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

Percentage Accurate: 99.9% → 99.9%

Time: 10.7s

Alternatives: 12

Speedup: 0.7×

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- N/A

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

   2. associate--l- N/A

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

   3. sub-neg N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

   8. distribute-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

   9. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

   11. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

   12. associate-+l- N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

   13. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

   15. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

   17. log-lowering-log.f64 99.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

3. Simplified 99.8%

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

   1. *-commutative N/A

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

   2. fma-define N/A

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

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

      \[\leadsto \mathsf{fma.f64}\left(\log y, \color{blue}{x}, \left(\left(\log t - z\right) - y\right)\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\left(\log t - z\right) - y\right)\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

   7. log-lowering-log.f64 99.8%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

6. Applied egg-rr 99.8%

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

Alternative 2: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ t_2 := \log y \cdot x\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+53}:\\ \;\;\;\;t\_2 - y\\ \mathbf{elif}\;x \leq 3700000000000:\\ \;\;\;\;t\_1 - y\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)) (t_2 (* (log y) x)))
   (if (<= x -1.6e+53)
     (- t_2 y)
     (if (<= x 3700000000000.0) (- t_1 y) (+ t_1 t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double t_2 = log(y) * x;
	double tmp;
	if (x <= -1.6e+53) {
		tmp = t_2 - y;
	} else if (x <= 3700000000000.0) {
		tmp = t_1 - y;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(t) - z
    t_2 = log(y) * x
    if (x <= (-1.6d+53)) then
        tmp = t_2 - y
    else if (x <= 3700000000000.0d0) then
        tmp = t_1 - y
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - z;
	double t_2 = Math.log(y) * x;
	double tmp;
	if (x <= -1.6e+53) {
		tmp = t_2 - y;
	} else if (x <= 3700000000000.0) {
		tmp = t_1 - y;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	t_2 = math.log(y) * x
	tmp = 0
	if x <= -1.6e+53:
		tmp = t_2 - y
	elif x <= 3700000000000.0:
		tmp = t_1 - y
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	t_2 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -1.6e+53)
		tmp = Float64(t_2 - y);
	elseif (x <= 3700000000000.0)
		tmp = Float64(t_1 - y);
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	t_2 = log(y) * x;
	tmp = 0.0;
	if (x <= -1.6e+53)
		tmp = t_2 - y;
	elseif (x <= 3700000000000.0)
		tmp = t_1 - y;
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.6e+53], N[(t$95$2 - y), $MachinePrecision], If[LessEqual[x, 3700000000000.0], N[(t$95$1 - y), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e53

   1. Initial program 99.7%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \color{blue}{\left(-1 \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(y\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(0 - \color{blue}{y}\right)\right) \]

      3. --lowering--.f64 93.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y}\right)\right) \]

   7. Simplified 93.7%

      \[\leadsto x \cdot \log y + \color{blue}{\left(0 - y\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

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

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{y}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log y \cdot x\right), y\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log y, x\right), y\right) \]

      6. log-lowering-log.f64 93.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(y\right), x\right), y\right) \]

   9. Applied egg-rr 93.7%

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

   if -1.6e53 < x < 3.7e12

   1. Initial program 100.0%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - z\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right) \]

      5. log-lowering-log.f64 96.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right) \]

   7. Simplified 96.5%

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

   if 3.7e12 < x

   1. Initial program 99.6%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \color{blue}{\left(\log t - z\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\log t, \color{blue}{z}\right)\right) \]

      2. log-lowering-log.f64 85.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right)\right) \]

   7. Simplified 85.6%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+53}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{elif}\;x \leq 3700000000000:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) + \log y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{+51}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{elif}\;x \leq 3800000000000:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, 0 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.95e+51)
   (- (* (log y) x) y)
   (if (<= x 3800000000000.0) (- (- (log t) z) y) (fma (log y) x (- 0.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.95e+51) {
		tmp = (log(y) * x) - y;
	} else if (x <= 3800000000000.0) {
		tmp = (log(t) - z) - y;
	} else {
		tmp = fma(log(y), x, (0.0 - z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.95e+51)
		tmp = Float64(Float64(log(y) * x) - y);
	elseif (x <= 3800000000000.0)
		tmp = Float64(Float64(log(t) - z) - y);
	else
		tmp = fma(log(y), x, Float64(0.0 - z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.95e+51], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 3800000000000.0], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + N[(0.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.94999999999999991e51

