Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 15.4s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y - y\right) - z\\ t_2 := \left(0 - y\right) - z\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 1:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (* x (log y)) y) z)) (t_2 (- (- 0.0 y) z)))
   (if (<= t_1 -2e+18) t_2 (if (<= t_1 1.0) (- (log t) y) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * log(y)) - y) - z;
	double t_2 = (0.0 - y) - z;
	double tmp;
	if (t_1 <= -2e+18) {
		tmp = t_2;
	} else if (t_1 <= 1.0) {
		tmp = log(t) - y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * log(y)) - y) - z
    t_2 = (0.0d0 - y) - z
    if (t_1 <= (-2d+18)) then
        tmp = t_2
    else if (t_1 <= 1.0d0) then
        tmp = log(t) - y
    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 = ((x * Math.log(y)) - y) - z;
	double t_2 = (0.0 - y) - z;
	double tmp;
	if (t_1 <= -2e+18) {
		tmp = t_2;
	} else if (t_1 <= 1.0) {
		tmp = Math.log(t) - y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * math.log(y)) - y) - z
	t_2 = (0.0 - y) - z
	tmp = 0
	if t_1 <= -2e+18:
		tmp = t_2
	elif t_1 <= 1.0:
		tmp = math.log(t) - y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * log(y)) - y) - z)
	t_2 = Float64(Float64(0.0 - y) - z)
	tmp = 0.0
	if (t_1 <= -2e+18)
		tmp = t_2;
	elseif (t_1 <= 1.0)
		tmp = Float64(log(t) - y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * log(y)) - y) - z;
	t_2 = (0.0 - y) - z;
	tmp = 0.0;
	if (t_1 <= -2e+18)
		tmp = t_2;
	elseif (t_1 <= 1.0)
		tmp = log(t) - y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(0.0 - y), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+18], t$95$2, If[LessEqual[t$95$1, 1.0], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -2e18 or 1 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)

   1. Initial program 99.9%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

      3. /-lowering-/.f64 N/A

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

      4. clear-num N/A

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

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. log-lowering-log.f64 99.4

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - \left(y + z\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \color{blue}{0 - \left(y + z\right)} \]

      4. +-lowering-+.f64 72.5

         \[\leadsto 0 - \color{blue}{\left(y + z\right)} \]

   10. Simplified 72.5%

       \[\leadsto \color{blue}{0 - \left(y + z\right)} \]

   if -2e18 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. associate-*r/ N/A

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

      4. mul-1-neg N/A

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

      5. log-rec N/A

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

      6. mul-1-neg N/A

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

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

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. associate-/l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. log-lowering-log.f64 97.5

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. log-rec N/A

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

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

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

   8. Simplified 95.7%

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

   9. Taylor expanded in x around 0

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

       1. mul-1-neg N/A

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

       2. sub-neg N/A

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

       3. --lowering--.f64 N/A

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

       4. log-lowering-log.f64 92.8

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

   11. Simplified 92.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \log y - y\right) - z \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\left(0 - y\right) - z\\ \mathbf{elif}\;\left(x \cdot \log y - y\right) - z \leq 1:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;\left(0 - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{1}{x \cdot \log y - \left(y + z\right)}}\\ \mathbf{if}\;z \leq -470:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 420:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ 1.0 (- (* x (log y)) (+ y z))))))
   (if (<= z -470.0) t_1 (if (<= z 420.0) (- (fma x (log y) (log t)) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (1.0 / ((x * log(y)) - (y + z)));
	double tmp;
	if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= 420.0) {
		tmp = fma(x, log(y), log(t)) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(1.0 / Float64(Float64(x * log(y)) - Float64(y + z))))
	tmp = 0.0
	if (z <= -470.0)
		tmp = t_1;
	elseif (z <= 420.0)
		tmp = Float64(fma(x, log(y), log(t)) - y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(1.0 / N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -470.0], t$95$1, If[LessEqual[z, 420.0], N[(N[(x * N[Log[y], $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -470 or 420 < z

