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

Percentage Accurate: 99.8% → 99.9%

Time: 14.9s

Alternatives: 26

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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Step-by-step derivation

   1. +-commutative N/A

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

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

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

   3. +-commutative N/A

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

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

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

   5. sub-neg N/A

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

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

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

   7. metadata-eval N/A

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

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

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

   9. associate-+l+ N/A

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

   10. +-commutative N/A

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

   11. associate-+l+ N/A

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

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

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

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

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

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

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

   15. +-lowering-+.f64 99.8

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

4. Applied egg-rr 99.8%

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

Alternative 2: 47.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;t\_1 \leq -200:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* y i)
          (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))))))
   (if (<= t_1 (- INFINITY))
     (* y i)
     (if (<= t_1 -200.0) (+ a (+ z t)) (fma y i a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * i;
	} else if (t_1 <= -200.0) {
		tmp = a + (z + t);
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * i);
	elseif (t_1 <= -200.0)
		tmp = Float64(a + Float64(z + t));
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * i), $MachinePrecision], If[LessEqual[t$95$1, -200.0], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(y * i + a), $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

   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. *-lowering-*.f64 100.0

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

   5. Simplified 100.0%

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

   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)) < -200

   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 x around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 86.5

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

   5. Simplified 86.5%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-commutative N/A

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 74.0

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

   8. Simplified 74.0%

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

   9. Taylor expanded in z around inf

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

   11. Simplified 50.4%

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

   if -200 < (+.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 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. Step-by-step derivation

      1. +-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

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

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

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

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

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

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

      15. +-lowering-+.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a}\right) \]
   6. Step-by-step derivation

   7. Simplified 40.7%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -\infty:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -200:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* y i)
          (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))))))
   (if (<= t_1 (- INFINITY))
     (* y i)
     (if (<= t_1 4e+307) (+ a (+ z t)) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * i;
	} else if (t_1 <= 4e+307) {
		tmp = a + (z + t);
	} else {
		tmp = y * i;
	}
	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 = (y * i) + ((a + (t + (z + (x * Math.log(y))))) + (Math.log(c) * (b - 0.5)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * i;
	} else if (t_1 <= 4e+307) {
		tmp = a + (z + t);
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + ((a + (t + (z + (x * math.log(y))))) + (math.log(c) * (b - 0.5)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * i
	elif t_1 <= 4e+307:
		tmp = a + (z + t)
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * i);
	elseif (t_1 <= 4e+307)
		tmp = Float64(a + Float64(z + t));
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * i;
	elseif (t_1 <= 4e+307)
		tmp = a + (z + t);
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * i), $MachinePrecision], If[LessEqual[t$95$1, 4e+307], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(y * i), $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)) < -inf.0 or 3.99999999999999994e307 < (+.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. *-lowering-*.f64 100.0

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

   5. Simplified 100.0%

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

   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)) < 3.99999999999999994e307

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 82.7

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-commutative N/A

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 71.3

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

   8. Simplified 71.3%

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

   9. Taylor expanded in z around inf

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

   11. Simplified 49.9%

       \[\leadsto a + \left(t + \color{blue}{z}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -\infty:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq 4 \cdot 10^{+307}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 42.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* y i)
          (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))))))
   (if (<= t_1 (- INFINITY)) (* y i) (if (<= t_1 4e+307) (+ z a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * i;
	} else if (t_1 <= 4e+307) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	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 = (y * i) + ((a + (t + (z + (x * Math.log(y))))) + (Math.log(c) * (b - 0.5)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * i;
	} else if (t_1 <= 4e+307) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + ((a + (t + (z + (x * math.log(y))))) + (math.log(c) * (b - 0.5)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * i
	elif t_1 <= 4e+307:
		tmp = z + a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * i);
	elseif (t_1 <= 4e+307)
		tmp = Float64(z + a);
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * i;
	elseif (t_1 <= 4e+307)
		tmp = z + a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * i), $MachinePrecision], If[LessEqual[t$95$1, 4e+307], N[(z + a), $MachinePrecision], N[(y * i), $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)) < -inf.0 or 3.99999999999999994e307 < (+.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. *-lowering-*.f64 100.0

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

   5. Simplified 100.0%

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

   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)) < 3.99999999999999994e307

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 82.7

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-commutative N/A

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 71.3

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

   8. Simplified 71.3%

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

   9. Taylor expanded in z around inf

      \[\leadsto a + \color{blue}{z} \]
   10. Step-by-step derivation

   11. Simplified 36.5%

       \[\leadsto a + \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -\infty:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq 4 \cdot 10^{+307}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + t\_1\right) \leq 200:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) t_1)) 200.0)
     (fma y i (fma (+ b -0.5) (log c) z))
     (+ (* y i) (+ 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(c) * (b - 0.5);
	double tmp;
	if (((y * i) + ((a + (t + (z + (x * log(y))))) + t_1)) <= 200.0) {
		tmp = fma(y, i, fma((b + -0.5), log(c), z));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	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 (Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + t_1)) <= 200.0)
		tmp = fma(y, i, fma(Float64(b + -0.5), log(c), z));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	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[N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], 200.0], N[(y * i + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $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)) < 200

   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. Step-by-step derivation

      1. +-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

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

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

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

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

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

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

      15. +-lowering-+.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 59.4%

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

   if 200 < (+.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 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 a around inf

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

   5. Simplified 56.8%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq 200:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\log c, b + -0.5, z\right)\\ t_2 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+50}:\\ \;\;\;\;a + \left(t + t\_1\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+133}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + t\_1\\ \end{array} \end{array} \]