   1. Initial program 99.7%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \color{blue}{\left(-1 \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(y\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(0 - \color{blue}{y}\right)\right) \]

      3. --lowering--.f64 93.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y}\right)\right) \]

   7. Simplified 93.7%

      \[\leadsto x \cdot \log y + \color{blue}{\left(0 - y\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

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

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{y}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log y \cdot x\right), y\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log y, x\right), y\right) \]

      6. log-lowering-log.f64 93.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(y\right), x\right), y\right) \]

   9. Applied egg-rr 93.7%

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

   if -2.94999999999999991e51 < x < 3.8e12

   1. Initial program 100.0%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - z\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right) \]

      5. log-lowering-log.f64 96.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right) \]

   7. Simplified 96.5%

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

   if 3.8e12 < x

   1. Initial program 99.6%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.6%

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

      1. *-commutative N/A

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

      2. fma-define N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(\log y, \color{blue}{x}, \left(\left(\log t - z\right) - y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\left(\log t - z\right) - y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      7. log-lowering-log.f64 99.6%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \color{blue}{\left(-1 \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(z\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(0 - z\right)\right) \]

      3. --lowering--.f64 85.2%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(0, z\right)\right) \]

   9. Simplified 85.2%

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

       1. sub0-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(z\right)\right)\right) \]

       2. +-lft-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\left(0 + z\right)\right)\right)\right) \]

       3. flip3-+ N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       4. sqr-pow N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{{0}^{3} + {z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       5. pow-prod-down N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{{0}^{3} + {\left(z \cdot z\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       6. sqr-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{{0}^{3} + {\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       7. sub0-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{{0}^{3} + {\left(\left(0 - z\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       8. sub0-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{{0}^{3} + {\left(\left(0 - z\right) \cdot \left(0 - z\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       9. pow-prod-down N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{{0}^{3} + {\left(0 - z\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(0 - z\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       10. sqr-pow N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{{0}^{3} + {\left(0 - z\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       11. metadata-eval N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{0 + {\left(0 - z\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       12. sub0-neg N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{0 + {\left(\mathsf{neg}\left(z\right)\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       13. cube-neg N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{0 + \left(\mathsf{neg}\left({z}^{3}\right)\right)}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right)\right) \]

       15. mul0-lft N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0\right)}\right)\right)\right) \]

       16. fmm-def N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, \mathsf{neg}\left(0\right)\right)}\right)\right)\right) \]

       17. metadata-eval N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0\right)}\right)\right)\right) \]

       18. mul0-lft N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0 \cdot z\right)}\right)\right)\right) \]

       19. fma-define N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right)\right)\right) \]

       20. metadata-eval N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\frac{{0}^{3} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right)\right)\right) \]

       21. flip3-- N/A

           \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\left(0 - z\right)\right)\right)\right) \]

   11. Applied egg-rr 85.2%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{+51}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{elif}\;x \leq 3800000000000:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, 0 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- N/A

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

   2. associate--l- N/A

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

   3. sub-neg N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

   8. distribute-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

   9. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

   11. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

   12. associate-+l- N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

   13. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

   15. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

   17. log-lowering-log.f64 99.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 5: 89.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -2 \cdot 10^{+47}:\\ \;\;\;\;t\_1 - y\\ \mathbf{elif}\;x \leq 3800000000000:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -2e+47)
     (- t_1 y)
     (if (<= x 3800000000000.0) (- (- (log t) z) y) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -2e+47) {
		tmp = t_1 - y;
	} else if (x <= 3800000000000.0) {
		tmp = (log(t) - z) - y;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(y) * x
    if (x <= (-2d+47)) then
        tmp = t_1 - y
    else if (x <= 3800000000000.0d0) then
        tmp = (log(t) - z) - y
    else
        tmp = t_1 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * x;
	double tmp;
	if (x <= -2e+47) {
		tmp = t_1 - y;
	} else if (x <= 3800000000000.0) {
		tmp = (Math.log(t) - z) - y;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -2e+47:
		tmp = t_1 - y
	elif x <= 3800000000000.0:
		tmp = (math.log(t) - z) - y
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -2e+47)
		tmp = Float64(t_1 - y);
	elseif (x <= 3800000000000.0)
		tmp = Float64(Float64(log(t) - z) - y);
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	tmp = 0.0;
	if (x <= -2e+47)
		tmp = t_1 - y;
	elseif (x <= 3800000000000.0)
		tmp = (log(t) - z) - y;
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2e+47], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[x, 3800000000000.0], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0000000000000001e47

