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

Percentage Accurate: 99.9% → 99.9%

Time: 11.9s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative N/A

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

   2. associate--l- N/A

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

   3. associate-+r- N/A

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

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

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

   5. +-commutative N/A

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

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

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

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

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

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

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

   9. +-lowering-+.f64 99.9

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

4. Applied egg-rr 99.9%

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

Alternative 2: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y - y\right) - z\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+279}:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+229}:\\ \;\;\;\;-z\\ \mathbf{elif}\;t\_1 \leq -4000000000000:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_1 \leq 10^{-5}:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (* x (log y)) y) z)))
   (if (<= t_1 -5e+279)
     (- y)
     (if (<= t_1 -1e+229)
       (- z)
       (if (<= t_1 -4000000000000.0)
         (- y)
         (if (<= t_1 1e-5) (log t) (- z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * log(y)) - y) - z;
	double tmp;
	if (t_1 <= -5e+279) {
		tmp = -y;
	} else if (t_1 <= -1e+229) {
		tmp = -z;
	} else if (t_1 <= -4000000000000.0) {
		tmp = -y;
	} else if (t_1 <= 1e-5) {
		tmp = log(t);
	} else {
		tmp = -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) - z
    if (t_1 <= (-5d+279)) then
        tmp = -y
    else if (t_1 <= (-1d+229)) then
        tmp = -z
    else if (t_1 <= (-4000000000000.0d0)) then
        tmp = -y
    else if (t_1 <= 1d-5) then
        tmp = log(t)
    else
        tmp = -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) - z;
	double tmp;
	if (t_1 <= -5e+279) {
		tmp = -y;
	} else if (t_1 <= -1e+229) {
		tmp = -z;
	} else if (t_1 <= -4000000000000.0) {
		tmp = -y;
	} else if (t_1 <= 1e-5) {
		tmp = Math.log(t);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * math.log(y)) - y) - z
	tmp = 0
	if t_1 <= -5e+279:
		tmp = -y
	elif t_1 <= -1e+229:
		tmp = -z
	elif t_1 <= -4000000000000.0:
		tmp = -y
	elif t_1 <= 1e-5:
		tmp = math.log(t)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * log(y)) - y) - z)
	tmp = 0.0
	if (t_1 <= -5e+279)
		tmp = Float64(-y);
	elseif (t_1 <= -1e+229)
		tmp = Float64(-z);
	elseif (t_1 <= -4000000000000.0)
		tmp = Float64(-y);
	elseif (t_1 <= 1e-5)
		tmp = log(t);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * log(y)) - y) - z;
	tmp = 0.0;
	if (t_1 <= -5e+279)
		tmp = -y;
	elseif (t_1 <= -1e+229)
		tmp = -z;
	elseif (t_1 <= -4000000000000.0)
		tmp = -y;
	elseif (t_1 <= 1e-5)
		tmp = log(t);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+279], (-y), If[LessEqual[t$95$1, -1e+229], (-z), If[LessEqual[t$95$1, -4000000000000.0], (-y), If[LessEqual[t$95$1, 1e-5], N[Log[t], $MachinePrecision], (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -5.0000000000000002e279 or -9.9999999999999999e228 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -4e12

   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 inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 47.1

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

   5. Simplified 47.1%

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

   if -5.0000000000000002e279 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -9.9999999999999999e228 or 1.00000000000000008e-5 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 52.6

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

   5. Simplified 52.6%

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

   if -4e12 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 1.00000000000000008e-5

   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 inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 94.9

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

   5. Simplified 94.9%

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

   6. Taylor expanded in z around 0

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

      1. log-lowering-log.f64 94.4

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

   8. Simplified 94.4%

      \[\leadsto \color{blue}{\log t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+286}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+84}:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_2 \leq 10^{-5}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -1e+286)
     (- (log t) y)
     (if (<= t_2 -2e+253)
       t_1
       (if (<= t_2 -2e+84) (- y) (if (<= t_2 1e-5) (- (log t) z) t_1))))))

