Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B

Percentage Accurate: 85.1% → 99.4%

Time: 17.5s

Alternatives: 10

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x \cdot {\log y}^{2}, \frac{1}{\log y}, z \cdot \mathsf{log1p}\left(-y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (fma (* x (pow (log y) 2.0)) (/ 1.0 (log y)) (* z (log1p (- y)))) t))

C

double code(double x, double y, double z, double t) {
	return fma((x * pow(log(y), 2.0)), (1.0 / log(y)), (z * log1p(-y))) - t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(Float64(x * (log(y) ^ 2.0)), Float64(1.0 / log(y)), Float64(z * log1p(Float64(-y)))) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * N[Power[N[Log[y], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Log[1 + (-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 86.2%

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

   1. lift-log.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-log.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. flip-+ N/A

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

   7. div-sub N/A

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

   8. sub-neg N/A

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

4. Applied egg-rr 95.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot {\log y}^{2}, \frac{x}{x \cdot \log y - z \cdot \mathsf{log1p}\left(-y\right)}, -\frac{{\left(z \cdot \mathsf{log1p}\left(-y\right)\right)}^{2}}{x \cdot \log y - z \cdot \mathsf{log1p}\left(-y\right)}\right)} - t \]

5. Taylor expanded in z around inf

   \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \frac{x}{x \cdot \log y - z \cdot \mathsf{log1p}\left(\mathsf{neg}\left(y\right)\right)}, \color{blue}{z \cdot \log \left(1 - y\right)}\right) - t \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \frac{x}{x \cdot \log y - z \cdot \mathsf{log1p}\left(\mathsf{neg}\left(y\right)\right)}, \color{blue}{z \cdot \log \left(1 - y\right)}\right) - t \]

   2. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \frac{x}{x \cdot \log y - z \cdot \mathsf{log1p}\left(\mathsf{neg}\left(y\right)\right)}, z \cdot \log \color{blue}{\left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)}\right) - t \]

   3. lower-log1p.f64 N/A

      \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \frac{x}{x \cdot \log y - z \cdot \mathsf{log1p}\left(\mathsf{neg}\left(y\right)\right)}, z \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{neg}\left(y\right)\right)}\right) - t \]

   4. lower-neg.f64 99.2

      \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \frac{x}{x \cdot \log y - z \cdot \mathsf{log1p}\left(-y\right)}, z \cdot \mathsf{log1p}\left(\color{blue}{-y}\right)\right) - t \]

7. Simplified 99.2%

   \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \frac{x}{x \cdot \log y - z \cdot \mathsf{log1p}\left(-y\right)}, \color{blue}{z \cdot \mathsf{log1p}\left(-y\right)}\right) - t \]

8. Taylor expanded in x around inf

   \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \color{blue}{\frac{1}{\log y}}, z \cdot \mathsf{log1p}\left(\mathsf{neg}\left(y\right)\right)\right) - t \]
9. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \color{blue}{\frac{1}{\log y}}, z \cdot \mathsf{log1p}\left(\mathsf{neg}\left(y\right)\right)\right) - t \]

   2. lower-log.f64 99.7

      \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \frac{1}{\color{blue}{\log y}}, z \cdot \mathsf{log1p}\left(-y\right)\right) - t \]

10. Simplified 99.7%

    \[\leadsto \mathsf{fma}\left(x \cdot {\log y}^{2}, \color{blue}{\frac{1}{\log y}}, z \cdot \mathsf{log1p}\left(-y\right)\right) - t \]
11. Add Preprocessing

