neg \left(x \leq 5.7 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{z} - y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3300000000.0) (not (<= x 5.7e+16)))
   (* x (log y))
   (- (* z (- (/ y z) y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3300000000.0) || !(x <= 5.7e+16)) {
		tmp = x * log(y);
	} else {
		tmp = (z * ((y / z) - y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3300000000.0d0)) .or. (.not. (x <= 5.7d+16))) then
        tmp = x * log(y)
    else
        tmp = (z * ((y / z) - y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3300000000.0) || !(x <= 5.7e+16)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (z * ((y / z) - y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3300000000.0) or not (x <= 5.7e+16):
		tmp = x * math.log(y)
	else:
		tmp = (z * ((y / z) - y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3300000000.0) || !(x <= 5.7e+16))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(z * Float64(Float64(y / z) - y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3300000000.0) || ~((x <= 5.7e+16)))
		tmp = x * log(y);
	else
		tmp = (z * ((y / z) - y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3300000000.0], N[Not[LessEqual[x, 5.7e+16]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3e9 or 5.7e16 < x

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 99.4%

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

   4. Taylor expanded in x around inf 74.6%

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

      1. *-commutative 74.6%

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

   6. Simplified 74.6%

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

   if -3.3e9 < x < 5.7e16

   1. Initial program 83.3%

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

   3. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. distribute-rgt-neg-in 98.5%

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

      3. sub-neg 98.5%

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

      4. metadata-eval 98.5%

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

      5. +-commutative 98.5%

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

      6. distribute-neg-in 98.5%

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

      7. metadata-eval 98.5%

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

      8. unsub-neg 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

      4. +-commutative 97.8%

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

      5. sub-neg 97.8%

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

      6. metadata-eval 97.8%

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

      7. associate-/l* 97.7%

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

      8. fma-define 97.6%

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

      9. +-commutative 97.6%

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

   8. Simplified 97.6%

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

   9. Taylor expanded in y around inf 59.0%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3300000000 \lor \neg \left(x \leq 5.7 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{z} - y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.0% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Taylor expanded in y around 0 98.9%

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

   1. mul-1-neg 98.9%

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

   2. distribute-rgt-neg-in 98.9%

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

   3. sub-neg 98.9%

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

   4. metadata-eval 98.9%

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

   5. +-commutative 98.9%

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

   6. distribute-neg-in 98.9%

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

   7. metadata-eval 98.9%

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

   8. unsub-neg 98.9%

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

5. Simplified 98.9%

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

6. Final simplification 98.9%

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

Alternative 15: 42.7% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -10500 \lor \neg \left(t \leq 3.5 \cdot 10^{+34}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -10500.0) (not (<= t 3.5e+34))) (- t) (* y (- 1.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -10500.0) || !(t <= 3.5e+34)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-10500.0d0)) .or. (.not. (t <= 3.5d+34))) then
        tmp = -t
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -10500.0) || !(t <= 3.5e+34)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -10500.0) or not (t <= 3.5e+34):
		tmp = -t
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -10500.0) || !(t <= 3.5e+34))
		tmp = Float64(-t);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -10500.0) || ~((t <= 3.5e+34)))
		tmp = -t;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -10500.0], N[Not[LessEqual[t, 3.5e+34]], $MachinePrecision]], (-t), N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -10500 or 3.49999999999999998e34 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 70.5%

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

      1. mul-1-neg 70.5%

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

   5. Simplified 70.5%

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

   if -10500 < t < 3.49999999999999998e34

   1. Initial program 83.8%

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

   3. Taylor expanded in y around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-in 98.9%

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

      3. sub-neg 98.9%

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

      4. metadata-eval 98.9%

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

      5. +-commutative 98.9%

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

      6. distribute-neg-in 98.9%

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

      7. metadata-eval 98.9%

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

      8. unsub-neg 98.9%

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

   5. Simplified 98.9%

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

      1. add-cube-cbrt 97.4%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(x - 1\right) \cdot \log y} \cdot \sqrt[3]{\left(x - 1\right) \cdot \log y}\right) \cdot \sqrt[3]{\left(x - 1\right) \cdot \log y}} + y \cdot \left(1 - z\right)\right) - t \]

      2. pow3 97.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\left(x - 1\right) \cdot \log y}\right)}^{3}} + y \cdot \left(1 - z\right)\right) - t \]