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+286) {
		tmp = log(t) - y;
	} else if (t_2 <= -2e+253) {
		tmp = t_1;
	} else if (t_2 <= -2e+84) {
		tmp = -y;
	} else if (t_2 <= 1e-5) {
		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 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-1d+286)) then
        tmp = log(t) - y
    else if (t_2 <= (-2d+253)) then
        tmp = t_1
    else if (t_2 <= (-2d+84)) then
        tmp = -y
    else if (t_2 <= 1d-5) 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 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+286) {
		tmp = Math.log(t) - y;
	} else if (t_2 <= -2e+253) {
		tmp = t_1;
	} else if (t_2 <= -2e+84) {
		tmp = -y;
	} else if (t_2 <= 1e-5) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	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+286:
		tmp = math.log(t) - y
	elif t_2 <= -2e+253:
		tmp = t_1
	elif t_2 <= -2e+84:
		tmp = -y
	elif t_2 <= 1e-5:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	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+286)
		tmp = Float64(log(t) - y);
	elseif (t_2 <= -2e+253)
		tmp = t_1;
	elseif (t_2 <= -2e+84)
		tmp = Float64(-y);
	elseif (t_2 <= 1e-5)
		tmp = Float64(log(t) - z);
	else
		tmp = t_1;
	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+286)
		tmp = log(t) - y;
	elseif (t_2 <= -2e+253)
		tmp = t_1;
	elseif (t_2 <= -2e+84)
		tmp = -y;
	elseif (t_2 <= 1e-5)
		tmp = log(t) - 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]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+286], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[t$95$2, -2e+253], t$95$1, If[LessEqual[t$95$2, -2e+84], (-y), If[LessEqual[t$95$2, 1e-5], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.00000000000000003e286

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 65.7

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

   5. Simplified 65.7%

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

   if -1.00000000000000003e286 < (-.f64 (*.f64 x (log.f64 y)) y) < -1.9999999999999999e253 or 1.00000000000000008e-5 < (-.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 83.1

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

   5. Simplified 83.1%

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

   if -1.9999999999999999e253 < (-.f64 (*.f64 x (log.f64 y)) y) < -2.00000000000000012e84

   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 inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 51.5

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

   5. Simplified 51.5%

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

   if -2.00000000000000012e84 < (-.f64 (*.f64 x (log.f64 y)) y) < 1.00000000000000008e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 83.6

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

   5. Simplified 83.6%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

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

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

      4. log-lowering-log.f64 83.6

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

   7. Applied egg-rr 83.6%

      \[\leadsto \color{blue}{\log t - z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -1 \cdot 10^{+286}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \cdot \log y - y \leq -2 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \cdot \log y - y \leq -2 \cdot 10^{+84}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \cdot \log y - y \leq 10^{-5}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+286}:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+84}:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_2 \leq 10^{-5}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -1e+286)
     (- y)
     (if (<= t_2 -2e+253)
       t_1
       (if (<= t_2 -2e+84) (- y) (if (<= t_2 1e-5) (- (log t) z) t_1))))))

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+286) {
		tmp = -y;
	} else if (t_2 <= -2e+253) {
		tmp = t_1;
	} else if (t_2 <= -2e+84) {
		tmp = -y;
	} else if (t_2 <= 1e-5) {
		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 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-1d+286)) then
        tmp = -y
    else if (t_2 <= (-2d+253)) then
        tmp = t_1
    else if (t_2 <= (-2d+84)) then
        tmp = -y
    else if (t_2 <= 1d-5) 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 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -1e+286) {
		tmp = -y;
	} else if (t_2 <= -2e+253) {
		tmp = t_1;
	} else if (t_2 <= -2e+84) {
		tmp = -y;
	} else if (t_2 <= 1e-5) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	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+286:
		tmp = -y
	elif t_2 <= -2e+253:
		tmp = t_1
	elif t_2 <= -2e+84:
		tmp = -y
	elif t_2 <= 1e-5:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	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+286)
		tmp = Float64(-y);
	elseif (t_2 <= -2e+253)
		tmp = t_1;
	elseif (t_2 <= -2e+84)
		tmp = Float64(-y);
	elseif (t_2 <= 1e-5)
		tmp = Float64(log(t) - z);
	else
		tmp = t_1;
	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+286)
		tmp = -y;
	elseif (t_2 <= -2e+253)
		tmp = t_1;
	elseif (t_2 <= -2e+84)
		tmp = -y;
	elseif (t_2 <= 1e-5)
		tmp = log(t) - 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]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+286], (-y), If[LessEqual[t$95$2, -2e+253], t$95$1, If[LessEqual[t$95$2, -2e+84], (-y), If[LessEqual[t$95$2, 1e-5], 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) < -1.00000000000000003e286 or -1.9999999999999999e253 < (-.f64 (*.f64 x (log.f64 y)) y) < -2.00000000000000012e84

   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 inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 53.7

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

   5. Simplified 53.7%

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

   if -1.00000000000000003e286 < (-.f64 (*.f64 x (log.f64 y)) y) < -1.9999999999999999e253 or 1.00000000000000008e-5 < (-.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 83.1

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

   5. Simplified 83.1%

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

   if -2.00000000000000012e84 < (-.f64 (*.f64 x (log.f64 y)) y) < 1.00000000000000008e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 83.6

