Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B

Percentage Accurate: 99.8% → 99.8%

Time: 10.4s

Alternatives: 15

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* i y) (+ (* (log c) (- b 0.5)) (+ a (+ t (+ z (* (log y) x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (i * y) + ((log(c) * (b - 0.5)) + (a + (t + (z + (log(y) * x)))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (i * y) + ((log(c) * (b - 0.5d0)) + (a + (t + (z + (log(y) * x)))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (i * y) + ((Math.log(c) * (b - 0.5)) + (a + (t + (z + (Math.log(y) * x)))));
}

Python

def code(x, y, z, t, a, b, c, i):
	return (i * y) + ((math.log(c) * (b - 0.5)) + (a + (t + (z + (math.log(y) * x)))))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(i * y) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(t + Float64(z + Float64(log(y) * x))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (i * y) + ((log(c) * (b - 0.5)) + (a + (t + (z + (log(y) * x)))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(i * y), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \]
4. Add Preprocessing

Alternative 2: 22.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -5000:\\ \;\;\;\;\frac{z}{y} \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+303}:\\ \;\;\;\;\frac{a}{y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* i y)
          (+ (* (log c) (- b 0.5)) (+ a (+ t (+ z (* (log y) x))))))))
   (if (<= t_1 (- INFINITY))
     (* i y)
     (if (<= t_1 -5000.0)
       (* (/ z y) y)
       (if (<= t_1 1e+303) (* (/ a y) y) (* i y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (i * y) + ((log(c) * (b - 0.5)) + (a + (t + (z + (log(y) * x)))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = i * y;
	} else if (t_1 <= -5000.0) {
		tmp = (z / y) * y;
	} else if (t_1 <= 1e+303) {
		tmp = (a / y) * y;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (i * y) + ((Math.log(c) * (b - 0.5)) + (a + (t + (z + (Math.log(y) * x)))));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = i * y;
	} else if (t_1 <= -5000.0) {
		tmp = (z / y) * y;
	} else if (t_1 <= 1e+303) {
		tmp = (a / y) * y;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (i * y) + ((math.log(c) * (b - 0.5)) + (a + (t + (z + (math.log(y) * x)))))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = i * y
	elif t_1 <= -5000.0:
		tmp = (z / y) * y
	elif t_1 <= 1e+303:
		tmp = (a / y) * y
	else:
		tmp = i * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(i * y) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(t + Float64(z + Float64(log(y) * x))))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(i * y);
	elseif (t_1 <= -5000.0)
		tmp = Float64(Float64(z / y) * y);
	elseif (t_1 <= 1e+303)
		tmp = Float64(Float64(a / y) * y);
	else
		tmp = Float64(i * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (i * y) + ((log(c) * (b - 0.5)) + (a + (t + (z + (log(y) * x)))));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = i * y;
	elseif (t_1 <= -5000.0)
		tmp = (z / y) * y;
	elseif (t_1 <= 1e+303)
		tmp = (a / y) * y;
	else
		tmp = i * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(i * y), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -5000.0], N[(N[(z / y), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+303], N[(N[(a / y), $MachinePrecision] * y), $MachinePrecision], N[(i * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -inf.0 or 1e303 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 85.7

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

   5. Applied rewrites 85.7%

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

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -5e3

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(i + \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{y}\right)\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i + \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{y}\right)\right)\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(i + \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{y}\right)\right)\right)\right)\right) \cdot y} \]

   5. Applied rewrites 66.8%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{fma}\left(\log y, x, a\right) + \left(\mathsf{fma}\left(b - 0.5, \log c, z\right) + t\right)}{y} + i\right) \cdot y} \]

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 14.7%

      \[\leadsto \frac{z}{y} \cdot y \]

   if -5e3 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1e303

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(i + \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{y}\right)\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i + \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{y}\right)\right)\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(i + \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{y}\right)\right)\right)\right)\right) \cdot y} \]

   5. Applied rewrites 62.6%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{fma}\left(\log y, x, a\right) + \left(\mathsf{fma}\left(b - 0.5, \log c, z\right) + t\right)}{y} + i\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \frac{a}{y} \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 13.2%

      \[\leadsto \frac{a}{y} \cdot y \]
3. Recombined 3 regimes into one program.