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 -5e+50)
     (+ a (+ t t_1))
     (if (<= t_2 5e+133) (+ (* y i) (+ t (+ z a))) (+ 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 = fma(log(c), (b + -0.5), z);
	double t_2 = log(c) * (b - 0.5);
	double tmp;
	if (t_2 <= -5e+50) {
		tmp = a + (t + t_1);
	} else if (t_2 <= 5e+133) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = a + t_1;
	}
	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 <= -5e+50)
		tmp = Float64(a + Float64(t + t_1));
	elseif (t_2 <= 5e+133)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	else
		tmp = Float64(a + t_1);
	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, -5e+50], N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+133], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -5e50

   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 x around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 87.6

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-commutative N/A

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 74.6

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

   8. Simplified 74.6%

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

   if -5e50 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 4.99999999999999961e133

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 81.5

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

   5. Simplified 81.5%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 79.1%

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]

   if 4.99999999999999961e133 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 93.6

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

   5. Simplified 93.6%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-commutative N/A

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 85.9

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

   8. Simplified 85.9%

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

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

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

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

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

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

       4. sub-neg N/A

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

       5. metadata-eval N/A

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

       6. +-lowering-+.f64 76.7

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

   11. Simplified 76.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -5 \cdot 10^{+50}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 5 \cdot 10^{+133}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\\ t_2 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+133}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (fma (log c) (+ b -0.5) z))) (t_2 (* (log c) (- b 0.5))))
   (if (<= t_2 -5e+50)
     t_1
     (if (<= t_2 5e+133) (+ (* y i) (+ t (+ 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 = a + fma(log(c), (b + -0.5), z);
	double t_2 = log(c) * (b - 0.5);
	double tmp;
	if (t_2 <= -5e+50) {
		tmp = t_1;
	} else if (t_2 <= 5e+133) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + fma(log(c), Float64(b + -0.5), z))
	t_2 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (t_2 <= -5e+50)
		tmp = t_1;
	elseif (t_2 <= 5e+133)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(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[(a + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+50], t$95$1, If[LessEqual[t$95$2, 5e+133], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -5e50 or 4.99999999999999961e133 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 89.8

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

   5. Simplified 89.8%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-commutative N/A

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 78.8

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

   8. Simplified 78.8%

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

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

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

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

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

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

       4. sub-neg N/A

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

       5. metadata-eval N/A

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

       6. +-lowering-+.f64 65.8

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

   11. Simplified 65.8%

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

   if -5e50 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 4.99999999999999961e133

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 81.5

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

   5. Simplified 81.5%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 79.1%

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -5 \cdot 10^{+50}:\\ \;\;\;\;a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 5 \cdot 10^{+133}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -5 \cdot 10^{+21}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))))
      -5e+21)
   (+ (* y i) (+ z t))
   (+ (+ t a) (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)))) <= -5e+21) {
		tmp = (y * i) + (z + t);
	} else {
		tmp = (t + a) + (y * i);
	}
	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 (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0)))) <= (-5d+21)) then
        tmp = (y * i) + (z + t)
    else
        tmp = (t + a) + (y * i)
    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 (((y * i) + ((a + (t + (z + (x * Math.log(y))))) + (Math.log(c) * (b - 0.5)))) <= -5e+21) {
		tmp = (y * i) + (z + t);
	} else {
		tmp = (t + a) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((y * i) + ((a + (t + (z + (x * math.log(y))))) + (math.log(c) * (b - 0.5)))) <= -5e+21:
		tmp = (y * i) + (z + t)
	else:
		tmp = (t + a) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5)))) <= -5e+21)
		tmp = Float64(Float64(y * i) + Float64(z + t));
	else
		tmp = Float64(Float64(t + a) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)))) <= -5e+21)
		tmp = (y * i) + (z + t);
	else
		tmp = (t + a) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+21], N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $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)) < -5e21

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 88.0

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

   5. Simplified 88.0%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 50.5%

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

   if -5e21 < (+.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 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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 81.5

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

   5. Simplified 81.5%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 52.0%

      \[\leadsto \left(t + \color{blue}{a}\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -5 \cdot 10^{+21}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))))
      -5e+21)
   (fma y i z)
   (+ (+ t a) (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)))) <= -5e+21) {
		tmp = fma(y, i, z);
	} else {
		tmp = (t + a) + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5)))) <= -5e+21)
		tmp = fma(y, i, z);
	else
		tmp = Float64(Float64(t + a) + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+21], N[(y * i + z), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $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)) < -5e21

   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. Step-by-step derivation

      1. +-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

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

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

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

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

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

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

      15. +-lowering-+.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 38.0%

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

   if -5e21 < (+.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 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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 81.5

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

   5. Simplified 81.5%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 52.0%

      \[\leadsto \left(t + \color{blue}{a}\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))))
      -5e+21)
   (fma y i z)
   (fma y i a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)))) <= -5e+21) {
		tmp = fma(y, i, z);
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5)))) <= -5e+21)
		tmp = fma(y, i, z);
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+21], N[(y * i + z), $MachinePrecision], N[(y * i + a), $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)) < -5e21

   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. Step-by-step derivation

      1. +-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

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

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

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

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

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

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

      15. +-lowering-+.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 38.0%

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

   if -5e21 < (+.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 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. Step-by-step derivation

      1. +-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

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

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

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

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

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

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

      15. +-lowering-+.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a}\right) \]
   6. Step-by-step derivation