   1. Initial program 99.9%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

      3. /-lowering-/.f64 N/A

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

      4. clear-num N/A

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

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. log-lowering-log.f64 99.2

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

   7. Simplified 99.2%

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

   if -470 < z < 420

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. --lowering--.f64 N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. log-lowering-log.f64 N/A

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

      5. log-lowering-log.f64 99.3

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

   5. Simplified 99.3%

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

Alternative 4: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 53:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x \cdot \log y - \left(y + z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 53.0)
   (fma x (log y) (- (log t) z))
   (/ 1.0 (/ 1.0 (- (* x (log y)) (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 53.0) {
		tmp = fma(x, log(y), (log(t) - z));
	} else {
		tmp = 1.0 / (1.0 / ((x * log(y)) - (y + z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 53.0)
		tmp = fma(x, log(y), Float64(log(t) - z));
	else
		tmp = Float64(1.0 / Float64(1.0 / Float64(Float64(x * log(y)) - Float64(y + z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 53.0], N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(1.0 / N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 53

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. log-lowering-log.f64 N/A

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

      6. unsub-neg N/A

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

      7. --lowering--.f64 N/A

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

      8. log-lowering-log.f64 99.2

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

   5. Simplified 99.2%

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

   if 53 < y

   1. Initial program 100.0%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

      3. /-lowering-/.f64 N/A

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

      4. clear-num N/A

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

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. log-lowering-log.f64 98.6

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

   7. Simplified 98.6%

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

Alternative 5: 98.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{1}{x \cdot \log y - \left(y + z\right)}}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.11:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ 1.0 (- (* x (log y)) (+ y z))))))
   (if (<= x -2.6e+27) t_1 (if (<= x 0.11) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (1.0 / ((x * log(y)) - (y + z)));
	double tmp;
	if (x <= -2.6e+27) {
		tmp = t_1;
	} else if (x <= 0.11) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / (1.0d0 / ((x * log(y)) - (y + z)))
    if (x <= (-2.6d+27)) then
        tmp = t_1
    else if (x <= 0.11d0) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (1.0 / ((x * Math.log(y)) - (y + z)));
	double tmp;
	if (x <= -2.6e+27) {
		tmp = t_1;
	} else if (x <= 0.11) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / (1.0 / ((x * math.log(y)) - (y + z)))
	tmp = 0
	if x <= -2.6e+27:
		tmp = t_1
	elif x <= 0.11:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(1.0 / Float64(Float64(x * log(y)) - Float64(y + z))))
	tmp = 0.0
	if (x <= -2.6e+27)
		tmp = t_1;
	elseif (x <= 0.11)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (1.0 / ((x * log(y)) - (y + z)));
	tmp = 0.0;
	if (x <= -2.6e+27)
		tmp = t_1;
	elseif (x <= 0.11)
		tmp = log(t) - (y + z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(1.0 / N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+27], t$95$1, If[LessEqual[x, 0.11], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000009e27 or 0.110000000000000001 < x

   1. Initial program 99.7%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

      3. /-lowering-/.f64 N/A

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

      4. clear-num N/A

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

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. log-lowering-log.f64 99.4

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

   7. Simplified 99.4%

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

   if -2.60000000000000009e27 < x < 0.110000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 N/A