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

   5. Simplified 83.6%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

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

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

      4. log-lowering-log.f64 83.6

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

   7. Applied egg-rr 83.6%

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

Alternative 5: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(t\_1 - y\right) - z\\ t_3 := t\_1 - \left(y + z\right)\\ \mathbf{if}\;t\_2 \leq -5000000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5000000000000:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- t_1 y) z)) (t_3 (- t_1 (+ y z))))
   (if (<= t_2 -5000000000000.0)
     t_3
     (if (<= t_2 5000000000000.0) (- (log t) (+ y z)) t_3))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = (t_1 - y) - z;
	double t_3 = t_1 - (y + z);
	double tmp;
	if (t_2 <= -5000000000000.0) {
		tmp = t_3;
	} else if (t_2 <= 5000000000000.0) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = (t_1 - y) - z
    t_3 = t_1 - (y + z)
    if (t_2 <= (-5000000000000.0d0)) then
        tmp = t_3
    else if (t_2 <= 5000000000000.0d0) then
        tmp = log(t) - (y + z)
    else
        tmp = t_3
    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) - z;
	double t_3 = t_1 - (y + z);
	double tmp;
	if (t_2 <= -5000000000000.0) {
		tmp = t_3;
	} else if (t_2 <= 5000000000000.0) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = (t_1 - y) - z
	t_3 = t_1 - (y + z)
	tmp = 0
	if t_2 <= -5000000000000.0:
		tmp = t_3
	elif t_2 <= 5000000000000.0:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(t_1 - y) - z)
	t_3 = Float64(t_1 - Float64(y + z))
	tmp = 0.0
	if (t_2 <= -5000000000000.0)
		tmp = t_3;
	elseif (t_2 <= 5000000000000.0)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = (t_1 - y) - z;
	t_3 = t_1 - (y + z);
	tmp = 0.0;
	if (t_2 <= -5000000000000.0)
		tmp = t_3;
	elseif (t_2 <= 5000000000000.0)
		tmp = log(t) - (y + z);
	else
		tmp = t_3;
	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[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5000000000000.0], t$95$3, If[LessEqual[t$95$2, 5000000000000.0], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -5e12 or 5e12 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l- N/A

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

      3. associate-+r- N/A

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

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

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. +-lowering-+.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 99.5

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

   7. Simplified 99.5%

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

   if -5e12 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 5e12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

      3. +-lowering-+.f64 96.9

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

   5. Simplified 96.9%

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

Alternative 6: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - \left(y + z\right)\\ \mathbf{if}\;z \leq -245:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, \log t - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) (+ y z))))
   (if (<= z -245.0)
     t_1
     (if (<= z 1.7e-5) (fma x (log y) (- (log t) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - (y + z);
	double tmp;
	if (z <= -245.0) {
		tmp = t_1;
	} else if (z <= 1.7e-5) {
		tmp = fma(x, log(y), (log(t) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - Float64(y + z))
	tmp = 0.0
	if (z <= -245.0)
		tmp = t_1;
	elseif (z <= 1.7e-5)
		tmp = fma(x, log(y), Float64(log(t) - y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -245.0], t$95$1, If[LessEqual[z, 1.7e-5], N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -245 or 1.7e-5 < z

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. associate--l- N/A

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

      3. associate-+r- N/A

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

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

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. +-lowering-+.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 99.1

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

   7. Simplified 99.1%

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

   if -245 < z < 1.7e-5

   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. +-commutative N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. log-lowering-log.f64 99.7

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

   5. Simplified 99.7%

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

Alternative 7: 99.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 420.0) (fma x (log y) (- (log t) z)) (- (* x (log y)) (+ y z))))

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 420.0], N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 420

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

      6. unsub-neg N/A

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

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

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

      8. log-lowering-log.f64 99.5

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

   5. Simplified 99.5%

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

   if 420 < y

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. associate--l- N/A

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

      3. associate-+r- N/A

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

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

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. +-lowering-+.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 99.6

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

   7. Simplified 99.6%

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

Alternative 8: 89.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \log y, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.6e+120)
   (- (* x (log y)) z)
   (if (<= x 4.2e+42) (- (log t) (+ y z)) (fma x (log y) (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e+120) {
		tmp = (x * log(y)) - z;
	} else if (x <= 4.2e+42) {
		tmp = log(t) - (y + z);
	} else {
		tmp = fma(x, log(y), -z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.6e+120)
		tmp = Float64(Float64(x * log(y)) - z);
	elseif (x <= 4.2e+42)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = fma(x, log(y), Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.6e+120], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 4.2e+42], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(x * N[Log[y], $MachinePrecision] + (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5999999999999995e120

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

      6. unsub-neg N/A

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

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

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

      8. log-lowering-log.f64 89.2

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

   5. Simplified 89.2%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 89.2

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

   8. Simplified 89.2%

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

      1. unsub-neg N/A

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

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

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

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

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

      4. log-lowering-log.f64 89.3

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

   10. Applied egg-rr 89.3%

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

   if -7.5999999999999995e120 < x < 4.19999999999999991e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