Alternative 2: 89.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \log y, -t\right)\\ t_2 := x \cdot \log y + z \cdot \log \left(1 - y\right)\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-102}:\\ \;\;\;\;\mathsf{fma}\left(z, \mathsf{log1p}\left(-y\right), -t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (log y) (- t)))
        (t_2 (+ (* x (log y)) (* z (log (- 1.0 y))))))
   (if (<= t_2 -4e-73)
     t_1
     (if (<= t_2 1e-102) (fma z (log1p (- y)) (- t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, log(y), -t);
	double t_2 = (x * log(y)) + (z * log((1.0 - y)));
	double tmp;
	if (t_2 <= -4e-73) {
		tmp = t_1;
	} else if (t_2 <= 1e-102) {
		tmp = fma(z, log1p(-y), -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, log(y), Float64(-t))
	t_2 = Float64(Float64(x * log(y)) + Float64(z * log(Float64(1.0 - y))))
	tmp = 0.0
	if (t_2 <= -4e-73)
		tmp = t_1;
	elseif (t_2 <= 1e-102)
		tmp = fma(z, log1p(Float64(-y)), Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision] + (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-73], t$95$1, If[LessEqual[t$95$2, 1e-102], N[(z * N[Log[1 + (-y)], $MachinePrecision] + (-t)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x (log.f64 y)) (*.f64 z (log.f64 (-.f64 #s(literal 1 binary64) y)))) < -3.99999999999999999e-73 or 9.99999999999999933e-103 < (+.f64 (*.f64 x (log.f64 y)) (*.f64 z (log.f64 (-.f64 #s(literal 1 binary64) y))))

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. lower-fma.f64 N/A

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

      8. log-rec N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. mul-1-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower-log.f64 N/A

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

      14. lower-neg.f64 94.4

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

   5. Simplified 94.4%

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

   if -3.99999999999999999e-73 < (+.f64 (*.f64 x (log.f64 y)) (*.f64 z (log.f64 (-.f64 #s(literal 1 binary64) y)))) < 9.99999999999999933e-103

   1. Initial program 70.8%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. lower-log1p.f64 N/A

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{log1p}\left(\mathsf{neg}\left(y\right)\right)}, \mathsf{neg}\left(t\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(z, \mathsf{log1p}\left(\color{blue}{\mathsf{neg}\left(y\right)}\right), \mathsf{neg}\left(t\right)\right) \]

      6. lower-neg.f64 94.3

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

   5. Simplified 94.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{log1p}\left(-y\right), -t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \log y, -t\right)\\ t_2 := x \cdot \log y + z \cdot \log \left(1 - y\right)\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-102}:\\ \;\;\;\;-\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (log y) (- t)))
        (t_2 (+ (* x (log y)) (* z (log (- 1.0 y))))))
   (if (<= t_2 -4e-73) t_1 (if (<= t_2 1e-102) (- (fma z y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, log(y), -t);
	double t_2 = (x * log(y)) + (z * log((1.0 - y)));
	double tmp;
	if (t_2 <= -4e-73) {
		tmp = t_1;
	} else if (t_2 <= 1e-102) {
		tmp = -fma(z, y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, log(y), Float64(-t))
	t_2 = Float64(Float64(x * log(y)) + Float64(z * log(Float64(1.0 - y))))
	tmp = 0.0
	if (t_2 <= -4e-73)
		tmp = t_1;
	elseif (t_2 <= 1e-102)
		tmp = Float64(-fma(z, y, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision] + (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-73], t$95$1, If[LessEqual[t$95$2, 1e-102], (-N[(z * y + t), $MachinePrecision]), t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x (log.f64 y)) (*.f64 z (log.f64 (-.f64 #s(literal 1 binary64) y)))) < -3.99999999999999999e-73 or 9.99999999999999933e-103 < (+.f64 (*.f64 x (log.f64 y)) (*.f64 z (log.f64 (-.f64 #s(literal 1 binary64) y))))

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. lower-fma.f64 N/A

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

      8. log-rec N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. mul-1-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower-log.f64 N/A

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

      14. lower-neg.f64 94.4

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

   5. Simplified 94.4%

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

   if -3.99999999999999999e-73 < (+.f64 (*.f64 x (log.f64 y)) (*.f64 z (log.f64 (-.f64 #s(literal 1 binary64) y)))) < 9.99999999999999933e-103