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

      2. log-lowering-log.f64 N/A

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

      3. +-lowering-+.f64 99.1

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

   5. Simplified 99.1%

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

Alternative 6: 70.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(0 - y\right) - z\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 390:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- 0.0 y) z)))
   (if (<= z -2.45e-21)
     t_1
     (if (<= z -2.6e-30) (* x (log y)) (if (<= z 390.0) (- (log t) y) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (0.0 - y) - z;
	double tmp;
	if (z <= -2.45e-21) {
		tmp = t_1;
	} else if (z <= -2.6e-30) {
		tmp = x * log(y);
	} else if (z <= 390.0) {
		tmp = log(t) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (0.0d0 - y) - z
    if (z <= (-2.45d-21)) then
        tmp = t_1
    else if (z <= (-2.6d-30)) then
        tmp = x * log(y)
    else if (z <= 390.0d0) then
        tmp = log(t) - y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (0.0 - y) - z;
	double tmp;
	if (z <= -2.45e-21) {
		tmp = t_1;
	} else if (z <= -2.6e-30) {
		tmp = x * Math.log(y);
	} else if (z <= 390.0) {
		tmp = Math.log(t) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (0.0 - y) - z
	tmp = 0
	if z <= -2.45e-21:
		tmp = t_1
	elif z <= -2.6e-30:
		tmp = x * math.log(y)
	elif z <= 390.0:
		tmp = math.log(t) - y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(0.0 - y) - z)
	tmp = 0.0
	if (z <= -2.45e-21)
		tmp = t_1;
	elseif (z <= -2.6e-30)
		tmp = Float64(x * log(y));
	elseif (z <= 390.0)
		tmp = Float64(log(t) - y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (0.0 - y) - z;
	tmp = 0.0;
	if (z <= -2.45e-21)
		tmp = t_1;
	elseif (z <= -2.6e-30)
		tmp = x * log(y);
	elseif (z <= 390.0)
		tmp = log(t) - y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(0.0 - y), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[z, -2.45e-21], t$95$1, If[LessEqual[z, -2.6e-30], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 390.0], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4500000000000001e-21 or 390 < z

   1. Initial program 99.9%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

      3. /-lowering-/.f64 N/A

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

      4. clear-num N/A

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

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. log-lowering-log.f64 98.5

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

   7. Simplified 98.5%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - \left(y + z\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \color{blue}{0 - \left(y + z\right)} \]

      4. +-lowering-+.f64 83.8

         \[\leadsto 0 - \color{blue}{\left(y + z\right)} \]

   10. Simplified 83.8%

       \[\leadsto \color{blue}{0 - \left(y + z\right)} \]

   if -2.4500000000000001e-21 < z < -2.59999999999999987e-30

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{x \cdot \log y + 0} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, 0\right)} \]

      3. log-lowering-log.f64 99.7

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\log y}, 0\right) \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. log-lowering-log.f64 99.7

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

   7. Applied egg-rr 99.7%

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

   if -2.59999999999999987e-30 < z < 390

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. associate-*r/ N/A

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

      4. mul-1-neg N/A

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

      5. log-rec N/A

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

      6. mul-1-neg N/A

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

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

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. associate-/l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. log-lowering-log.f64 88.0

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

   5. Simplified 88.0%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. log-rec N/A

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

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

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

   8. Simplified 87.8%

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

   9. Taylor expanded in x around 0

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

       1. mul-1-neg N/A

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

       2. sub-neg N/A

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

       3. --lowering--.f64 N/A

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

       4. log-lowering-log.f64 69.2

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

   11. Simplified 69.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-21}:\\ \;\;\;\;\left(0 - y\right) - z\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 390:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;\left(0 - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, 0 - z\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+28}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5e+28)
   (fma x (log y) (- 0.0 z))
   (if (<= x 2.4e+28) (- (log t) (+ y z)) (- (* x (log y)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5e+28) {
		tmp = fma(x, log(y), (0.0 - z));
	} else if (x <= 2.4e+28) {
		tmp = log(t) - (y + z);
	} else {
		tmp = (x * log(y)) - y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5e+28)
		tmp = fma(x, log(y), Float64(0.0 - z));
	elseif (x <= 2.4e+28)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(Float64(x * log(y)) - y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5e+28], N[(x * N[Log[y], $MachinePrecision] + N[(0.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+28], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.99999999999999957e28

   1. Initial program 99.7%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

      3. /-lowering-/.f64 N/A

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

      4. clear-num N/A

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

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. log-lowering-log.f64 99.6

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. log-lowering-log.f64 N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - z}\right) \]

      5. --lowering--.f64 84.3

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - z}\right) \]

