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

Percentage Accurate: 99.9% → 99.9%

Time: 11.7s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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- 99.9%

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

   2. sub-neg 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--l+ 99.9%

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

   5. sub-neg 99.9%

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

   6. +-commutative 99.9%

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

   7. unsub-neg 99.9%

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

   8. fma-undefine 99.9%

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

   9. neg-sub0 99.9%

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

   10. associate-+l- 99.9%

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

   11. neg-sub0 99.9%

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

   12. +-commutative 99.9%

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

   13. unsub-neg 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 90.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + t\_1\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -1e+147)
     t_2
     (if (<= t_2 -2e-11) (- (- (log t) z) y) (- (+ (log t) t_1) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+147) {
		tmp = t_2;
	} else if (t_2 <= -2e-11) {
		tmp = (log(t) - z) - y;
	} else {
		tmp = (log(t) + 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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-1d+147)) then
        tmp = t_2
    else if (t_2 <= (-2d-11)) then
        tmp = (log(t) - z) - y
    else
        tmp = (log(t) + 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 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+147) {
		tmp = t_2;
	} else if (t_2 <= -2e-11) {
		tmp = (Math.log(t) - z) - y;
	} else {
		tmp = (Math.log(t) + t_1) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if t_2 <= -1e+147:
		tmp = t_2
	elif t_2 <= -2e-11:
		tmp = (math.log(t) - z) - y
	else:
		tmp = (math.log(t) + t_1) - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (t_2 <= -1e+147)
		tmp = t_2;
	elseif (t_2 <= -2e-11)
		tmp = Float64(Float64(log(t) - z) - y);
	else
		tmp = Float64(Float64(log(t) + t_1) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -1e+147)
		tmp = t_2;
	elseif (t_2 <= -2e-11)
		tmp = (log(t) - z) - y;
	else
		tmp = (log(t) + t_1) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+147], t$95$2, If[LessEqual[t$95$2, -2e-11], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -9.9999999999999998e146

   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- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 88.2%

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

   if -9.9999999999999998e146 < (-.f64 (*.f64 x (log.f64 y)) y) < -1.99999999999999988e-11

   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- 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. unsub-neg 99.9%

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

      8. fma-undefine 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. neg-sub0 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 87.0%

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

   if -1.99999999999999988e-11 < (-.f64 (*.f64 x (log.f64 y)) y)

   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- 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. unsub-neg 99.8%

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

      8. fma-undefine 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. neg-sub0 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.8%

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

Alternative 3: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+41} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (or (<= t_1 -1e+41) (not (<= t_1 5e-7))) t_1 (- (log t) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if ((t_1 <= -1e+41) || !(t_1 <= 5e-7)) {
		tmp = t_1;
	} else {
		tmp = log(t) - 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 = (x * log(y)) - y
    if ((t_1 <= (-1d+41)) .or. (.not. (t_1 <= 5d-7))) then
        tmp = t_1
    else
        tmp = log(t) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - y;
	double tmp;
	if ((t_1 <= -1e+41) || !(t_1 <= 5e-7)) {
		tmp = t_1;
	} else {
		tmp = Math.log(t) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if (t_1 <= -1e+41) or not (t_1 <= 5e-7):
		tmp = t_1
	else:
		tmp = math.log(t) - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if ((t_1 <= -1e+41) || !(t_1 <= 5e-7))
		tmp = t_1;
	else
		tmp = Float64(log(t) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if ((t_1 <= -1e+41) || ~((t_1 <= 5e-7)))
		tmp = t_1;
	else
		tmp = log(t) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+41], N[Not[LessEqual[t$95$1, 5e-7]], $MachinePrecision]], t$95$1, N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.00000000000000001e41 or 4.99999999999999977e-7 < (-.f64 (*.f64 x (log.f64 y)) y)

   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- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 83.8%

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

   if -1.00000000000000001e41 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.99999999999999977e-7

   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- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 75.3%

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

      1. fma-define 75.3%

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

      2. log-rec 75.3%

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

      3. mul-1-neg 75.3%

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

      4. associate-/l* 75.2%

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

      5. mul-1-neg 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in x around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. associate--r+ 74.1%