4. Final simplification 25.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq -\infty:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq -5000:\\ \;\;\;\;\frac{z}{y} \cdot y\\ \mathbf{elif}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq 10^{+303}:\\ \;\;\;\;\frac{a}{y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* i y)
          (+ (* (log c) (- b 0.5)) (+ a (+ t (+ z (* (log y) x))))))))
   (if (<= t_1 -2e+304)
     (fma (/ (* i y) z) z z)
     (if (<= t_1 1e+308) (+ (+ (fma (log c) (- b 0.5) z) t) a) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (i * y) + ((log(c) * (b - 0.5)) + (a + (t + (z + (log(y) * x)))));
	double tmp;
	if (t_1 <= -2e+304) {
		tmp = fma(((i * y) / z), z, z);
	} else if (t_1 <= 1e+308) {
		tmp = (fma(log(c), (b - 0.5), z) + t) + a;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(i * y) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(t + Float64(z + Float64(log(y) * x))))))
	tmp = 0.0
	if (t_1 <= -2e+304)
		tmp = fma(Float64(Float64(i * y) / z), z, z);
	elseif (t_1 <= 1e+308)
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), z) + t) + a);
	else
		tmp = Float64(i * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(i * y), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+304], N[(N[(N[(i * y), $MachinePrecision] / z), $MachinePrecision] * z + z), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], N[(i * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1.9999999999999999e304

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) + 1\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + 1 \cdot z} \]

      3. *-lft-identity N/A

         \[\leadsto \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + \color{blue}{z} \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right), z, z\right)} \]

   5. Applied rewrites 95.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, t\right)\right)\right) + a}{z}, z, z\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 81.0%

      \[\leadsto \mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right) \]

   if -1.9999999999999999e304 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1e308

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right)} + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\left(z + i \cdot y\right) + \log c \cdot \left(b - \frac{1}{2}\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + \left(z + i \cdot y\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(a + t\right) + \left(\color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c} + \left(z + i \cdot y\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\mathsf{fma}\left(b - \frac{1}{2}, \log c, z + i \cdot y\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(\color{blue}{b - \frac{1}{2}}, \log c, z + i \cdot y\right) \]

      9. lower-log.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \color{blue}{\log c}, z + i \cdot y\right) \]

      10. +-commutative N/A

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \log c, \color{blue}{i \cdot y + z}\right) \]

      11. lower-fma.f64 82.9

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \color{blue}{\mathsf{fma}\left(i, y, z\right)}\right) \]

   5. Applied rewrites 82.9%

      \[\leadsto \color{blue}{\left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto a + \color{blue}{\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 72.9%

      \[\leadsto \left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + t\right) + \color{blue}{a} \]

   if 1e308 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 95.0

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

   5. Applied rewrites 95.0%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right)\\ \mathbf{elif}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq 10^{+308}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\mathsf{fma}\left(\log c, b - 0.5, z\right) + a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* i y)
          (+ (* (log c) (- b 0.5)) (+ a (+ t (+ z (* (log y) x))))))))
   (if (<= t_1 -1e+302)
     (fma (/ (* i y) z) z z)
     (if (<= t_1 1e+308) (+ (fma (log c) (- b 0.5) z) a) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (i * y) + ((log(c) * (b - 0.5)) + (a + (t + (z + (log(y) * x)))));
	double tmp;
	if (t_1 <= -1e+302) {
		tmp = fma(((i * y) / z), z, z);
	} else if (t_1 <= 1e+308) {
		tmp = fma(log(c), (b - 0.5), z) + a;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(i * y) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(t + Float64(z + Float64(log(y) * x))))))
	tmp = 0.0
	if (t_1 <= -1e+302)
		tmp = fma(Float64(Float64(i * y) / z), z, z);
	elseif (t_1 <= 1e+308)
		tmp = Float64(fma(log(c), Float64(b - 0.5), z) + a);
	else
		tmp = Float64(i * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(i * y), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+302], N[(N[(N[(i * y), $MachinePrecision] / z), $MachinePrecision] * z + z), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision] + a), $MachinePrecision], N[(i * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1.0000000000000001e302