   10. Simplified 84.3%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, 0 - z\right)} \]

   if -4.99999999999999957e28 < x < 2.39999999999999981e28

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 N/A

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

      2. log-lowering-log.f64 N/A

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

      3. +-lowering-+.f64 98.4

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

   5. Simplified 98.4%

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

   if 2.39999999999999981e28 < x

   1. Initial program 99.8%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

      3. /-lowering-/.f64 N/A

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

      4. clear-num N/A

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

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. log-lowering-log.f64 99.6

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0

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

      1. --lowering--.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. log-lowering-log.f64 83.2

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

   10. Simplified 83.2%

       \[\leadsto \color{blue}{x \cdot \log y - y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 89.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+29}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= x -5.8e+62) t_1 (if (<= x 3.4e+29) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if (x <= -5.8e+62) {
		tmp = t_1;
	} else if (x <= 3.4e+29) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - y
    if (x <= (-5.8d+62)) then
        tmp = t_1
    else if (x <= 3.4d+29) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - y;
	double tmp;
	if (x <= -5.8e+62) {
		tmp = t_1;
	} else if (x <= 3.4e+29) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if x <= -5.8e+62:
		tmp = t_1
	elif x <= 3.4e+29:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (x <= -5.8e+62)
		tmp = t_1;
	elseif (x <= 3.4e+29)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if (x <= -5.8e+62)
		tmp = t_1;
	elseif (x <= 3.4e+29)
		tmp = log(t) - (y + z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -5.8e+62], t$95$1, If[LessEqual[x, 3.4e+29], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999968e62 or 3.39999999999999981e29 < x

   1. Initial program 99.8%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

      3. /-lowering-/.f64 N/A

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

      4. clear-num N/A

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

      5. flip3-+ N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. log-lowering-log.f64 99.6

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0

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

      1. --lowering--.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. log-lowering-log.f64 84.5

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

   10. Simplified 84.5%

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

   if -5.79999999999999968e62 < x < 3.39999999999999981e29

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 N/A

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

      2. log-lowering-log.f64 N/A

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

      3. +-lowering-+.f64 96.7

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

   5. Simplified 96.7%

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

Alternative 9: 84.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+140}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.6e+145) t_1 (if (<= x 1.7e+140) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.6e+145) {
		tmp = t_1;
	} else if (x <= 1.7e+140) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-2.6d+145)) then
        tmp = t_1
    else if (x <= 1.7d+140) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -2.6e+145) {
		tmp = t_1;
	} else if (x <= 1.7e+140) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -2.6e+145:
		tmp = t_1
	elif x <= 1.7e+140:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.6e+145)
		tmp = t_1;
	elseif (x <= 1.7e+140)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -2.6e+145)
		tmp = t_1;
	elseif (x <= 1.7e+140)
		tmp = log(t) - (y + z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+145], t$95$1, If[LessEqual[x, 1.7e+140], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000003e145 or 1.7e140 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{x \cdot \log y + 0} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, 0\right)} \]

      3. log-lowering-log.f64 76.9

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\log y}, 0\right) \]

   5. Simplified 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. log-lowering-log.f64 76.9

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

   7. Applied egg-rr 76.9%

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

   if -2.60000000000000003e145 < x < 1.7e140

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 N/A

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

      2. log-lowering-log.f64 N/A

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

      3. +-lowering-+.f64 90.0

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

   5. Simplified 90.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+140}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.9% accurate, 21.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 400000000000:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 400000000000.0) (- 0.0 z) (- 0.0 y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 400000000000.0) {
		tmp = 0.0 - z;
	} else {
		tmp = 0.0 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 400000000000.0d0) then
        tmp = 0.0d0 - z
    else
        tmp = 0.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 400000000000.0) {
		tmp = 0.0 - z;
	} else {
		tmp = 0.0 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 400000000000.0:
		tmp = 0.0 - z
	else:
		tmp = 0.0 - y
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 400000000000.0], N[(0.0 - z), $MachinePrecision], N[(0.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4e11