      3. +-lowering-+.f64 93.5

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

   5. Simplified 93.5%

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

   if 4.19999999999999991e42 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

      6. unsub-neg N/A

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

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

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

      8. log-lowering-log.f64 92.5

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

   5. Simplified 92.5%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 92.5

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

   8. Simplified 92.5%

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

Alternative 9: 89.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - z\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+43}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) z)))
   (if (<= x -7.6e+120) t_1 (if (<= x 1.55e+43) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - z;
	double tmp;
	if (x <= -7.6e+120) {
		tmp = t_1;
	} else if (x <= 1.55e+43) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - z
    if (x <= (-7.6d+120)) then
        tmp = t_1
    else if (x <= 1.55d+43) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - z;
	double tmp;
	if (x <= -7.6e+120) {
		tmp = t_1;
	} else if (x <= 1.55e+43) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - z
	tmp = 0
	if x <= -7.6e+120:
		tmp = t_1
	elif x <= 1.55e+43:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - z)
	tmp = 0.0
	if (x <= -7.6e+120)
		tmp = t_1;
	elseif (x <= 1.55e+43)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - z;
	tmp = 0.0;
	if (x <= -7.6e+120)
		tmp = t_1;
	elseif (x <= 1.55e+43)
		tmp = log(t) - (y + z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -7.6e+120], t$95$1, If[LessEqual[x, 1.55e+43], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5999999999999995e120 or 1.5500000000000001e43 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

      6. unsub-neg N/A

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

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

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

      8. log-lowering-log.f64 91.2

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

   5. Simplified 91.2%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 91.2

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

   8. Simplified 91.2%

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

      1. unsub-neg N/A

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

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

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

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

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

      4. log-lowering-log.f64 91.2

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

   10. Applied egg-rr 91.2%

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

   if -7.5999999999999995e120 < x < 1.5500000000000001e43

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

      3. +-lowering-+.f64 93.5

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

   5. Simplified 93.5%

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

Alternative 10: 84.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+91}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.75e+147) t_1 (if (<= x 1.45e+91) (- (log t) (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.75e+147) {
		tmp = t_1;
	} else if (x <= 1.45e+91) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.75d+147)) then
        tmp = t_1
    else if (x <= 1.45d+91) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -1.75e+147) {
		tmp = t_1;
	} else if (x <= 1.45e+91) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.75e+147:
		tmp = t_1
	elif x <= 1.45e+91:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.75e+147)
		tmp = t_1;
	elseif (x <= 1.45e+91)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.75e+147)
		tmp = t_1;
	elseif (x <= 1.45e+91)
		tmp = log(t) - (y + z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+147], t$95$1, If[LessEqual[x, 1.45e+91], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.74999999999999987e147 or 1.45000000000000007e91 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 81.4

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

   5. Simplified 81.4%

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

   if -1.74999999999999987e147 < x < 1.45000000000000007e91

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

      3. +-lowering-+.f64 90.8

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

   5. Simplified 90.8%

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

Alternative 11: 61.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1.9e+38) (- (log t) z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.9e+38) {
		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 <= 1.9d+38) 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 <= 1.9e+38) {
		tmp = Math.log(t) - z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.9e+38:
		tmp = math.log(t) - z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.9e+38)
		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 <= 1.9e+38)
		tmp = log(t) - z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.9e+38], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.8999999999999999e38

   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

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 62.7

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

   5. Simplified 62.7%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

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

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

      4. log-lowering-log.f64 62.7

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

   7. Applied egg-rr 62.7%

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

   if 1.8999999999999999e38 < 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 y around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 55.5

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

   5. Simplified 55.5%

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

Alternative 12: 47.3% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1900:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+17}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1900.0) (- z) (if (<= z 6.4e+17) (- y) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1900.0) {
		tmp = -z;
	} else if (z <= 6.4e+17) {
		tmp = -y;
	} else {
		tmp = -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) :: tmp
    if (z <= (-1900.0d0)) then
        tmp = -z
    else if (z <= 6.4d+17) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1900.0) {
		tmp = -z;
	} else if (z <= 6.4e+17) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1900.0:
		tmp = -z
	elif z <= 6.4e+17:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1900.0)
		tmp = Float64(-z);
	elseif (z <= 6.4e+17)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1900.0)
		tmp = -z;
	elseif (z <= 6.4e+17)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1900.0], (-z), If[LessEqual[z, 6.4e+17], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -1900 or 6.4e17 < 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 z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 64.9

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

   5. Simplified 64.9%

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

   if -1900 < z < 6.4e17

   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 inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 35.3

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

   5. Simplified 35.3%

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

Alternative 13: 30.0% 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 99.9%

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

3. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

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

   2. neg-lowering-neg.f64 24.8

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

5. Simplified 24.8%

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

Reproduce

herbie shell --seed 2024204 
(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)))