   7. Simplified 40.3%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 23.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -200:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))))
      -200.0)
   z
   (+ t a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)))) <= -200.0) {
		tmp = z;
	} else {
		tmp = t + a;
	}
	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 (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0)))) <= (-200.0d0)) then
        tmp = z
    else
        tmp = t + a
    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 (((y * i) + ((a + (t + (z + (x * Math.log(y))))) + (Math.log(c) * (b - 0.5)))) <= -200.0) {
		tmp = z;
	} else {
		tmp = t + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((y * i) + ((a + (t + (z + (x * math.log(y))))) + (math.log(c) * (b - 0.5)))) <= -200.0:
		tmp = z
	else:
		tmp = t + a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5)))) <= -200.0)
		tmp = z;
	else
		tmp = Float64(t + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)))) <= -200.0)
		tmp = z;
	else
		tmp = t + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -200.0], z, N[(t + a), $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)) < -200

   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

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

   5. Simplified 17.1%

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

   if -200 < (+.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 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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 81.4

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

   5. Simplified 81.4%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-commutative N/A

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 60.8

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

   8. Simplified 60.8%

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

   9. Taylor expanded in t around inf

      \[\leadsto a + \color{blue}{t} \]
   10. Step-by-step derivation

   11. Simplified 32.3%

       \[\leadsto a + \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -200:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 16.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -200:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))))
      -200.0)
   z
   a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)))) <= -200.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	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 (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0)))) <= (-200.0d0)) then
        tmp = z
    else
        tmp = a
    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 (((y * i) + ((a + (t + (z + (x * Math.log(y))))) + (Math.log(c) * (b - 0.5)))) <= -200.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((y * i) + ((a + (t + (z + (x * math.log(y))))) + (math.log(c) * (b - 0.5)))) <= -200.0:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5)))) <= -200.0)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)))) <= -200.0)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -200.0], z, a]

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)) < -200

   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

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

   5. Simplified 17.1%

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

   if -200 < (+.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 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 a around inf

      \[\leadsto \color{blue}{a} \]
   4. Step-by-step derivation

   5. Simplified 20.4%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 18.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) \leq -200:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\log c, b + -0.5, z\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+110}:\\ \;\;\;\;a + \left(t\_1 + \mathsf{fma}\left(x, \log y, t\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+202}:\\ \;\;\;\;\left(t + \left(a + t\_1\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a + \left(t + \mathsf{fma}\left(i, y, z\right)\right)}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma (log c) (+ b -0.5) z)))
   (if (<= x -1.02e+110)
     (+ a (+ t_1 (fma x (log y) t)))
     (if (<= x 6e+202)
       (+ (+ t (+ a t_1)) (* y i))
       (* x (+ (log y) (/ (+ a (+ t (fma i y z))) x)))))))

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 tmp;
	if (x <= -1.02e+110) {
		tmp = a + (t_1 + fma(x, log(y), t));
	} else if (x <= 6e+202) {
		tmp = (t + (a + t_1)) + (y * i);
	} else {
		tmp = x * (log(y) + ((a + (t + fma(i, y, z))) / x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(log(c), Float64(b + -0.5), z)
	tmp = 0.0
	if (x <= -1.02e+110)
		tmp = Float64(a + Float64(t_1 + fma(x, log(y), t)));
	elseif (x <= 6e+202)
		tmp = Float64(Float64(t + Float64(a + t_1)) + Float64(y * i));
	else
		tmp = Float64(x * Float64(log(y) + Float64(Float64(a + Float64(t + fma(i, y, z))) / x)));
	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]}, If[LessEqual[x, -1.02e+110], N[(a + N[(t$95$1 + N[(x * N[Log[y], $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+202], N[(N[(t + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(a + N[(t + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02e110

   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 y around 0

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

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

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

      11. associate-+l+ N/A

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

   5. Simplified 91.8%

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

   if -1.02e110 < x < 6.0000000000000003e202

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 97.7

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

   5. Simplified 97.7%

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

   if 6.0000000000000003e202 < 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 x around -inf

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

      1. mul-1-neg N/A

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

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

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

      3. distribute-lft-out N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

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

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

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

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

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

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

      9. /-lowering-/.f64 N/A

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

   5. Simplified 99.6%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 99.6%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+110}:\\ \;\;\;\;a + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + \mathsf{fma}\left(x, \log y, t\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+202}:\\ \;\;\;\;\left(t + \left(a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a + \left(t + \mathsf{fma}\left(i, y, z\right)\right)}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+110}:\\ \;\;\;\;z + \mathsf{fma}\left(x, \log y, \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+202}:\\ \;\;\;\;\left(t + \left(a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a + \left(t + \mathsf{fma}\left(i, y, z\right)\right)}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2e+110)
   (+ z (fma x (log y) (fma (log c) (+ b -0.5) a)))
   (if (<= x 7.2e+202)
     (+ (+ t (+ a (fma (log c) (+ b -0.5) z))) (* y i))
     (* x (+ (log y) (/ (+ a (+ t (fma i y z))) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2e+110) {
		tmp = z + fma(x, log(y), fma(log(c), (b + -0.5), a));
	} else if (x <= 7.2e+202) {
		tmp = (t + (a + fma(log(c), (b + -0.5), z))) + (y * i);
	} else {
		tmp = x * (log(y) + ((a + (t + fma(i, y, z))) / x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2e+110)
		tmp = Float64(z + fma(x, log(y), fma(log(c), Float64(b + -0.5), a)));
	elseif (x <= 7.2e+202)
		tmp = Float64(Float64(t + Float64(a + fma(log(c), Float64(b + -0.5), z))) + Float64(y * i));
	else
		tmp = Float64(x * Float64(log(y) + Float64(Float64(a + Float64(t + fma(i, y, z))) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2e+110], N[(z + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+202], N[(N[(t + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(a + N[(t + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e110