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 44.9

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

   5. Simplified 44.9%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 44.9

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

   7. Applied egg-rr 44.9%

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

   if 4e11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 64.1

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

   5. Simplified 64.1%

      \[\leadsto \color{blue}{0 - y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 64.1

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

   7. Applied egg-rr 64.1%

      \[\leadsto \color{blue}{-y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 400000000000:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 30.7× speedup

Math

\[\begin{array}{l} \\ \left(0 - y\right) - z \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (- 0.0 y) z))

C

double code(double x, double y, double z, double t) {
	return (0.0 - y) - z;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (0.0d0 - y) - z
end function

Java

public static double code(double x, double y, double z, double t) {
	return (0.0 - y) - z;
}

Python

def code(x, y, z, t):
	return (0.0 - y) - z

Julia

function code(x, y, z, t)
	return Float64(Float64(0.0 - y) - z)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (0.0 - y) - z;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(0.0 - y), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. flip3-+ N/A

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

   2. clear-num N/A

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

   3. /-lowering-/.f64 N/A

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

   4. clear-num N/A

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

   5. flip3-+ N/A

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

4. Applied egg-rr 99.6%

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

5. Taylor expanded in x around inf

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

   1. *-lowering-*.f64 N/A

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

   2. log-lowering-log.f64 85.4

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

7. Simplified 85.4%

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

8. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - \left(y + z\right)} \]

   3. --lowering--.f64 N/A

      \[\leadsto \color{blue}{0 - \left(y + z\right)} \]

   4. +-lowering-+.f64 62.4

      \[\leadsto 0 - \color{blue}{\left(y + z\right)} \]

10. Simplified 62.4%

    \[\leadsto \color{blue}{0 - \left(y + z\right)} \]

11. Final simplification 62.4%

    \[\leadsto \left(0 - y\right) - z \]
12. Add Preprocessing

Alternative 12: 30.5% accurate, 53.8× speedup

Math

\[\begin{array}{l} \\ 0 - y \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- 0.0 y))

C

double code(double x, double y, double z, double t) {
	return 0.0 - 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 = 0.0d0 - y
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.0 - y;
}

Python

def code(x, y, z, t):
	return 0.0 - y

Julia

function code(x, y, z, t)
	return Float64(0.0 - y)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.0 - y;
end

Wolfram

code[x_, y_, z_, t_] := N[(0.0 - y), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

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

   3. --lowering--.f64 30.9

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

5. Simplified 30.9%

   \[\leadsto \color{blue}{0 - y} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 30.9

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

7. Applied egg-rr 30.9%

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

8. Final simplification 30.9%

   \[\leadsto 0 - y \]
9. Add Preprocessing

Alternative 13: 2.2% accurate, 215.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

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

   3. --lowering--.f64 30.9

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

5. Simplified 30.9%

   \[\leadsto \color{blue}{0 - y} \]
6. Step-by-step derivation

   1. flip3-- N/A

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

   2. div-inv N/A

      \[\leadsto \color{blue}{\left({0}^{3} - {y}^{3}\right) \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)}} \]

   3. metadata-eval N/A

      \[\leadsto \left(\color{blue}{0} - {y}^{3}\right) \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   4. sub0-neg N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left({y}^{3}\right)\right)} \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   5. cube-neg N/A

      \[\leadsto \color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{3}} \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{3} \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)}} \]

   7. cube-neg N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left({y}^{3}\right)\right)} \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   8. sub0-neg N/A

      \[\leadsto \color{blue}{\left(0 - {y}^{3}\right)} \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   9. --lowering--.f64 N/A

      \[\leadsto \color{blue}{\left(0 - {y}^{3}\right)} \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   10. cube-mult N/A

       \[\leadsto \left(0 - \color{blue}{y \cdot \left(y \cdot y\right)}\right) \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   11. *-lowering-*.f64 N/A

       \[\leadsto \left(0 - \color{blue}{y \cdot \left(y \cdot y\right)}\right) \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   12. +-lft-identity N/A

       \[\leadsto \left(0 - y \cdot \left(y \cdot \color{blue}{\left(0 + y\right)}\right)\right) \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   13. +-commutative N/A