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

      3. div-sub 74.1%

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

   10. Simplified 74.1%

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

   11. Taylor expanded in y around 0 90.2%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -1 \cdot 10^{+41} \lor \neg \left(x \cdot \log y - y \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-32}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -1e+147)
     t_2
     (if (<= t_2 5e-32) (- (- (log t) z) y) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+147) {
		tmp = t_2;
	} else if (t_2 <= 5e-32) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-1d+147)) then
        tmp = t_2
    else if (t_2 <= 5d-32) 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 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+147) {
		tmp = t_2;
	} else if (t_2 <= 5e-32) {
		tmp = (Math.log(t) - z) - y;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if t_2 <= -1e+147:
		tmp = t_2
	elif t_2 <= 5e-32:
		tmp = (math.log(t) - z) - y
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (t_2 <= -1e+147)
		tmp = t_2;
	elseif (t_2 <= 5e-32)
		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 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -1e+147)
		tmp = t_2;
	elseif (t_2 <= 5e-32)
		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[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+147], t$95$2, If[LessEqual[t$95$2, 5e-32], 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 (-.f64 (*.f64 x (log.f64 y)) y) < -9.9999999999999998e146

   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- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 88.2%

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

   if -9.9999999999999998e146 < (-.f64 (*.f64 x (log.f64 y)) y) < 5e-32

   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- 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. unsub-neg 99.9%

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

      8. fma-undefine 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. neg-sub0 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 93.4%

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

   if 5e-32 < (-.f64 (*.f64 x (log.f64 y)) y)

   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- 99.7%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.2%

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

Alternative 5: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-32}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -1e+41) t_2 (if (<= t_2 5e-32) (- (log t) z) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+41) {
		tmp = t_2;
	} else if (t_2 <= 5e-32) {
		tmp = log(t) - z;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-1d+41)) then
        tmp = t_2
    else if (t_2 <= 5d-32) then
        tmp = log(t) - z
    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 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+41) {
		tmp = t_2;
	} else if (t_2 <= 5e-32) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if t_2 <= -1e+41:
		tmp = t_2
	elif t_2 <= 5e-32:
		tmp = math.log(t) - z
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (t_2 <= -1e+41)
		tmp = t_2;
	elseif (t_2 <= 5e-32)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -1e+41)
		tmp = t_2;
	elseif (t_2 <= 5e-32)
		tmp = log(t) - z;
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+41], t$95$2, If[LessEqual[t$95$2, 5e-32], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.00000000000000001e41

   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- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 83.9%

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

   if -1.00000000000000001e41 < (-.f64 (*.f64 x (log.f64 y)) y) < 5e-32

   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- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 78.1%

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

      1. fma-define 78.1%

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

      2. log-rec 78.1%

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

      3. mul-1-neg 78.1%

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

      4. associate-/l* 78.1%

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

      5. mul-1-neg 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in x around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. associate--r+ 76.9%

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

      3. div-sub 77.0%

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

   10. Simplified 77.0%

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

   11. Taylor expanded in y around 0 89.8%

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

   if 5e-32 < (-.f64 (*.f64 x (log.f64 y)) y)

   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- 99.7%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.2%

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

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

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(x * log(y)) - Float64(y + Float64(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[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + N[(z - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

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

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 8: 62.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-45}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{-1}{x} - \frac{y}{x \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.7e+17)
     t_1
     (if (<= x 9.5e-45)
       (- (log t) z)
       (if (<= x 2.6e+138) (* x (* z (- (/ -1.0 x) (/ y (* x z))))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.7e+17) {
		tmp = t_1;
	} else if (x <= 9.5e-45) {
		tmp = log(t) - z;
	} else if (x <= 2.6e+138) {
		tmp = x * (z * ((-1.0 / x) - (y / (x * z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.7d+17)) then
        tmp = t_1
    else if (x <= 9.5d-45) then
        tmp = log(t) - z
    else if (x <= 2.6d+138) then
        tmp = x * (z * (((-1.0d0) / x) - (y / (x * z))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -1.7e+17) {
		tmp = t_1;
	} else if (x <= 9.5e-45) {
		tmp = Math.log(t) - z;
	} else if (x <= 2.6e+138) {
		tmp = x * (z * ((-1.0 / x) - (y / (x * z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.7e+17:
		tmp = t_1
	elif x <= 9.5e-45:
		tmp = math.log(t) - z
	elif x <= 2.6e+138:
		tmp = x * (z * ((-1.0 / x) - (y / (x * z))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.7e+17)
		tmp = t_1;
	elseif (x <= 9.5e-45)
		tmp = Float64(log(t) - z);
	elseif (x <= 2.6e+138)
		tmp = Float64(x * Float64(z * Float64(Float64(-1.0 / x) - Float64(y / Float64(x * z)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.7e+17)
		tmp = t_1;
	elseif (x <= 9.5e-45)
		tmp = log(t) - z;
	elseif (x <= 2.6e+138)
		tmp = x * (z * ((-1.0 / x) - (y / (x * z))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+17], t$95$1, If[LessEqual[x, 9.5e-45], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 2.6e+138], N[(x * N[(z * N[(N[(-1.0 / x), $MachinePrecision] - N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e17 or 2.6000000000000001e138 < x