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) + 1\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + 1 \cdot z} \]

      3. *-lft-identity N/A

         \[\leadsto \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + \color{blue}{z} \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right), z, z\right)} \]

   5. Applied rewrites 92.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, t\right)\right)\right) + a}{z}, z, z\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 71.8%

      \[\leadsto \mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right) \]

   if -1.0000000000000001e302 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1e308

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 81.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in y around 0

      \[\leadsto a + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 71.7%

      \[\leadsto \left(a + z\right) + \color{blue}{\mathsf{fma}\left(\log c, -0.5 + b, \log y \cdot x\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto a + \left(z + \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 54.8%

       \[\leadsto \mathsf{fma}\left(\log c, b - 0.5, z\right) + a \]

   if 1e308 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 95.0

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

   5. Applied rewrites 95.0%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq -1 \cdot 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right)\\ \mathbf{elif}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq 10^{+308}:\\ \;\;\;\;\mathsf{fma}\left(\log c, b - 0.5, z\right) + a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{z}, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* i y)
          (+ (* (log c) (- b 0.5)) (+ a (+ t (+ z (* (log y) x))))))))
   (if (<= t_1 -5e+62)
     (fma (/ (* i y) z) z z)
     (if (<= t_1 1e+308) (fma (/ a z) z z) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (i * y) + ((log(c) * (b - 0.5)) + (a + (t + (z + (log(y) * x)))));
	double tmp;
	if (t_1 <= -5e+62) {
		tmp = fma(((i * y) / z), z, z);
	} else if (t_1 <= 1e+308) {
		tmp = fma((a / z), z, z);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(i * y) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(t + Float64(z + Float64(log(y) * x))))))
	tmp = 0.0
	if (t_1 <= -5e+62)
		tmp = fma(Float64(Float64(i * y) / z), z, z);
	elseif (t_1 <= 1e+308)
		tmp = fma(Float64(a / z), z, z);
	else
		tmp = Float64(i * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(i * y), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+62], N[(N[(N[(i * y), $MachinePrecision] / z), $MachinePrecision] * z + z), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(a / z), $MachinePrecision] * z + z), $MachinePrecision], N[(i * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -5.00000000000000029e62

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) + 1\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + 1 \cdot z} \]

      3. *-lft-identity N/A

         \[\leadsto \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + \color{blue}{z} \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right), z, z\right)} \]

   5. Applied rewrites 75.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, t\right)\right)\right) + a}{z}, z, z\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 37.2%

      \[\leadsto \mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right) \]

   if -5.00000000000000029e62 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1e308

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) + 1\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + 1 \cdot z} \]

      3. *-lft-identity N/A

         \[\leadsto \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + \color{blue}{z} \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right), z, z\right)} \]