       \[\leadsto \left(0 - y \cdot \left(y \cdot \color{blue}{\left(y + 0\right)}\right)\right) \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   14. distribute-rgt-out N/A

       \[\leadsto \left(0 - y \cdot \color{blue}{\left(y \cdot y + 0 \cdot y\right)}\right) \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   15. mul0-lft N/A

       \[\leadsto \left(0 - y \cdot \left(y \cdot y + \color{blue}{0}\right)\right) \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   16. accelerator-lowering-fma.f64 N/A

       \[\leadsto \left(0 - y \cdot \color{blue}{\mathsf{fma}\left(y, y, 0\right)}\right) \cdot \frac{1}{0 \cdot 0 + \left(y \cdot y + 0 \cdot y\right)} \]

   17. metadata-eval N/A

       \[\leadsto \left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \frac{1}{\color{blue}{0} + \left(y \cdot y + 0 \cdot y\right)} \]

   18. +-lft-identity N/A

       \[\leadsto \left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \frac{1}{\color{blue}{y \cdot y + 0 \cdot y}} \]

   19. distribute-rgt-out N/A

       \[\leadsto \left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \frac{1}{\color{blue}{y \cdot \left(y + 0\right)}} \]

   20. +-commutative N/A

       \[\leadsto \left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \frac{1}{y \cdot \color{blue}{\left(0 + y\right)}} \]

   21. +-lft-identity N/A

       \[\leadsto \left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \frac{1}{y \cdot \color{blue}{y}} \]

   22. /-lowering-/.f64 N/A

       \[\leadsto \left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \color{blue}{\frac{1}{y \cdot y}} \]

   23. +-lft-identity N/A

       \[\leadsto \left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \frac{1}{y \cdot \color{blue}{\left(0 + y\right)}} \]

   24. +-commutative N/A

       \[\leadsto \left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \frac{1}{y \cdot \color{blue}{\left(y + 0\right)}} \]

   25. distribute-rgt-out N/A

       \[\leadsto \left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \frac{1}{\color{blue}{y \cdot y + 0 \cdot y}} \]

7. Applied egg-rr 6.9%

   \[\leadsto \color{blue}{\left(0 - y \cdot \mathsf{fma}\left(y, y, 0\right)\right) \cdot \frac{1}{\mathsf{fma}\left(y, y, 0\right)}} \]
8. Step-by-step derivation

   1. un-div-inv N/A

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

   2. sub0-neg N/A

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

   3. +-rgt-identity N/A

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

   4. cube-unmult N/A

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

   5. cube-neg N/A

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

   6. sub0-neg N/A

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

   7. sqr-pow N/A

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

   8. unpow-prod-down N/A

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

   9. sub0-neg N/A

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

   10. sub0-neg N/A

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

   11. sqr-neg N/A

       \[\leadsto \frac{{\color{blue}{\left(y \cdot y\right)}}^{\left(\frac{3}{2}\right)}}{y \cdot y + 0} \]

   12. unpow-prod-down N/A

       \[\leadsto \frac{\color{blue}{{y}^{\left(\frac{3}{2}\right)} \cdot {y}^{\left(\frac{3}{2}\right)}}}{y \cdot y + 0} \]

   13. sqr-pow N/A

       \[\leadsto \frac{\color{blue}{{y}^{3}}}{y \cdot y + 0} \]

   14. +-rgt-identity N/A

       \[\leadsto \frac{{y}^{3}}{\color{blue}{y \cdot y}} \]

   15. pow2 N/A

       \[\leadsto \frac{{y}^{3}}{\color{blue}{{y}^{2}}} \]

   16. pow-div N/A

       \[\leadsto \color{blue}{{y}^{\left(3 - 2\right)}} \]

   17. metadata-eval N/A

       \[\leadsto {y}^{\color{blue}{1}} \]

   18. unpow1 2.2

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

9. Applied egg-rr 2.2%

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

Reproduce

herbie shell --seed 2024196 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))