   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. Step-by-step derivation

      1. +-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

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

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

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

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

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

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

      15. +-lowering-+.f64 99.6

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

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

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

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

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

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

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

      10. /-lowering-/.f64 80.5

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

   7. Simplified 80.5%

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

   8. Taylor expanded in x around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. log-lowering-log.f64 74.9

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

   10. Simplified 74.9%

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

   11. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. associate-+l+ N/A

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

       3. +-commutative N/A

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

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

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

       5. +-commutative N/A

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

       6. associate-+l+ N/A

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

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

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

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

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

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

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

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

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

       11. sub-neg N/A

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

       12. metadata-eval N/A

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

       13. +-lowering-+.f64 84.2

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

   13. Simplified 84.2%

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

   if -2e110 < x < 7.20000000000000016e202

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 97.7

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

   5. Simplified 97.7%

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

   if 7.20000000000000016e202 < 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 x around -inf

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

      1. mul-1-neg N/A

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

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

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

      3. distribute-lft-out N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

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

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

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

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

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

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

      9. /-lowering-/.f64 N/A

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

   5. Simplified 99.6%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 99.6%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+110}:\\ \;\;\;\;z + \mathsf{fma}\left(x, \log y, \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+202}:\\ \;\;\;\;\left(t + \left(a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a + \left(t + \mathsf{fma}\left(i, y, z\right)\right)}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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 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. +-lowering-+.f64 N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. +-commutative N/A

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

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

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

   6. associate-+r+ N/A

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

   7. +-commutative N/A

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

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

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

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

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

   10. sub-neg N/A

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

   11. metadata-eval N/A

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

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

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

   13. +-commutative N/A

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

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

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

   15. log-lowering-log.f64 86.9

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

5. Simplified 86.9%

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

Alternative 16: 94.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\log y + \frac{a + \left(t + \mathsf{fma}\left(i, y, z\right)\right)}{x}\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+202}:\\ \;\;\;\;\left(t + \left(a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (+ (log y) (/ (+ a (+ t (fma i y z))) x)))))
   (if (<= x -1.35e+107)
     t_1
     (if (<= x 6e+202)
       (+ (+ t (+ a (fma (log c) (+ b -0.5) z))) (* y i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (log(y) + ((a + (t + fma(i, y, z))) / x));
	double tmp;
	if (x <= -1.35e+107) {
		tmp = t_1;
	} else if (x <= 6e+202) {
		tmp = (t + (a + fma(log(c), (b + -0.5), z))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * Float64(log(y) + Float64(Float64(a + Float64(t + fma(i, y, z))) / x)))
	tmp = 0.0
	if (x <= -1.35e+107)
		tmp = t_1;
	elseif (x <= 6e+202)
		tmp = Float64(Float64(t + Float64(a + fma(log(c), Float64(b + -0.5), z))) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(a + N[(t + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+107], t$95$1, If[LessEqual[x, 6e+202], N[(N[(t + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3500000000000001e107 or 6.0000000000000003e202 < x

   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 x around -inf

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

      1. mul-1-neg N/A

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

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

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

      3. distribute-lft-out N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

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

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

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

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

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

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

      9. /-lowering-/.f64 N/A

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

   5. Simplified 99.6%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 86.3%

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

   if -1.3500000000000001e107 < x < 6.0000000000000003e202

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 98.2

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

   5. Simplified 98.2%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a + \left(t + \mathsf{fma}\left(i, y, z\right)\right)}{x}\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+202}:\\ \;\;\;\;\left(t + \left(a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a + \left(t + \mathsf{fma}\left(i, y, z\right)\right)}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 89.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+236}:\\ \;\;\;\;\left(t + \left(a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, x \cdot \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.15e+210)
   (* x (+ (log y) (/ a x)))
   (if (<= x 1.8e+236)
     (+ (+ t (+ a (fma (log c) (+ b -0.5) z))) (* y i))
     (fma y i (* x (log y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.15e+210) {
		tmp = x * (log(y) + (a / x));
	} else if (x <= 1.8e+236) {
		tmp = (t + (a + fma(log(c), (b + -0.5), z))) + (y * i);
	} else {
		tmp = fma(y, i, (x * log(y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.15e+210)
		tmp = Float64(x * Float64(log(y) + Float64(a / x)));
	elseif (x <= 1.8e+236)
		tmp = Float64(Float64(t + Float64(a + fma(log(c), Float64(b + -0.5), z))) + Float64(y * i));
	else
		tmp = fma(y, i, Float64(x * log(y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.15e+210], N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+236], N[(N[(t + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1499999999999999e210