   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- 99.7%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

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

      1. add-cube-cbrt 98.6%

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

      2. fmm-def 98.6%

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

      3. pow2 98.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{2}}, \sqrt[3]{x \cdot \log y}, -\left(y + \left(z - \log t\right)\right)\right) \]

   6. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x \cdot \log y}\right)}^{2}, \sqrt[3]{x \cdot \log y}, -\left(y + \left(z - \log t\right)\right)\right)} \]

   7. Taylor expanded in x around inf 65.0%

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

   if -1.7e17 < x < 9.5000000000000002e-45

   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- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 85.1%

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

      1. fma-define 85.1%

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

      2. log-rec 85.1%

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

      3. mul-1-neg 85.1%

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

      4. associate-/l* 85.1%

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

      5. mul-1-neg 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in x around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate--r+ 84.3%

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

      3. div-sub 84.4%

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

   10. Simplified 84.4%

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

   11. Taylor expanded in y around 0 63.0%

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

   if 9.5000000000000002e-45 < x < 2.6000000000000001e138

   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- 99.9%

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

      2. sub-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. unsub-neg 99.9%

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

      8. fma-undefine 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. neg-sub0 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 97.2%

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

      1. associate--l+ 97.2%

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

      2. +-commutative 97.2%

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

      3. associate--r+ 97.2%

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

      4. div-sub 97.2%

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

      5. div-sub 97.2%

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

      6. associate--l- 97.2%

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

      7. +-commutative 97.2%

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

      8. associate--r+ 97.2%

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

   7. Simplified 97.2%

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

   8. Taylor expanded in z around -inf 88.9%

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

      1. mul-1-neg 88.9%

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

      2. *-commutative 88.9%

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

      3. distribute-rgt-neg-in 88.9%

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

      4. +-commutative 88.9%

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

      5. mul-1-neg 88.9%

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

      6. unsub-neg 88.9%

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

      7. associate--l+ 88.9%

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

      8. div-sub 88.9%

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

   10. Simplified 88.9%

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

   11. Taylor expanded in y around inf 64.0%

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

       1. associate-*r/ 64.0%

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

       2. mul-1-neg 64.0%

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

       3. *-commutative 64.0%

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

   13. Simplified 64.0%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-45}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{-1}{x} - \frac{y}{x \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 4.8e+70) (* x (log y)) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.8e+70) {
		tmp = x * log(y);
	} else {
		tmp = -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 <= 4.8d+70) then
        tmp = x * log(y)
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.8e+70) {
		tmp = x * Math.log(y);
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4.8e+70:
		tmp = x * math.log(y)
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.8e+70)
		tmp = Float64(x * log(y));
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4.8e+70)
		tmp = x * log(y);
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4.8e+70], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 4.79999999999999974e70

   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- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

      1. add-cube-cbrt 99.1%

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

      2. fmm-def 99.1%

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

      3. pow2 99.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{2}}, \sqrt[3]{x \cdot \log y}, -\left(y + \left(z - \log t\right)\right)\right) \]

   6. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x \cdot \log y}\right)}^{2}, \sqrt[3]{x \cdot \log y}, -\left(y + \left(z - \log t\right)\right)\right)} \]

   7. Taylor expanded in x around inf 43.8%

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

   if 4.79999999999999974e70 < y

   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- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 70.3%