   5. Applied rewrites 73.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, t\right)\right)\right) + a}{z}, z, z\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(\frac{a}{z}, z, z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 31.2%

      \[\leadsto \mathsf{fma}\left(\frac{a}{z}, z, z\right) \]

   if 1e308 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 95.0

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

   5. Applied rewrites 95.0%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(\frac{i \cdot y}{z}, z, z\right)\\ \mathbf{elif}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq 10^{+308}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{z}, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+307}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{z}, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* i y)
          (+ (* (log c) (- b 0.5)) (+ a (+ t (+ z (* (log y) x))))))))
   (if (<= t_1 -5e+307)
     (* i y)
     (if (<= t_1 1e+308) (fma (/ a z) z z) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (i * y) + ((log(c) * (b - 0.5)) + (a + (t + (z + (log(y) * x)))));
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= 1e+308) {
		tmp = fma((a / z), z, z);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(i * y) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(t + Float64(z + Float64(log(y) * x))))))
	tmp = 0.0
	if (t_1 <= -5e+307)
		tmp = Float64(i * y);
	elseif (t_1 <= 1e+308)
		tmp = fma(Float64(a / z), z, z);
	else
		tmp = Float64(i * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(i * y), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+307], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(a / z), $MachinePrecision] * z + z), $MachinePrecision], N[(i * y), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -5e307 or 1e308 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 92.2

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

   5. Applied rewrites 92.2%

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

   if -5e307 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1e308

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) + 1\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + 1 \cdot z} \]

      3. *-lft-identity N/A

         \[\leadsto \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right)\right) \cdot z + \color{blue}{z} \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{i \cdot y}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{z}\right)\right)\right), z, z\right)} \]

   5. Applied rewrites 72.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, t\right)\right)\right) + a}{z}, z, z\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(\frac{a}{z}, z, z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 31.1%

      \[\leadsto \mathsf{fma}\left(\frac{a}{z}, z, z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq -5 \cdot 10^{+307}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \log y \cdot x\right)\right)\right)\right) \leq 10^{+308}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{z}, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+167}:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right) + \left(a + t\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(-0.5, \log c, z\right)\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, a + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= t_1 -1e+167)
     (+ (fma (- b 0.5) (log c) (fma i y z)) (+ a t))
     (if (<= t_1 4e+148)
       (+ (fma i y (fma (log y) x (fma -0.5 (log c) z))) a)
       (fma (log y) x (fma (- b 0.5) (log c) (+ a z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (t_1 <= -1e+167) {
		tmp = fma((b - 0.5), log(c), fma(i, y, z)) + (a + t);
	} else if (t_1 <= 4e+148) {
		tmp = fma(i, y, fma(log(y), x, fma(-0.5, log(c), z))) + a;
	} else {
		tmp = fma(log(y), x, fma((b - 0.5), log(c), (a + z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (t_1 <= -1e+167)
		tmp = Float64(fma(Float64(b - 0.5), log(c), fma(i, y, z)) + Float64(a + t));
	elseif (t_1 <= 4e+148)
		tmp = Float64(fma(i, y, fma(log(y), x, fma(-0.5, log(c), z))) + a);
	else
		tmp = fma(log(y), x, fma(Float64(b - 0.5), log(c), Float64(a + z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+167], N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+148], N[(N[(i * y + N[(N[Log[y], $MachinePrecision] * x + N[(-0.5 * N[Log[c], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -1e167

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right)} + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\left(z + i \cdot y\right) + \log c \cdot \left(b - \frac{1}{2}\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + \left(z + i \cdot y\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(a + t\right) + \left(\color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c} + \left(z + i \cdot y\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\mathsf{fma}\left(b - \frac{1}{2}, \log c, z + i \cdot y\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(\color{blue}{b - \frac{1}{2}}, \log c, z + i \cdot y\right) \]

      9. lower-log.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \color{blue}{\log c}, z + i \cdot y\right) \]

      10. +-commutative N/A

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \log c, \color{blue}{i \cdot y + z}\right) \]

      11. lower-fma.f64 92.0

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \color{blue}{\mathsf{fma}\left(i, y, z\right)}\right) \]

   5. Applied rewrites 92.0%

      \[\leadsto \color{blue}{\left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right)} \]

   if -1e167 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 4.0000000000000002e148

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 81.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, z + \frac{-1}{2} \cdot \log c\right)\right) + a \]
   7. Step-by-step derivation