   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 x around -inf

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

      1. mul-1-neg N/A

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

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

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

      3. distribute-lft-out N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

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

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

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

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

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

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

      9. /-lowering-/.f64 N/A

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

   5. Simplified 99.5%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 69.6

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

   8. Simplified 69.6%

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

   if -1.1499999999999999e210 < x < 1.8e236

   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

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-lowering-+.f64 93.0

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

   5. Simplified 93.0%

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

   if 1.8e236 < x

   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. Step-by-step derivation

      1. +-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

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

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

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

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

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

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

      15. +-lowering-+.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 88.7

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

   7. Simplified 88.7%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+236}:\\ \;\;\;\;\left(t + \left(a + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 89.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 1.48 \cdot 10^{+228}:\\ \;\;\;\;a + \left(\mathsf{fma}\left(i, y, z\right) + \mathsf{fma}\left(\log c, b + -0.5, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, x \cdot \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -8e+211)
   (* x (+ (log y) (/ a x)))
   (if (<= x 1.48e+228)
     (+ a (+ (fma i y z) (fma (log c) (+ b -0.5) t)))
     (fma y i (* x (log y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -8e+211) {
		tmp = x * (log(y) + (a / x));
	} else if (x <= 1.48e+228) {
		tmp = a + (fma(i, y, z) + fma(log(c), (b + -0.5), t));
	} else {
		tmp = fma(y, i, (x * log(y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -8e+211)
		tmp = Float64(x * Float64(log(y) + Float64(a / x)));
	elseif (x <= 1.48e+228)
		tmp = Float64(a + Float64(fma(i, y, z) + fma(log(c), Float64(b + -0.5), t)));
	else
		tmp = fma(y, i, Float64(x * log(y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -8e+211], N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.48e+228], N[(a + N[(N[(i * y + z), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.9999999999999997e211

   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 x around -inf

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

      1. mul-1-neg N/A

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

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

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

      3. distribute-lft-out N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

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

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

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

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

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

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

      9. /-lowering-/.f64 N/A

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

   5. Simplified 99.5%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 69.6

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

   8. Simplified 69.6%

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

   if -7.9999999999999997e211 < x < 1.48e228

   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. +-lowering-+.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. associate-+l+ N/A

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

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

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

      6. +-commutative N/A

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

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

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

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

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

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

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-lowering-+.f64 93.0

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

   5. Simplified 93.0%

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

   if 1.48e228 < x

   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. Step-by-step derivation

      1. +-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. associate-+l+ N/A

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

      10. +-commutative N/A

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

      11. associate-+l+ N/A

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

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

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{z + \left(x \cdot \log y + \left(t + a\right)\right)}\right)\right) \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, z + \color{blue}{\mathsf{fma}\left(x, \log y, t + a\right)}\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, z + \mathsf{fma}\left(x, \color{blue}{\log y}, t + a\right)\right)\right) \]

      15. +-lowering-+.f64 99.7

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, \color{blue}{t + a}\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{x \cdot \log y}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{x \cdot \log y}\right) \]

      2. log-lowering-log.f64 88.7

         \[\leadsto \mathsf{fma}\left(y, i, x \cdot \color{blue}{\log y}\right) \]

   7. Simplified 88.7%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{x \cdot \log y}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 73.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(y, i, t\_1\right)\\ \mathbf{elif}\;b - 0.5 \leq 4 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= (- b 0.5) -1e+168)
     (fma y i t_1)
     (if (<= (- b 0.5) 4e+240) (+ (* y i) (+ t (+ 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 = b * log(c);
	double tmp;
	if ((b - 0.5) <= -1e+168) {
		tmp = fma(y, i, t_1);
	} else if ((b - 0.5) <= 4e+240) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (Float64(b - 0.5) <= -1e+168)
		tmp = fma(y, i, t_1);
	elseif (Float64(b - 0.5) <= 4e+240)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(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[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+168], N[(y * i + t$95$1), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 4e+240], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -9.9999999999999993e167

   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. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - \frac{1}{2}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)}\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{\frac{-1}{2}}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      8. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \color{blue}{\log c}, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{\left(x \cdot \log y + z\right) + \left(t + a\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{\left(z + x \cdot \log y\right)} + \left(t + a\right)\right)\right) \]

      11. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{z + \left(x \cdot \log y + \left(t + a\right)\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{z + \left(x \cdot \log y + \left(t + a\right)\right)}\right)\right) \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, z + \color{blue}{\mathsf{fma}\left(x, \log y, t + a\right)}\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, z + \mathsf{fma}\left(x, \color{blue}{\log y}, t + a\right)\right)\right) \]

      15. +-lowering-+.f64 99.7

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, \color{blue}{t + a}\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{b \cdot \log c}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot b}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot b}\right) \]

      3. log-lowering-log.f64 78.4

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c} \cdot b\right) \]

   7. Simplified 78.4%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot b}\right) \]

   if -9.9999999999999993e167 < (-.f64 b #s(literal 1/2 binary64)) < 4.00000000000000006e240

   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

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) + a\right)} + y \cdot i \]

      2. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \left(t + \color{blue}{\left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)}\right) + y \cdot i \]

      5. +-commutative N/A

         \[\leadsto \left(t + \left(\color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)} + a\right)\right) + y \cdot i \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \left(t + \left(\color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)} + a\right)\right) + y \cdot i \]

      7. log-lowering-log.f64 N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right) + a\right)\right) + y \cdot i \]

      8. sub-neg N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right) + a\right)\right) + y \cdot i \]

      9. metadata-eval N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right) + a\right)\right) + y \cdot i \]

      10. +-lowering-+.f64 82.4

          \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right) + a\right)\right) + y \cdot i \]

   5. Simplified 82.4%

      \[\leadsto \color{blue}{\left(t + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + a\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
   7. Step-by-step derivation

   8. Simplified 74.5%

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]

   if 4.00000000000000006e240 < (-.f64 b #s(literal 1/2 binary64))

   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 b around inf

      \[\leadsto \color{blue}{b \cdot \log c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\log c \cdot b} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\log c \cdot b} \]