   1. Initial program 99.7%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \color{blue}{\left(-1 \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(y\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(0 - \color{blue}{y}\right)\right) \]

      3. --lowering--.f64 93.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y}\right)\right) \]

   7. Simplified 93.7%

      \[\leadsto x \cdot \log y + \color{blue}{\left(0 - y\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

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

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{y}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log y \cdot x\right), y\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log y, x\right), y\right) \]

      6. log-lowering-log.f64 93.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(y\right), x\right), y\right) \]

   9. Applied egg-rr 93.7%

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

   if -2.0000000000000001e47 < x < 3.8e12

   1. Initial program 100.0%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - z\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right) \]

      5. log-lowering-log.f64 96.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right) \]

   7. Simplified 96.5%

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

   if 3.8e12 < x

   1. Initial program 99.6%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.6%

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

      1. *-commutative N/A

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

      2. fma-define N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(\log y, \color{blue}{x}, \left(\left(\log t - z\right) - y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\left(\log t - z\right) - y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      7. log-lowering-log.f64 99.6%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \color{blue}{\left(-1 \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(z\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(0 - z\right)\right) \]

      3. --lowering--.f64 85.2%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(0, z\right)\right) \]

   9. Simplified 85.2%

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

       1. sub0-neg N/A

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

       2. +-lft-identity N/A

          \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\left(0 + z\right)\right)\right) \]

       3. flip3-+ N/A

          \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       4. sqr-pow N/A

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

       5. pow-prod-down N/A

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

       6. sqr-neg N/A

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

       7. sub0-neg N/A

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

       8. sub0-neg N/A

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

       9. pow-prod-down N/A

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

       10. sqr-pow N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{{0}^{3} + {\left(0 - z\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       11. metadata-eval N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 + {\left(0 - z\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       12. sub0-neg N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 + {\left(\mathsf{neg}\left(z\right)\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       13. cube-neg N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 + \left(\mathsf{neg}\left({z}^{3}\right)\right)}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       15. mul0-lft N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0\right)}\right)\right) \]

       16. fmm-def N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, \mathsf{neg}\left(0\right)\right)}\right)\right) \]

       17. metadata-eval N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0\right)}\right)\right) \]

       18. mul0-lft N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0 \cdot z\right)}\right)\right) \]

       19. fma-define N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right)\right) \]

       20. metadata-eval N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{{0}^{3} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right)\right) \]

   11. Applied egg-rr 85.2%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+47}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{elif}\;x \leq 3800000000000:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+51}:\\ \;\;\;\;t\_1 - y\\ \mathbf{elif}\;x \leq 3700000000000:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -1.5e+51)
     (- t_1 y)
     (if (<= x 3700000000000.0) (- (- 0.0 z) y) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -1.5e+51) {
		tmp = t_1 - y;
	} else if (x <= 3700000000000.0) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(y) * x
    if (x <= (-1.5d+51)) then
        tmp = t_1 - y
    else if (x <= 3700000000000.0d0) then
        tmp = (0.0d0 - z) - y
    else
        tmp = t_1 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * x;
	double tmp;
	if (x <= -1.5e+51) {
		tmp = t_1 - y;
	} else if (x <= 3700000000000.0) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -1.5e+51:
		tmp = t_1 - y
	elif x <= 3700000000000.0:
		tmp = (0.0 - z) - y
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -1.5e+51)
		tmp = Float64(t_1 - y);
	elseif (x <= 3700000000000.0)
		tmp = Float64(Float64(0.0 - z) - y);
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	tmp = 0.0;
	if (x <= -1.5e+51)
		tmp = t_1 - y;
	elseif (x <= 3700000000000.0)
		tmp = (0.0 - z) - y;
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.5e+51], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[x, 3700000000000.0], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5e51

   1. Initial program 99.7%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \color{blue}{\left(-1 \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(y\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(0 - \color{blue}{y}\right)\right) \]

      3. --lowering--.f64 93.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y}\right)\right) \]

   7. Simplified 93.7%

      \[\leadsto x \cdot \log y + \color{blue}{\left(0 - y\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