   8. Applied rewrites 79.2%

      \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(-0.5, \log c, z\right)\right)\right) + a \]

   if 4.0000000000000002e148 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 94.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in y around 0

      \[\leadsto a + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 94.9%

      \[\leadsto \left(a + z\right) + \color{blue}{\mathsf{fma}\left(\log c, -0.5 + b, \log y \cdot x\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 94.9%

       \[\leadsto \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, a + z\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -1 \cdot 10^{+167}:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right) + \left(a + t\right)\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 4 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(-0.5, \log c, z\right)\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, a + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\log c, b - 0.5, z\right)\\ t_2 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+221}:\\ \;\;\;\;\left(t\_1 + t\right) + a\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(-0.5, \log c, z\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1 + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma (log c) (- b 0.5) z)) (t_2 (* (log c) (- b 0.5))))
   (if (<= t_2 -1e+221)
     (+ (+ t_1 t) a)
     (if (<= t_2 4e+148) (+ (fma i y (fma -0.5 (log c) z)) a) (+ t_1 a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(log(c), (b - 0.5), z);
	double t_2 = log(c) * (b - 0.5);
	double tmp;
	if (t_2 <= -1e+221) {
		tmp = (t_1 + t) + a;
	} else if (t_2 <= 4e+148) {
		tmp = fma(i, y, fma(-0.5, log(c), z)) + a;
	} else {
		tmp = t_1 + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(log(c), Float64(b - 0.5), z)
	t_2 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (t_2 <= -1e+221)
		tmp = Float64(Float64(t_1 + t) + a);
	elseif (t_2 <= 4e+148)
		tmp = Float64(fma(i, y, fma(-0.5, log(c), z)) + a);
	else
		tmp = Float64(t_1 + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+221], N[(N[(t$95$1 + t), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t$95$2, 4e+148], N[(N[(i * y + N[(-0.5 * N[Log[c], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(t$95$1 + a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -1e221

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right)} + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\left(z + i \cdot y\right) + \log c \cdot \left(b - \frac{1}{2}\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + \left(z + i \cdot y\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(a + t\right) + \left(\color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c} + \left(z + i \cdot y\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\mathsf{fma}\left(b - \frac{1}{2}, \log c, z + i \cdot y\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(\color{blue}{b - \frac{1}{2}}, \log c, z + i \cdot y\right) \]

      9. lower-log.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \color{blue}{\log c}, z + i \cdot y\right) \]

      10. +-commutative N/A

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \log c, \color{blue}{i \cdot y + z}\right) \]

      11. lower-fma.f64 96.8

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \color{blue}{\mathsf{fma}\left(i, y, z\right)}\right) \]

   5. Applied rewrites 96.8%

      \[\leadsto \color{blue}{\left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto a + \color{blue}{\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 90.4%

      \[\leadsto \left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + t\right) + \color{blue}{a} \]

   if -1e221 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 4.0000000000000002e148

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 82.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(i, y, z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a \]
   7. Step-by-step derivation

   8. Applied rewrites 64.8%

      \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, z\right)\right) + a \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{fma}\left(i, y, z + \frac{-1}{2} \cdot \log c\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 61.3%

       \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(-0.5, \log c, z\right)\right) + a \]

   if 4.0000000000000002e148 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 94.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in y around 0

      \[\leadsto a + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 94.9%

      \[\leadsto \left(a + z\right) + \color{blue}{\mathsf{fma}\left(\log c, -0.5 + b, \log y \cdot x\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto a + \left(z + \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 81.0%