      3. log-lowering-log.f64 92.2

         \[\leadsto \color{blue}{\log c} \cdot b \]

   5. Simplified 92.2%

      \[\leadsto \color{blue}{\log c \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(y, i, b \cdot \log c\right)\\ \mathbf{elif}\;b - 0.5 \leq 4 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 72.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;a + t\_1\\ \mathbf{elif}\;b - 0.5 \leq 4 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= (- b 0.5) -5e+163)
     (+ a t_1)
     (if (<= (- b 0.5) 4e+240) (+ (* y i) (+ t (+ 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 = b * log(c);
	double tmp;
	if ((b - 0.5) <= -5e+163) {
		tmp = a + t_1;
	} else if ((b - 0.5) <= 4e+240) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if ((b - 0.5d0) <= (-5d+163)) then
        tmp = a + t_1
    else if ((b - 0.5d0) <= 4d+240) then
        tmp = (y * i) + (t + (z + a))
    else
        tmp = t_1
    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 t_1 = b * Math.log(c);
	double tmp;
	if ((b - 0.5) <= -5e+163) {
		tmp = a + t_1;
	} else if ((b - 0.5) <= 4e+240) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if (b - 0.5) <= -5e+163:
		tmp = a + t_1
	elif (b - 0.5) <= 4e+240:
		tmp = (y * i) + (t + (z + a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (Float64(b - 0.5) <= -5e+163)
		tmp = Float64(a + t_1);
	elseif (Float64(b - 0.5) <= 4e+240)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if ((b - 0.5) <= -5e+163)
		tmp = a + t_1;
	elseif ((b - 0.5) <= 4e+240)
		tmp = (y * i) + (t + (z + a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -5e+163], N[(a + t$95$1), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 4e+240], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -5e163

   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 x around 0

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) + a\right)} + y \cdot i \]

      2. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \left(t + \color{blue}{\left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)}\right) + y \cdot i \]

      5. +-commutative N/A

         \[\leadsto \left(t + \left(\color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)} + a\right)\right) + y \cdot i \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \left(t + \left(\color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)} + a\right)\right) + y \cdot i \]

      7. log-lowering-log.f64 N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right) + a\right)\right) + y \cdot i \]

      8. sub-neg N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right) + a\right)\right) + y \cdot i \]

      9. metadata-eval N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right) + a\right)\right) + y \cdot i \]

      10. +-lowering-+.f64 93.5

          \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right) + a\right)\right) + y \cdot i \]

   5. Simplified 93.5%

      \[\leadsto \color{blue}{\left(t + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + a\right)\right)} + y \cdot i \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto a + \color{blue}{\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a + \left(t + \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto a + \left(t + \color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)}\right) \]

      5. log-lowering-log.f64 N/A

         \[\leadsto a + \left(t + \mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right)\right) \]

      6. sub-neg N/A

         \[\leadsto a + \left(t + \mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto a + \left(t + \mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right)\right) \]

      8. +-lowering-+.f64 77.9

         \[\leadsto a + \left(t + \mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right)\right) \]

   8. Simplified 77.9%

      \[\leadsto \color{blue}{a + \left(t + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a + \color{blue}{b \cdot \log c} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a + \color{blue}{\log c \cdot b} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto a + \color{blue}{\log c \cdot b} \]

       3. log-lowering-log.f64 71.6

          \[\leadsto a + \color{blue}{\log c} \cdot b \]

   11. Simplified 71.6%

       \[\leadsto a + \color{blue}{\log c \cdot b} \]

   if -5e163 < (-.f64 b #s(literal 1/2 binary64)) < 4.00000000000000006e240

   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

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) + a\right)} + y \cdot i \]

      2. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \left(t + \color{blue}{\left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)}\right) + y \cdot i \]

      5. +-commutative N/A

         \[\leadsto \left(t + \left(\color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)} + a\right)\right) + y \cdot i \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \left(t + \left(\color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)} + a\right)\right) + y \cdot i \]

      7. log-lowering-log.f64 N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right) + a\right)\right) + y \cdot i \]

      8. sub-neg N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right) + a\right)\right) + y \cdot i \]

      9. metadata-eval N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right) + a\right)\right) + y \cdot i \]

      10. +-lowering-+.f64 82.3

          \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right) + a\right)\right) + y \cdot i \]

   5. Simplified 82.3%

      \[\leadsto \color{blue}{\left(t + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + a\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
   7. Step-by-step derivation

   8. Simplified 74.5%

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]

   if 4.00000000000000006e240 < (-.f64 b #s(literal 1/2 binary64))

   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 b around inf

      \[\leadsto \color{blue}{b \cdot \log c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\log c \cdot b} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\log c \cdot b} \]

      3. log-lowering-log.f64 92.2

         \[\leadsto \color{blue}{\log c} \cdot b \]

