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

Percentage Accurate: 99.9% → 99.9%

Time: 8.9s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. remove-double-neg N/A

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

   4. mul-1-neg N/A

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

   5. *-commutative N/A

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

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

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

   7. metadata-eval N/A

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

   8. cancel-sign-sub N/A

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

   9. mul-1-neg N/A

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

   10. *-inverses N/A

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

   11. associate-/l* N/A

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

   12. associate-*l/ N/A

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

   13. associate-*r/ N/A

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

   14. sub-neg N/A

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

   15. *-commutative N/A

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

   16. lower-fma.f64 N/A

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

5. Applied rewrites 99.8%

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

Alternative 2: 67.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+84}:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+93}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)) (t_2 (- t_1 y)))
   (if (<= t_2 -1e+84) (- y) (if (<= t_2 5e+93) (- (log t) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+84) {
		tmp = -y;
	} else if (t_2 <= 5e+93) {
		tmp = log(t) - 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) :: t_2
    real(8) :: tmp
    t_1 = log(y) * x
    t_2 = t_1 - y
    if (t_2 <= (-1d+84)) then
        tmp = -y
    else if (t_2 <= 5d+93) then
        tmp = log(t) - 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 = Math.log(y) * x;
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+84) {
		tmp = -y;
	} else if (t_2 <= 5e+93) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	t_2 = t_1 - y
	tmp = 0
	if t_2 <= -1e+84:
		tmp = -y
	elif t_2 <= 5e+93:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (t_2 <= -1e+84)
		tmp = Float64(-y);
	elseif (t_2 <= 5e+93)
		tmp = Float64(log(t) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -1e+84)
		tmp = -y;
	elseif (t_2 <= 5e+93)
		tmp = log(t) - z;
	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]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+84], (-y), If[LessEqual[t$95$2, 5e+93], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.00000000000000006e84

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. metadata-eval N/A

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

      8. cancel-sign-sub N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. associate-*r/ N/A

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

      14. sub-neg N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 49.7

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

   8. Applied rewrites 49.7%

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

   if -1.00000000000000006e84 < (-.f64 (*.f64 x (log.f64 y)) y) < 5.0000000000000001e93

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 93.0

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

   5. Applied rewrites 93.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \log t - z \]
   7. Step-by-step derivation

   8. Applied rewrites 81.5%

      \[\leadsto \log t - z \]

   if 5.0000000000000001e93 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.6%

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

      1. lift-+.f64 N/A

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

      2. flip3-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip3-+ N/A

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

   4. Applied rewrites 99.5%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 66.4

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

   7. Applied rewrites 66.4%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log y \cdot x - y \leq -1 \cdot 10^{+84}:\\ \;\;\;\;-y\\ \mathbf{elif}\;\log y \cdot x - y \leq 5 \cdot 10^{+93}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\log t - y\right) - z\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (log t) y) z)))
   (if (<= z -1.12e+74)
     t_1
     (if (<= z 1.65e+23) (- (fma (log y) x (log t)) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (log(t) - y) - z;
	double tmp;
	if (z <= -1.12e+74) {
		tmp = t_1;
	} else if (z <= 1.65e+23) {
		tmp = fma(log(y), x, log(t)) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(log(t) - y) - z)
	tmp = 0.0
	if (z <= -1.12e+74)
		tmp = t_1;
	elseif (z <= 1.65e+23)
		tmp = Float64(fma(log(y), x, log(t)) - y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[z, -1.12e+74], t$95$1, If[LessEqual[z, 1.65e+23], N[(N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12000000000000003e74 or 1.65000000000000015e23 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if -1.12000000000000003e74 < z < 1.65000000000000015e23

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 97.2

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

   5. Applied rewrites 97.2%

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

Alternative 4: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6.6e+59)
   (fma (log y) x (- (log t) z))
   (fma (log y) x (- (log t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.6e+59) {
		tmp = fma(log(y), x, (log(t) - z));
	} else {
		tmp = fma(log(y), x, (log(t) - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6.6e+59)
		tmp = fma(log(y), x, Float64(log(t) - z));
	else
		tmp = fma(log(y), x, Float64(log(t) - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6.6e+59], N[(N[Log[y], $MachinePrecision] * x + N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.5999999999999999e59

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. metadata-eval N/A

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

      8. cancel-sign-sub N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. associate-*r/ N/A

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

      14. sub-neg N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-log.f64 96.2

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

   8. Applied rewrites 96.2%

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

   if 6.5999999999999999e59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. metadata-eval N/A

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

      8. cancel-sign-sub N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. associate-*r/ N/A

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

      14. sub-neg N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\log y, x, \log t - y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 82.8%