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

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{y}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log y \cdot x\right), y\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log y, x\right), y\right) \]

      6. log-lowering-log.f64 93.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(y\right), x\right), y\right) \]

   9. Applied egg-rr 93.7%

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

   if -1.5e51 < x < 3.7e12

   1. Initial program 100.0%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - z\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right) \]

      5. log-lowering-log.f64 96.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right) \]

   7. Simplified 96.5%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot z\right)}, y\right) \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

      3. --lowering--.f64 73.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

   10. Simplified 73.0%

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

   if 3.7e12 < x

   1. Initial program 99.6%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.6%

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

      1. *-commutative N/A

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

      2. fma-define N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(\log y, \color{blue}{x}, \left(\left(\log t - z\right) - y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\left(\log t - z\right) - y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      7. log-lowering-log.f64 99.6%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \color{blue}{\left(-1 \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(z\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(0 - z\right)\right) \]

      3. --lowering--.f64 85.2%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(0, z\right)\right) \]

   9. Simplified 85.2%

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

       1. sub0-neg N/A

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

       2. +-lft-identity N/A

          \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\left(0 + z\right)\right)\right) \]

       3. flip3-+ N/A

          \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       4. sqr-pow N/A

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

       5. pow-prod-down N/A

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

       6. sqr-neg N/A

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

       7. sub0-neg N/A

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

       8. sub0-neg N/A

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

       9. pow-prod-down N/A

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

       10. sqr-pow N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{{0}^{3} + {\left(0 - z\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       11. metadata-eval N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 + {\left(0 - z\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       12. sub0-neg N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 + {\left(\mathsf{neg}\left(z\right)\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       13. cube-neg N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 + \left(\mathsf{neg}\left({z}^{3}\right)\right)}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       15. mul0-lft N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0\right)}\right)\right) \]

       16. fmm-def N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, \mathsf{neg}\left(0\right)\right)}\right)\right) \]

       17. metadata-eval N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0\right)}\right)\right) \]

       18. mul0-lft N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0 \cdot z\right)}\right)\right) \]

       19. fma-define N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right)\right) \]

       20. metadata-eval N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{{0}^{3} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right)\right) \]

   11. Applied egg-rr 85.2%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+51}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{elif}\;x \leq 3700000000000:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.95 \cdot 10^{-220}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+122}:\\ \;\;\;\;\log y \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.95e-220)
   (- (log t) z)
   (if (<= y 9e+122) (- (* (log y) x) z) (- (- 0.0 z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.95e-220) {
		tmp = log(t) - z;
	} else if (y <= 9e+122) {
		tmp = (log(y) * x) - z;
	} else {
		tmp = (0.0 - z) - 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 <= 2.95d-220) then
        tmp = log(t) - z
    else if (y <= 9d+122) then
        tmp = (log(y) * x) - z
    else
        tmp = (0.0d0 - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.95e-220) {
		tmp = Math.log(t) - z;
	} else if (y <= 9e+122) {
		tmp = (Math.log(y) * x) - z;
	} else {
		tmp = (0.0 - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.95e-220:
		tmp = math.log(t) - z
	elif y <= 9e+122:
		tmp = (math.log(y) * x) - z
	else:
		tmp = (0.0 - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.95e-220)
		tmp = Float64(log(t) - z);
	elseif (y <= 9e+122)
		tmp = Float64(Float64(log(y) * x) - z);
	else
		tmp = Float64(Float64(0.0 - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.95e-220)
		tmp = log(t) - z;
	elseif (y <= 9e+122)
		tmp = (log(y) * x) - z;
	else
		tmp = (0.0 - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.95e-220], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 9e+122], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.9499999999999998e-220

   1. Initial program 99.7%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - z\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right) \]

      5. log-lowering-log.f64 67.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right) \]

   7. Simplified 67.7%

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

   8. Taylor expanded in y around 0

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

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

         \[\leadsto \mathsf{\_.f64}\left(\log t, \color{blue}{z}\right) \]

      2. log-lowering-log.f64 67.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right) \]

   10. Simplified 67.7%

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

   if 2.9499999999999998e-220 < y < 8.99999999999999995e122

   1. Initial program 99.8%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.8%

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

      1. *-commutative N/A

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

      2. fma-define N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(\log y, \color{blue}{x}, \left(\left(\log t - z\right) - y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\left(\log t - z\right) - y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      7. log-lowering-log.f64 99.8%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \color{blue}{\left(-1 \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(z\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(0 - z\right)\right) \]