   5. Simplified 92.2%

      \[\leadsto \color{blue}{\log c \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{elif}\;b - 0.5 \leq 4 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 72.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b - 0.5 \leq -3.84 \cdot 10^{+199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b - 0.5 \leq 4 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= (- b 0.5) -3.84e+199)
     t_1
     (if (<= (- b 0.5) 4e+240) (+ (* y i) (+ t (+ 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 = b * log(c);
	double tmp;
	if ((b - 0.5) <= -3.84e+199) {
		tmp = t_1;
	} else if ((b - 0.5) <= 4e+240) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if ((b - 0.5d0) <= (-3.84d+199)) then
        tmp = t_1
    else if ((b - 0.5d0) <= 4d+240) then
        tmp = (y * i) + (t + (z + a))
    else
        tmp = t_1
    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 t_1 = b * Math.log(c);
	double tmp;
	if ((b - 0.5) <= -3.84e+199) {
		tmp = t_1;
	} else if ((b - 0.5) <= 4e+240) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if (b - 0.5) <= -3.84e+199:
		tmp = t_1
	elif (b - 0.5) <= 4e+240:
		tmp = (y * i) + (t + (z + a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (Float64(b - 0.5) <= -3.84e+199)
		tmp = t_1;
	elseif (Float64(b - 0.5) <= 4e+240)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if ((b - 0.5) <= -3.84e+199)
		tmp = t_1;
	elseif ((b - 0.5) <= 4e+240)
		tmp = (y * i) + (t + (z + a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -3.84e+199], t$95$1, If[LessEqual[N[(b - 0.5), $MachinePrecision], 4e+240], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -3.8400000000000002e199 or 4.00000000000000006e240 < (-.f64 b #s(literal 1/2 binary64))

   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 b around inf

      \[\leadsto \color{blue}{b \cdot \log c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\log c \cdot b} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\log c \cdot b} \]

      3. log-lowering-log.f64 78.0

         \[\leadsto \color{blue}{\log c} \cdot b \]

   5. Simplified 78.0%

      \[\leadsto \color{blue}{\log c \cdot b} \]

   if -3.8400000000000002e199 < (-.f64 b #s(literal 1/2 binary64)) < 4.00000000000000006e240

   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

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) + a\right)} + y \cdot i \]

      2. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \left(t + \color{blue}{\left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)}\right) + y \cdot i \]

      5. +-commutative N/A

         \[\leadsto \left(t + \left(\color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)} + a\right)\right) + y \cdot i \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \left(t + \left(\color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)} + a\right)\right) + y \cdot i \]

      7. log-lowering-log.f64 N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right) + a\right)\right) + y \cdot i \]

      8. sub-neg N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right) + a\right)\right) + y \cdot i \]

      9. metadata-eval N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right) + a\right)\right) + y \cdot i \]

      10. +-lowering-+.f64 82.9

          \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right) + a\right)\right) + y \cdot i \]

   5. Simplified 82.9%

      \[\leadsto \color{blue}{\left(t + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + a\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
   7. Step-by-step derivation

   8. Simplified 73.6%

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -3.84 \cdot 10^{+199}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b - 0.5 \leq 4 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 61.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.45 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.45e+104)
   (fma y i (fma (+ b -0.5) (log c) z))
   (+ (* y i) (+ t (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.45e+104) {
		tmp = fma(y, i, fma((b + -0.5), log(c), z));
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.45e+104)
		tmp = fma(y, i, fma(Float64(b + -0.5), log(c), z));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.45e+104], N[(y * i + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.44999999999999993e104

   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. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - \frac{1}{2}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)}\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{\frac{-1}{2}}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      8. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \color{blue}{\log c}, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{\left(x \cdot \log y + z\right) + \left(t + a\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{\left(z + x \cdot \log y\right)} + \left(t + a\right)\right)\right) \]

      11. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{z + \left(x \cdot \log y + \left(t + a\right)\right)}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{z + \left(x \cdot \log y + \left(t + a\right)\right)}\right)\right) \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, z + \color{blue}{\mathsf{fma}\left(x, \log y, t + a\right)}\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, z + \mathsf{fma}\left(x, \color{blue}{\log y}, t + a\right)\right)\right) \]

      15. +-lowering-+.f64 99.8

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, \color{blue}{t + a}\right)\right)\right) \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \frac{-1}{2}, \log c, \color{blue}{z}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 59.9%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z}\right)\right) \]

   if 2.44999999999999993e104 < a

   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

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) + a\right)} + y \cdot i \]

      2. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \left(t + \color{blue}{\left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)}\right) + y \cdot i \]

      5. +-commutative N/A

         \[\leadsto \left(t + \left(\color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)} + a\right)\right) + y \cdot i \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \left(t + \left(\color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)} + a\right)\right) + y \cdot i \]

      7. log-lowering-log.f64 N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right) + a\right)\right) + y \cdot i \]

      8. sub-neg N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right) + a\right)\right) + y \cdot i \]

      9. metadata-eval N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right) + a\right)\right) + y \cdot i \]

      10. +-lowering-+.f64 91.3

          \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right) + a\right)\right) + y \cdot i \]

   5. Simplified 91.3%

      \[\leadsto \color{blue}{\left(t + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + a\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
   7. Step-by-step derivation

   8. Simplified 87.1%

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.45 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 71.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+235}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -3.2e+205)
     t_1
     (if (<= x 1.7e+235) (+ (* y i) (+ t (+ 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 = x * log(y);
	double tmp;
	if (x <= -3.2e+205) {
		tmp = t_1;
	} else if (x <= 1.7e+235) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-3.2d+205)) then
        tmp = t_1
    else if (x <= 1.7d+235) then
        tmp = (y * i) + (t + (z + a))
    else
        tmp = t_1
    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 t_1 = x * Math.log(y);
	double tmp;
	if (x <= -3.2e+205) {
		tmp = t_1;
	} else if (x <= 1.7e+235) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -3.2e+205:
		tmp = t_1
	elif x <= 1.7e+235:
		tmp = (y * i) + (t + (z + a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -3.2e+205)
		tmp = t_1;
	elseif (x <= 1.7e+235)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -3.2e+205)
		tmp = t_1;
	elseif (x <= 1.7e+235)
		tmp = (y * i) + (t + (z + a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+205], t$95$1, If[LessEqual[x, 1.7e+235], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999996e205 or 1.69999999999999998e235 < x