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

      1. neg-mul-1 70.3%

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

   7. Simplified 70.3%

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

Alternative 10: 48.4% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+51}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2.4e+51) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.4e+51) {
		tmp = -z;
	} else {
		tmp = -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 <= 2.4d+51) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.4e+51) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.4e+51:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.4e+51)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.4e+51)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.4e+51], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.3999999999999999e51

   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- 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. unsub-neg 99.8%

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

      8. fma-undefine 99.8%

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

      9. neg-sub0 99.8%

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

      10. associate-+l- 99.8%

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

      11. neg-sub0 99.8%

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

      12. +-commutative 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 34.0%

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

      1. neg-mul-1 34.0%

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

   7. Simplified 34.0%

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

   if 2.3999999999999999e51 < y

   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- 100.0%

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

      2. sub-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-undefine 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 68.9%

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

      1. neg-mul-1 68.9%

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

   7. Simplified 68.9%

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

Alternative 11: 29.9% accurate, 104.5× 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 Float64(-y)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-y)

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. sub-neg 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--l+ 99.9%

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

   5. sub-neg 99.9%

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

   6. +-commutative 99.9%

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

   7. unsub-neg 99.9%

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

   8. fma-undefine 99.9%

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

   9. neg-sub0 99.9%

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

   10. associate-+l- 99.9%

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

   11. neg-sub0 99.9%

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

   12. +-commutative 99.9%

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

   13. unsub-neg 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 30.2%

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

   1. neg-mul-1 30.2%

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

7. Simplified 30.2%

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

Alternative 12: 2.2% accurate, 209.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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- 99.9%

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

   2. sub-neg 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--l+ 99.9%

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

   5. sub-neg 99.9%

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

   6. +-commutative 99.9%

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

   7. unsub-neg 99.9%

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

   8. fma-undefine 99.9%

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

   9. neg-sub0 99.9%

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

   10. associate-+l- 99.9%

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

   11. neg-sub0 99.9%

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

   12. +-commutative 99.9%

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

   13. unsub-neg 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 76.3%

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

   1. fma-define 76.3%

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

   2. log-rec 76.3%

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

   3. mul-1-neg 76.3%

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

   4. associate-/l* 76.3%

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

   5. mul-1-neg 76.3%

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

7. Simplified 76.3%

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

8. Taylor expanded in z around inf 17.5%

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

   1. associate-*r/ 17.5%

      \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot z}{y}} \]

   2. neg-mul-1 17.5%

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

10. Simplified 17.5%

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

    1. clear-num 17.4%

       \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{y}{-z}}} \]

    2. inv-pow 17.4%

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

    3. add-sqr-sqrt 8.3%

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

    4. sqrt-unprod 4.6%

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

    5. sqr-neg 4.6%

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

    6. sqrt-unprod 0.9%

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

    7. add-sqr-sqrt 2.2%

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

12. Applied egg-rr 2.2%

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

    1. unpow-1 2.2%

       \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{y}{z}}} \]

14. Simplified 2.2%

    \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{y}{z}}} \]

15. Taylor expanded in y around 0 2.2%

    \[\leadsto \color{blue}{z} \]
16. Add Preprocessing

Alternative 13: 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 99.9%

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

   1. associate-+l- 99.9%

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

   2. sub-neg 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--l+ 99.9%

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

   5. sub-neg 99.9%

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

   6. +-commutative 99.9%

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

   7. unsub-neg 99.9%

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

   8. fma-undefine 99.9%

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

   9. neg-sub0 99.9%

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

   10. associate-+l- 99.9%

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

   11. neg-sub0 99.9%

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

   12. +-commutative 99.9%

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

   13. unsub-neg 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 30.2%

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

   1. neg-mul-1 30.2%

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

7. Simplified 30.2%

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

   1. add-sqr-sqrt 0.0%

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

   2. sqrt-unprod 2.1%

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

   3. sqr-neg 2.1%

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

   4. sqrt-unprod 2.2%

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

   5. add-sqr-sqrt 2.2%

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

   6. *-un-lft-identity 2.2%

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

9. Applied egg-rr 2.2%

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

    1. *-lft-identity 2.2%

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

11. Simplified 2.2%

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

Reproduce

herbie shell --seed 2024170 
(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)))