      3. --lowering--.f64 74.3%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(0, z\right)\right) \]

   9. Simplified 74.3%

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

       1. sub0-neg N/A

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

       2. +-lft-identity N/A

          \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\left(0 + z\right)\right)\right) \]

       3. flip3-+ N/A

          \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       4. sqr-pow N/A

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

       5. pow-prod-down N/A

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

       6. sqr-neg N/A

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

       7. sub0-neg N/A

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

       8. sub0-neg N/A

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

       9. pow-prod-down N/A

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

       10. sqr-pow N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{{0}^{3} + {\left(0 - z\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       11. metadata-eval N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 + {\left(0 - z\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       12. sub0-neg N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 + {\left(\mathsf{neg}\left(z\right)\right)}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       13. cube-neg N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 + \left(\mathsf{neg}\left({z}^{3}\right)\right)}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)}\right)\right) \]

       15. mul0-lft N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0\right)}\right)\right) \]

       16. fmm-def N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, \mathsf{neg}\left(0\right)\right)}\right)\right) \]

       17. metadata-eval N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0\right)}\right)\right) \]

       18. mul0-lft N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0 \cdot z\right)}\right)\right) \]

       19. fma-define N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right)\right) \]

       20. metadata-eval N/A

           \[\leadsto \log y \cdot x + \left(\mathsf{neg}\left(\frac{{0}^{3} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right)\right) \]

   11. Applied egg-rr 74.3%

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

   if 8.99999999999999995e122 < y

   1. Initial program 99.9%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - z\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right) \]

      5. log-lowering-log.f64 87.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right) \]

   7. Simplified 87.3%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot z\right)}, y\right) \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

      3. --lowering--.f64 87.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

   10. Simplified 87.3%

       \[\leadsto \color{blue}{\left(0 - z\right)} - y \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.95 \cdot 10^{-220}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+122}:\\ \;\;\;\;\log y \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+129}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -4.8e+169) t_1 (if (<= x 1.25e+129) (- (- 0.0 z) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -4.8e+169) {
		tmp = t_1;
	} else if (x <= 1.25e+129) {
		tmp = (0.0 - z) - 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 = log(y) * x
    if (x <= (-4.8d+169)) then
        tmp = t_1
    else if (x <= 1.25d+129) then
        tmp = (0.0d0 - z) - 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 = Math.log(y) * x;
	double tmp;
	if (x <= -4.8e+169) {
		tmp = t_1;
	} else if (x <= 1.25e+129) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -4.8e+169:
		tmp = t_1
	elif x <= 1.25e+129:
		tmp = (0.0 - z) - y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -4.8e+169)
		tmp = t_1;
	elseif (x <= 1.25e+129)
		tmp = Float64(Float64(0.0 - z) - y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	tmp = 0.0;
	if (x <= -4.8e+169)
		tmp = t_1;
	elseif (x <= 1.25e+129)
		tmp = (0.0 - z) - y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -4.8e+169], t$95$1, If[LessEqual[x, 1.25e+129], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7999999999999997e169 or 1.2500000000000001e129 < x

   1. Initial program 99.6%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\log y}\right) \]

      2. log-lowering-log.f64 77.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right) \]

   7. Simplified 77.5%

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

   if -4.7999999999999997e169 < x < 1.2500000000000001e129

   1. Initial program 99.9%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - z\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right) \]

      5. log-lowering-log.f64 90.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right) \]

   7. Simplified 90.4%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot z\right)}, y\right) \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

      3. --lowering--.f64 71.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

   10. Simplified 71.1%

       \[\leadsto \color{blue}{\left(0 - z\right)} - y \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+169}:\\ \;\;\;\;\log y \cdot x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+129}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.5% accurate, 26.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.6 \cdot 10^{+101}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 9.6e+101) (- 0.0 z) (- 0.0 y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.6e+101) {
		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 <= 9.6d+101) 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 <= 9.6e+101) {
		tmp = 0.0 - z;
	} else {
		tmp = 0.0 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9.6e+101:
		tmp = 0.0 - z
	else:
		tmp = 0.0 - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9.6e+101)
		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 <= 9.6e+101)
		tmp = 0.0 - z;
	else
		tmp = 0.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9.6e+101], N[(0.0 - z), $MachinePrecision], N[(0.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.59999999999999953e101