       \[\leadsto \mathsf{fma}\left(\log c, b - 0.5, z\right) + a \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -1 \cdot 10^{+221}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + t\right) + a\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 4 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(-0.5, \log c, z\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log c, b - 0.5, z\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \left(-0.5 + b\right) \cdot \log c\right)\right) + a\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right) + \left(a + t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(\frac{z}{x} + \log y\right) \cdot x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.5e+137)
   (+ (fma i y (fma (log y) x (* (+ -0.5 b) (log c)))) a)
   (if (<= x 3e+52)
     (+ (fma (- b 0.5) (log c) (fma i y z)) (+ a t))
     (+ (fma i y (* (+ (/ z x) (log y)) x)) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.5e+137) {
		tmp = fma(i, y, fma(log(y), x, ((-0.5 + b) * log(c)))) + a;
	} else if (x <= 3e+52) {
		tmp = fma((b - 0.5), log(c), fma(i, y, z)) + (a + t);
	} else {
		tmp = fma(i, y, (((z / x) + log(y)) * x)) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.5e+137)
		tmp = Float64(fma(i, y, fma(log(y), x, Float64(Float64(-0.5 + b) * log(c)))) + a);
	elseif (x <= 3e+52)
		tmp = Float64(fma(Float64(b - 0.5), log(c), fma(i, y, z)) + Float64(a + t));
	else
		tmp = Float64(fma(i, y, Float64(Float64(Float64(z / x) + log(y)) * x)) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.5e+137], N[(N[(i * y + N[(N[Log[y], $MachinePrecision] * x + N[(N[(-0.5 + b), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[x, 3e+52], N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision], N[(N[(i * y + N[(N[(N[(z / x), $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5000000000000001e137

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 89.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) + a \]
   7. Step-by-step derivation

   8. Applied rewrites 87.0%

      \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \log c \cdot \left(-0.5 + b\right)\right)\right) + a \]

   if -2.5000000000000001e137 < x < 3e52

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right)} + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\left(z + i \cdot y\right) + \log c \cdot \left(b - \frac{1}{2}\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + \left(z + i \cdot y\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(a + t\right) + \left(\color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c} + \left(z + i \cdot y\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\mathsf{fma}\left(b - \frac{1}{2}, \log c, z + i \cdot y\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(\color{blue}{b - \frac{1}{2}}, \log c, z + i \cdot y\right) \]

      9. lower-log.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \color{blue}{\log c}, z + i \cdot y\right) \]

      10. +-commutative N/A

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \log c, \color{blue}{i \cdot y + z}\right) \]

      11. lower-fma.f64 98.3

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \color{blue}{\mathsf{fma}\left(i, y, z\right)}\right) \]

   5. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right)} \]

   if 3e52 < x

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 95.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(i, y, x \cdot \left(\log y + \left(\frac{z}{x} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{x}\right)\right)\right) + a \]
   7. Step-by-step derivation

   8. Applied rewrites 95.4%

      \[\leadsto \mathsf{fma}\left(i, y, \left(\frac{\mathsf{fma}\left(\log c, b - 0.5, z\right)}{x} + \log y\right) \cdot x\right) + a \]

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(i, y, \left(\frac{z}{x} + \log y\right) \cdot x\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 85.9%

       \[\leadsto \mathsf{fma}\left(i, y, \left(\frac{z}{x} + \log y\right) \cdot x\right) + a \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \left(-0.5 + b\right) \cdot \log c\right)\right) + a\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right) + \left(a + t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(\frac{z}{x} + \log y\right) \cdot x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (fma i y (fma (log y) x (fma (- b 0.5) (log c) z))) a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return fma(i, y, fma(log(y), x, fma((b - 0.5), log(c), z))) + a;
}

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(fma(i, y, fma(log(y), x, fma(Float64(b - 0.5), log(c), z))) + a)
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(i * y + N[(N[Log[y], $MachinePrecision] * x + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   2. lower-+.f64 N/A