      3. sub-neg 97.4%

         \[\leadsto \left({\left(\sqrt[3]{\color{blue}{\left(x + \left(-1\right)\right)} \cdot \log y}\right)}^{3} + y \cdot \left(1 - z\right)\right) - t \]

      4. metadata-eval 97.4%

         \[\leadsto \left({\left(\sqrt[3]{\left(x + \color{blue}{-1}\right) \cdot \log y}\right)}^{3} + y \cdot \left(1 - z\right)\right) - t \]

   7. Applied egg-rr 97.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\left(x + -1\right) \cdot \log y}\right)}^{3}} + y \cdot \left(1 - z\right)\right) - t \]

   8. Taylor expanded in y around inf 18.3%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -10500 \lor \neg \left(t \leq 3.5 \cdot 10^{+34}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.9% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+18} \lor \neg \left(t \leq 34000000000000\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e+18) (not (<= t 34000000000000.0))) (- t) (* y (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e+18) || !(t <= 34000000000000.0)) {
		tmp = -t;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.2d+18)) .or. (.not. (t <= 34000000000000.0d0))) then
        tmp = -t
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e+18) || !(t <= 34000000000000.0)) {
		tmp = -t;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.2e+18) or not (t <= 34000000000000.0):
		tmp = -t
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e+18) || !(t <= 34000000000000.0))
		tmp = Float64(-t);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.2e+18) || ~((t <= 34000000000000.0)))
		tmp = -t;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e+18], N[Not[LessEqual[t, 34000000000000.0]], $MachinePrecision]], (-t), N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2e18 or 3.4e13 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf 69.8%

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

      1. mul-1-neg 69.8%

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

   5. Simplified 69.8%

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

   if -3.2e18 < t < 3.4e13

   1. Initial program 83.6%

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

   3. Taylor expanded in y around 0 99.1%

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

   4. Taylor expanded in z around inf 18.0%

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

   5. Taylor expanded in y around 0 17.8%

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

      1. associate-*r* 17.8%

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

      2. mul-1-neg 17.8%

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

   7. Simplified 17.8%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+18} \lor \neg \left(t \leq 34000000000000\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.9% accurate, 23.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Taylor expanded in y around 0 98.9%

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

   1. mul-1-neg 98.9%

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

   2. distribute-rgt-neg-in 98.9%

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

   3. sub-neg 98.9%

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

   4. metadata-eval 98.9%

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

   5. +-commutative 98.9%

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

   6. distribute-neg-in 98.9%

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

   7. metadata-eval 98.9%

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

   8. unsub-neg 98.9%

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

5. Simplified 98.9%

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

6. Taylor expanded in z around inf 86.1%

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

   1. +-commutative 86.1%

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

   2. mul-1-neg 86.1%

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

   3. unsub-neg 86.1%

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

   4. +-commutative 86.1%

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

   5. sub-neg 86.1%

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

   6. metadata-eval 86.1%

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

   7. associate-/l* 86.0%

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

   8. fma-define 86.0%

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

   9. +-commutative 86.0%

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

8. Simplified 86.0%

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

9. Taylor expanded in y around inf 41.4%

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

10. Final simplification 41.4%

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

Alternative 18: 45.7% accurate, 35.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Taylor expanded in y around 0 98.9%

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

   1. mul-1-neg 98.9%

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

   2. distribute-rgt-neg-in 98.9%

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

   3. sub-neg 98.9%

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

   4. metadata-eval 98.9%

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

   5. +-commutative 98.9%

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

   6. distribute-neg-in 98.9%

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

   7. metadata-eval 98.9%

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

   8. unsub-neg 98.9%

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

5. Simplified 98.9%

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

6. Taylor expanded in z around inf 86.1%

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

   1. +-commutative 86.1%

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

   2. mul-1-neg 86.1%

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

   3. unsub-neg 86.1%

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

   4. +-commutative 86.1%

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

   5. sub-neg 86.1%

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

   6. metadata-eval 86.1%

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

   7. associate-/l* 86.0%

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

   8. fma-define 86.0%

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

   9. +-commutative 86.0%

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

8. Simplified 86.0%

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

9. Taylor expanded in z around inf 41.1%

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

    1. neg-mul-1 41.1%

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

11. Simplified 41.1%

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

12. Final simplification 41.1%

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

Alternative 19: 34.9% 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 87.9%

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

3. Taylor expanded in t around inf 29.8%

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

   1. mul-1-neg 29.8%

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

5. Simplified 29.8%

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

6. Final simplification 29.8%

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

Reproduce

herbie shell --seed 2024078 
(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))