   1. Initial program 99.8%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 36.6%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   7. Simplified 36.6%

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

   if 9.59999999999999953e101 < y

   1. Initial program 99.9%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. sub-neg N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

      17. log-lowering-log.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 69.6%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

   7. Simplified 69.6%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 69.6%

         \[\leadsto \mathsf{neg.f64}\left(y\right) \]

   9. Applied egg-rr 69.6%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9.6 \cdot 10^{+101}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.9% accurate, 41.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- N/A

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

   2. associate--l- N/A

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

   3. sub-neg N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

   8. distribute-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

   9. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

   11. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

   12. associate-+l- N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

   13. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

   15. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

   17. log-lowering-log.f64 99.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

3. Simplified 99.8%

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

5. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate--r+ N/A

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

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

      \[\leadsto \mathsf{\_.f64}\left(\left(\log t - z\right), \color{blue}{y}\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right) \]

   5. log-lowering-log.f64 71.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right) \]

7. Simplified 71.2%

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

8. Taylor expanded in z around inf

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot z\right)}, y\right) \]
9. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

   3. --lowering--.f64 57.1%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

10. Simplified 57.1%

    \[\leadsto \color{blue}{\left(0 - z\right)} - y \]
11. Add Preprocessing

Alternative 11: 30.0% accurate, 69.7× 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 99.8%

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

   1. associate-+l- N/A

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

   2. associate--l- N/A

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

   3. sub-neg N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

   8. distribute-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

   9. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

   11. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

   12. associate-+l- N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

   13. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

   15. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

   17. log-lowering-log.f64 99.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

3. Simplified 99.8%

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

5. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

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

   3. --lowering--.f64 31.0%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

7. Simplified 31.0%

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

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 31.0%

      \[\leadsto \mathsf{neg.f64}\left(y\right) \]

9. Applied egg-rr 31.0%

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

10. Final simplification 31.0%

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

Alternative 12: 2.3% accurate, 209.0× 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 99.8%

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

   1. associate-+l- N/A

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

   2. associate--l- N/A

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

   3. sub-neg N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\mathsf{neg}\left(\left(y + \left(z - \log t\right)\right)\right)\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(z - \log t\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(z - \log t\right)}\right)\right)\right)\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\mathsf{neg}\left(\left(\left(z - \log t\right) + y\right)\right)\right)\right) \]

   8. distribute-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

   9. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right) - \color{blue}{y}\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\left(z - \log t\right)\right)\right), \color{blue}{y}\right)\right) \]

   11. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(0 - \left(z - \log t\right)\right), y\right)\right) \]

   12. associate-+l- N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(0 - z\right) + \log t\right), y\right)\right) \]

   13. neg-sub0 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log t\right), y\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t + \left(\mathsf{neg}\left(z\right)\right)\right), y\right)\right) \]

   15. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\left(\log t - z\right), y\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, z\right), y\right)\right) \]

   17. log-lowering-log.f64 99.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), z\right), y\right)\right) \]

3. Simplified 99.8%

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

5. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

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

   3. --lowering--.f64 31.0%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

7. Simplified 31.0%

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

   1. flip3-- N/A

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

   2. metadata-eval N/A

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

   3. sub-neg N/A

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

   4. metadata-eval N/A

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

   5. cube-neg N/A

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

   6. sub0-neg N/A

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

   7. sqr-pow N/A

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

   8. pow-prod-down N/A

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

   9. sub0-neg N/A

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

   10. sub0-neg N/A

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

   11. sqr-neg N/A

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

   12. pow-prod-down N/A

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

   13. sqr-pow N/A

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

   14. fma-define N/A

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

   15. mul0-lft N/A

       \[\leadsto \frac{{0}^{3} + {y}^{3}}{0 \cdot 0 + \mathsf{fma}\left(y, y, 0\right)} \]

   16. metadata-eval N/A

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

   17. fmm-def N/A

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

   18. mul0-lft N/A

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

   19. flip3-+ N/A

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

   20. +-lft-identity 2.2%

       \[\leadsto y \]

9. Applied egg-rr 2.2%

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

Reproduce

herbie shell --seed 2024152 
(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)))