      \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

5. Applied rewrites 84.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]
6. Add Preprocessing

Alternative 11: 89.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, y, \left(\frac{z}{x} + \log y\right) \cdot x\right) + a\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right) + \left(a + t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (fma i y (* (+ (/ z x) (log y)) x)) a)))
   (if (<= x -4.8e+45)
     t_1
     (if (<= x 3e+52) (+ (fma (- b 0.5) (log c) (fma i y z)) (+ a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(i, y, (((z / x) + log(y)) * x)) + a;
	double tmp;
	if (x <= -4.8e+45) {
		tmp = t_1;
	} else if (x <= 3e+52) {
		tmp = fma((b - 0.5), log(c), fma(i, y, z)) + (a + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(i, y, Float64(Float64(Float64(z / x) + log(y)) * x)) + a)
	tmp = 0.0
	if (x <= -4.8e+45)
		tmp = t_1;
	elseif (x <= 3e+52)
		tmp = Float64(fma(Float64(b - 0.5), log(c), fma(i, y, z)) + Float64(a + t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(i * y + N[(N[(N[(z / x), $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[x, -4.8e+45], t$95$1, If[LessEqual[x, 3e+52], N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999979e45 or 3e52 < x

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 92.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(i, y, x \cdot \left(\log y + \left(\frac{z}{x} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{x}\right)\right)\right) + a \]
   7. Step-by-step derivation

   8. Applied rewrites 92.6%

      \[\leadsto \mathsf{fma}\left(i, y, \left(\frac{\mathsf{fma}\left(\log c, b - 0.5, z\right)}{x} + \log y\right) \cdot x\right) + a \]

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(i, y, \left(\frac{z}{x} + \log y\right) \cdot x\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 81.5%

       \[\leadsto \mathsf{fma}\left(i, y, \left(\frac{z}{x} + \log y\right) \cdot x\right) + a \]

   if -4.79999999999999979e45 < x < 3e52

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right)} + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\left(z + i \cdot y\right) + \log c \cdot \left(b - \frac{1}{2}\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + \left(z + i \cdot y\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(a + t\right) + \left(\color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c} + \left(z + i \cdot y\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\mathsf{fma}\left(b - \frac{1}{2}, \log c, z + i \cdot y\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(\color{blue}{b - \frac{1}{2}}, \log c, z + i \cdot y\right) \]

      9. lower-log.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \color{blue}{\log c}, z + i \cdot y\right) \]

      10. +-commutative N/A

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \log c, \color{blue}{i \cdot y + z}\right) \]

      11. lower-fma.f64 99.9

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \color{blue}{\mathsf{fma}\left(i, y, z\right)}\right) \]

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(\frac{z}{x} + \log y\right) \cdot x\right) + a\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right) + \left(a + t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(\frac{z}{x} + \log y\right) \cdot x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -6 \cdot 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right) + \left(a + t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -6e+241)
     t_1
     (if (<= x 1.56e+193)
       (+ (fma (- b 0.5) (log c) (fma i y z)) (+ a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -6e+241) {
		tmp = t_1;
	} else if (x <= 1.56e+193) {
		tmp = fma((b - 0.5), log(c), fma(i, y, z)) + (a + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -6e+241)
		tmp = t_1;
	elseif (x <= 1.56e+193)
		tmp = Float64(fma(Float64(b - 0.5), log(c), fma(i, y, z)) + Float64(a + t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -6e+241], t$95$1, If[LessEqual[x, 1.56e+193], N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000031e241 or 1.5599999999999999e193 < x

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   7. 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 87.1

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

   8. Applied rewrites 87.1%

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

   if -6.00000000000000031e241 < x < 1.5599999999999999e193

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right) + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(a + t\right)} + \left(z + \left(i \cdot y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\left(z + i \cdot y\right) + \log c \cdot \left(b - \frac{1}{2}\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + \left(z + i \cdot y\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(a + t\right) + \left(\color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c} + \left(z + i \cdot y\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\mathsf{fma}\left(b - \frac{1}{2}, \log c, z + i \cdot y\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(\color{blue}{b - \frac{1}{2}}, \log c, z + i \cdot y\right) \]

      9. lower-log.f64 N/A

         \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \color{blue}{\log c}, z + i \cdot y\right) \]