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

Alternative 5: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6.6e+59)
   (- (fma (log y) x (log t)) z)
   (fma (log y) x (- (log t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.6e+59) {
		tmp = fma(log(y), x, log(t)) - z;
	} else {
		tmp = fma(log(y), x, (log(t) - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6.6e+59)
		tmp = Float64(fma(log(y), x, log(t)) - z);
	else
		tmp = fma(log(y), x, Float64(log(t) - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6.6e+59], N[(N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.5999999999999999e59

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 96.2

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

   5. Applied rewrites 96.2%

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

   if 6.5999999999999999e59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. metadata-eval N/A

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

      8. cancel-sign-sub N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. associate-*r/ N/A

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

      14. sub-neg N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\log y, x, \log t - y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 82.8%

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

Alternative 6: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\log y, x, \log t\right)\\ \mathbf{if}\;y \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;t\_1 - z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (log y) x (log t))))
   (if (<= y 6.6e+59) (- t_1 z) (- t_1 y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(log(y), x, log(t));
	double tmp;
	if (y <= 6.6e+59) {
		tmp = t_1 - z;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(log(y), x, log(t))
	tmp = 0.0
	if (y <= 6.6e+59)
		tmp = Float64(t_1 - z);
	else
		tmp = Float64(t_1 - y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 6.6e+59], N[(t$95$1 - z), $MachinePrecision], N[(t$95$1 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 6.5999999999999999e59

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 96.2

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

   5. Applied rewrites 96.2%

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

   if 6.5999999999999999e59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 82.8

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

   5. Applied rewrites 82.8%

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

Alternative 7: 83.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+96}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -6.2e+115) t_1 (if (<= x 4.4e+96) (- (- (log t) y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -6.2e+115) {
		tmp = t_1;
	} else if (x <= 4.4e+96) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(y) * x
    if (x <= (-6.2d+115)) then
        tmp = t_1
    else if (x <= 4.4d+96) then
        tmp = (log(t) - y) - z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * x;
	double tmp;
	if (x <= -6.2e+115) {
		tmp = t_1;
	} else if (x <= 4.4e+96) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -6.2e+115:
		tmp = t_1
	elif x <= 4.4e+96:
		tmp = (math.log(t) - y) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -6.2e+115)
		tmp = t_1;
	elseif (x <= 4.4e+96)
		tmp = Float64(Float64(log(t) - y) - z);
	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 <= -6.2e+115)
		tmp = t_1;
	elseif (x <= 4.4e+96)
		tmp = (log(t) - y) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -6.2e+115], t$95$1, If[LessEqual[x, 4.4e+96], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000001e115 or 4.3999999999999998e96 < x

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. flip3-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip3-+ N/A

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

   4. Applied rewrites 99.5%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 68.2

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

   7. Applied rewrites 68.2%

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

   if -6.2000000000000001e115 < x < 4.3999999999999998e96

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 91.8

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

   5. Applied rewrites 91.8%

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

Alternative 8: 60.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 6.6e+59) (- (log t) z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.6e+59) {
		tmp = log(t) - 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 <= 6.6d+59) then
        tmp = log(t) - 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 <= 6.6e+59) {
		tmp = Math.log(t) - z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 6.6e+59:
		tmp = math.log(t) - z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6.6e+59)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 6.6e+59)
		tmp = log(t) - z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6.6e+59], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 6.5999999999999999e59

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 96.2

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

   5. Applied rewrites 96.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \log t - z \]
   7. Step-by-step derivation

   8. Applied rewrites 63.6%

      \[\leadsto \log t - z \]

   if 6.5999999999999999e59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. metadata-eval N/A

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

      8. cancel-sign-sub N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. associate-*r/ N/A

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

      14. sub-neg N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 60.3

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

   8. Applied rewrites 60.3%

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

Alternative 9: 47.8% accurate, 23.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+59}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 6e+59) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6e+59) {
		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 <= 6d+59) 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 <= 6e+59) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 6e+59:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6e+59)
		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 <= 6e+59)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6e+59], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 6.0000000000000001e59

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 43.0

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

   5. Applied rewrites 43.0%

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

   if 6.0000000000000001e59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. metadata-eval N/A

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

      8. cancel-sign-sub N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. associate-*r/ N/A

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

      14. sub-neg N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 60.3

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

   8. Applied rewrites 60.3%

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

Alternative 10: 29.9% accurate, 71.7× 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 99.8%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. remove-double-neg N/A

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

   4. mul-1-neg N/A

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

   5. *-commutative N/A

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

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

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

   7. metadata-eval N/A

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

   8. cancel-sign-sub N/A

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

   9. mul-1-neg N/A

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

   10. *-inverses N/A

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

   11. associate-/l* N/A

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

   12. associate-*l/ N/A

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

   13. associate-*r/ N/A

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

   14. sub-neg N/A

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

   15. *-commutative N/A

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

   16. lower-fma.f64 N/A

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

5. Applied rewrites 99.8%

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

6. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 27.0

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

8. Applied rewrites 27.0%

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

Reproduce

herbie shell --seed 2024296 
(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)))