   1. Initial program 70.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. lower-fma.f64 N/A

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

      8. log-rec N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. mul-1-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower-log.f64 N/A

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

      14. mul-1-neg N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-*.f64 N/A

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

      18. mul-1-neg N/A

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

      19. lower-neg.f64 99.1

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

   5. Simplified 99.1%

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

   6. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. distribute-neg-out N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 93.4

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

   8. Simplified 93.4%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(z, y, t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.6% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

   1. lift-log.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-log.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. flip-- N/A

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

   8. clear-num N/A

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

   9. lower-/.f64 N/A

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

   10. clear-num N/A

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

4. Applied egg-rr 99.6%

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

Alternative 5: 77.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 13600000:\\ \;\;\;\;-\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -3.6e-32) t_1 (if (<= x 13600000.0) (- (fma z y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -3.6e-32) {
		tmp = t_1;
	} else if (x <= 13600000.0) {
		tmp = -fma(z, y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -3.6e-32)
		tmp = t_1;
	elseif (x <= 13600000.0)
		tmp = Float64(-fma(z, y, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e-32], t$95$1, If[LessEqual[x, 13600000.0], (-N[(z * y + t), $MachinePrecision]), t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.59999999999999993e-32 or 1.36e7 < x

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

      1. remove-double-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right)} \]

      2. mul-1-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. log-rec N/A

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

      6. lower-*.f64 N/A

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

      7. log-rec N/A

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

      8. mul-1-neg N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\log y\right)\right)}\right)\right) \]

      11. remove-double-neg N/A

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

      12. lower-log.f64 78.1

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

   5. Simplified 78.1%

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

   if -3.59999999999999993e-32 < x < 1.36e7

   1. Initial program 75.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. lower-fma.f64 N/A

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

      8. log-rec N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. mul-1-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower-log.f64 N/A

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

      14. mul-1-neg N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-*.f64 N/A

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

      18. mul-1-neg N/A

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

      19. lower-neg.f64 99.4

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

   5. Simplified 99.4%

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

   6. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. distribute-neg-out N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 84.5

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

   8. Simplified 84.5%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(z, y, t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. unsub-neg N/A

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

   4. remove-double-neg N/A

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

   5. mul-1-neg N/A

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

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

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

   7. neg-mul-1 N/A

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

   8. mul-1-neg N/A

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

   9. log-rec N/A

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

   10. associate--l- N/A

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

   11. lower--.f64 N/A

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

5. Simplified 99.4%

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

Alternative 7: 48.8% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-98}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4e-98) (- t) (if (<= t 1.95e-76) (* y (- z)) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-98) {
		tmp = -t;
	} else if (t <= 1.95e-76) {
		tmp = y * -z;
	} else {
		tmp = -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4d-98)) then
        tmp = -t
    else if (t <= 1.95d-76) then
        tmp = y * -z
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-98) {
		tmp = -t;
	} else if (t <= 1.95e-76) {
		tmp = y * -z;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4e-98:
		tmp = -t
	elif t <= 1.95e-76:
		tmp = y * -z
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4e-98)
		tmp = Float64(-t);
	elseif (t <= 1.95e-76)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4e-98)
		tmp = -t;
	elseif (t <= 1.95e-76)
		tmp = y * -z;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4e-98], (-t), If[LessEqual[t, 1.95e-76], N[(y * (-z)), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -3.99999999999999976e-98 or 1.95000000000000013e-76 < t

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 61.9

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

   5. Simplified 61.9%

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

   if -3.99999999999999976e-98 < t < 1.95000000000000013e-76

   1. Initial program 78.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. lower-fma.f64 N/A

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

      8. log-rec N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. mul-1-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower-log.f64 N/A