      10. +-commutative N/A

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - \frac{1}{2}, \log c, \color{blue}{i \cdot y + z}\right) \]

      11. lower-fma.f64 92.3

          \[\leadsto \left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \color{blue}{\mathsf{fma}\left(i, y, z\right)}\right) \]

   5. Applied rewrites 92.3%

      \[\leadsto \color{blue}{\left(a + t\right) + \mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+241}:\\ \;\;\;\;\log y \cdot x\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, \mathsf{fma}\left(i, y, z\right)\right) + \left(a + t\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -6 \cdot 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, z\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -6e+241)
     t_1
     (if (<= x 1.56e+193) (+ (fma i y (fma (log c) (- b 0.5) z)) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -6e+241) {
		tmp = t_1;
	} else if (x <= 1.56e+193) {
		tmp = fma(i, y, fma(log(c), (b - 0.5), z)) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -6e+241)
		tmp = t_1;
	elseif (x <= 1.56e+193)
		tmp = Float64(fma(i, y, fma(log(c), Float64(b - 0.5), z)) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -6e+241], t$95$1, If[LessEqual[x, 1.56e+193], N[(N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000031e241 or 1.5599999999999999e193 < x

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   7. 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 87.1

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

   8. Applied rewrites 87.1%

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

   if -6.00000000000000031e241 < x < 1.5599999999999999e193

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + a} \]

   5. Applied rewrites 82.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\right) + a} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(i, y, z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a \]
   7. Step-by-step derivation

   8. Applied rewrites 74.6%

      \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, z\right)\right) + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 27.4% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6.8:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{+43}:\\ \;\;\;\;\frac{a}{y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -6.8) (* i y) (if (<= i 1.95e+43) (* (/ a y) y) (* i y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -6.8) {
		tmp = i * y;
	} else if (i <= 1.95e+43) {
		tmp = (a / y) * y;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= (-6.8d0)) then
        tmp = i * y
    else if (i <= 1.95d+43) then
        tmp = (a / y) * y
    else
        tmp = i * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -6.8) {
		tmp = i * y;
	} else if (i <= 1.95e+43) {
		tmp = (a / y) * y;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -6.8:
		tmp = i * y
	elif i <= 1.95e+43:
		tmp = (a / y) * y
	else:
		tmp = i * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -6.8)
		tmp = Float64(i * y);
	elseif (i <= 1.95e+43)
		tmp = Float64(Float64(a / y) * y);
	else
		tmp = Float64(i * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -6.8)
		tmp = i * y;
	elseif (i <= 1.95e+43)
		tmp = (a / y) * y;
	else
		tmp = i * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -6.8], N[(i * y), $MachinePrecision], If[LessEqual[i, 1.95e+43], N[(N[(a / y), $MachinePrecision] * y), $MachinePrecision], N[(i * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -6.79999999999999982 or 1.95e43 < i

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 42.1

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

   5. Applied rewrites 42.1%

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

   if -6.79999999999999982 < i < 1.95e43

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(i + \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{y}\right)\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i + \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{y}\right)\right)\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(i + \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - \frac{1}{2}\right)}{y}\right)\right)\right)\right)\right) \cdot y} \]

   5. Applied rewrites 69.9%

      \[\leadsto \color{blue}{\left(\frac{\mathsf{fma}\left(\log y, x, a\right) + \left(\mathsf{fma}\left(b - 0.5, \log c, z\right) + t\right)}{y} + i\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \frac{a}{y} \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 17.8%

      \[\leadsto \frac{a}{y} \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 23.6% accurate, 39.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* i y))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return i * y;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = i * y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return i * y;
}

Python

def code(x, y, z, t, a, b, c, i):
	return i * y

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(i * y)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = i * y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(i * y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

   1. lower-*.f64 23.4

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

5. Applied rewrites 23.4%

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

Reproduce

herbie shell --seed 2024298 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))