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

      14. mul-1-neg N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-*.f64 N/A

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

      18. mul-1-neg N/A

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

      19. lower-neg.f64 99.0

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

   5. Simplified 99.0%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 24.5

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

   8. Simplified 24.5%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-98}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.3% accurate, 24.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. remove-double-neg N/A

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

   3. mul-1-neg N/A

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

   4. mul-1-neg N/A

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

   5. mul-1-neg N/A

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

   6. log-rec N/A

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

   7. lower-fma.f64 N/A

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

   8. log-rec N/A

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

   9. mul-1-neg N/A

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

   10. mul-1-neg N/A

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

   11. mul-1-neg N/A

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

   12. remove-double-neg N/A

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

   13. lower-log.f64 N/A

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

   14. mul-1-neg N/A

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

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

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

   16. mul-1-neg N/A

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

   17. lower-*.f64 N/A

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

   18. mul-1-neg N/A

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

   19. lower-neg.f64 99.4

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

5. Simplified 99.4%

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

6. Taylor expanded in x around 0

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

   1. sub-neg N/A

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

   2. mul-1-neg N/A

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

   3. distribute-neg-out N/A

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

   4. lower-neg.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 54.2

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

8. Simplified 54.2%

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

Alternative 9: 42.6% accurate, 73.3× 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 86.2%

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

3. Taylor expanded in t around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 40.3

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

5. Simplified 40.3%

   \[\leadsto \color{blue}{-t} \]
6. Add Preprocessing

Alternative 10: 2.3% accurate, 220.0× 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 t
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

3. Taylor expanded in t around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 40.3

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

5. Simplified 40.3%

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

   1. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - t} \]

   2. sub-neg N/A

      \[\leadsto \color{blue}{0 + \left(\mathsf{neg}\left(t\right)\right)} \]

   3. lift-neg.f64 N/A

      \[\leadsto 0 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \]

   4. flip3-+ N/A

      \[\leadsto \color{blue}{\frac{{0}^{3} + {\left(\mathsf{neg}\left(t\right)\right)}^{3}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) - 0 \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}} \]

   5. sqr-pow N/A

      \[\leadsto \frac{{0}^{3} + \color{blue}{{\left(\mathsf{neg}\left(t\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(t\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) - 0 \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \]

   6. pow-prod-down N/A

      \[\leadsto \frac{{0}^{3} + \color{blue}{{\left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) - 0 \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \]

   7. lift-neg.f64 N/A

      \[\leadsto \frac{{0}^{3} + {\left(\color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) - 0 \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \]

   8. lift-neg.f64 N/A

      \[\leadsto \frac{{0}^{3} + {\left(\left(\mathsf{neg}\left(t\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) - 0 \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \]

   9. sqr-neg N/A

      \[\leadsto \frac{{0}^{3} + {\color{blue}{\left(t \cdot t\right)}}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) - 0 \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \]

   10. pow-prod-down N/A

       \[\leadsto \frac{{0}^{3} + \color{blue}{{t}^{\left(\frac{3}{2}\right)} \cdot {t}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) - 0 \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \]

   11. sqr-pow N/A

       \[\leadsto \frac{{0}^{3} + \color{blue}{{t}^{3}}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) - 0 \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \]

   12. lower-/.f64 N/A

       \[\leadsto \color{blue}{\frac{{0}^{3} + {t}^{3}}{0 \cdot 0 + \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) - 0 \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}} \]

7. Applied egg-rr 1.2%

   \[\leadsto \color{blue}{\frac{0 + t \cdot \left(t \cdot t\right)}{0 + \left(t \cdot t - 0 \cdot \left(-t\right)\right)}} \]

9. Applied egg-rr 2.2%

   \[\leadsto \color{blue}{t} \]
10. Add Preprocessing

Developer Target 1: 99.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024212 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* (- z) (+ (+ (* 1/2 (* y y)) y) (* (/ 1/3 (* 1 (* 1 1))) (* y (* y y))))) (- t (* x (log y)))))

  (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))