   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 x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \log y} \]

      2. log-lowering-log.f64 67.8

         \[\leadsto x \cdot \color{blue}{\log y} \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if -3.19999999999999996e205 < x < 1.69999999999999998e235

   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

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) + a\right)} + y \cdot i \]

      2. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \left(t + \color{blue}{\left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)}\right) + y \cdot i \]

      5. +-commutative N/A

         \[\leadsto \left(t + \left(\color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)} + a\right)\right) + y \cdot i \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \left(t + \left(\color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)} + a\right)\right) + y \cdot i \]

      7. log-lowering-log.f64 N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right) + a\right)\right) + y \cdot i \]

      8. sub-neg N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right) + a\right)\right) + y \cdot i \]

      9. metadata-eval N/A

         \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right) + a\right)\right) + y \cdot i \]

      10. +-lowering-+.f64 92.9

          \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right) + a\right)\right) + y \cdot i \]

   5. Simplified 92.9%

      \[\leadsto \color{blue}{\left(t + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + a\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
   7. Step-by-step derivation

   8. Simplified 72.3%

      \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+205}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+235}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 67.5% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ y \cdot i + \left(t + \left(z + a\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (+ (* y i) (+ t (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (t + (z + a));
}

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 = (y * i) + (t + (z + a))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (t + (z + a));
}

Python

def code(x, y, z, t, a, b, c, i):
	return (y * i) + (t + (z + a))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(y * i) + Float64(t + Float64(z + a)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + (t + (z + a));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

   \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} + y \cdot i \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) + a\right)} + y \cdot i \]

   2. associate-+l+ N/A

      \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

   4. +-lowering-+.f64 N/A

      \[\leadsto \left(t + \color{blue}{\left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)}\right) + y \cdot i \]

   5. +-commutative N/A

      \[\leadsto \left(t + \left(\color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)} + a\right)\right) + y \cdot i \]

   6. accelerator-lowering-fma.f64 N/A

      \[\leadsto \left(t + \left(\color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)} + a\right)\right) + y \cdot i \]

   7. log-lowering-log.f64 N/A

      \[\leadsto \left(t + \left(\mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right) + a\right)\right) + y \cdot i \]

   8. sub-neg N/A

      \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right) + a\right)\right) + y \cdot i \]

   9. metadata-eval N/A

      \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right) + a\right)\right) + y \cdot i \]

   10. +-lowering-+.f64 84.7

       \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right) + a\right)\right) + y \cdot i \]

5. Simplified 84.7%

   \[\leadsto \color{blue}{\left(t + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + a\right)\right)} + y \cdot i \]

6. Taylor expanded in z around inf

   \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]
7. Step-by-step derivation

8. Simplified 65.3%

   \[\leadsto \left(t + \left(\color{blue}{z} + a\right)\right) + y \cdot i \]

9. Final simplification 65.3%

   \[\leadsto y \cdot i + \left(t + \left(z + a\right)\right) \]
10. Add Preprocessing

Alternative 25: 30.7% accurate, 58.5× speedup

Math

\[\begin{array}{l} \\ z + a \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (+ z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return z + a;
}

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 = z + a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return z + a;
}

Python

def code(x, y, z, t, a, b, c, i):
	return z + a

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(z + a)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = z + a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(z + a), $MachinePrecision]

Derivation

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

   \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} + y \cdot i \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) + a\right)} + y \cdot i \]

   2. associate-+l+ N/A

      \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \color{blue}{\left(t + \left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)\right)} + y \cdot i \]

   4. +-lowering-+.f64 N/A

      \[\leadsto \left(t + \color{blue}{\left(\left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right) + a\right)}\right) + y \cdot i \]

   5. +-commutative N/A

      \[\leadsto \left(t + \left(\color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)} + a\right)\right) + y \cdot i \]

   6. accelerator-lowering-fma.f64 N/A

      \[\leadsto \left(t + \left(\color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)} + a\right)\right) + y \cdot i \]

   7. log-lowering-log.f64 N/A

      \[\leadsto \left(t + \left(\mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right) + a\right)\right) + y \cdot i \]

   8. sub-neg N/A

      \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right) + a\right)\right) + y \cdot i \]

   9. metadata-eval N/A

      \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right) + a\right)\right) + y \cdot i \]

   10. +-lowering-+.f64 84.7

       \[\leadsto \left(t + \left(\mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right) + a\right)\right) + y \cdot i \]

5. Simplified 84.7%

   \[\leadsto \color{blue}{\left(t + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + a\right)\right)} + y \cdot i \]

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
7. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

   2. +-lowering-+.f64 N/A

      \[\leadsto a + \color{blue}{\left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

   3. +-commutative N/A

      \[\leadsto a + \left(t + \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right) + z\right)}\right) \]

   4. accelerator-lowering-fma.f64 N/A

      \[\leadsto a + \left(t + \color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, z\right)}\right) \]

   5. log-lowering-log.f64 N/A

      \[\leadsto a + \left(t + \mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, z\right)\right) \]

   6. sub-neg N/A

      \[\leadsto a + \left(t + \mathsf{fma}\left(\log c, \color{blue}{b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, z\right)\right) \]

   7. metadata-eval N/A

      \[\leadsto a + \left(t + \mathsf{fma}\left(\log c, b + \color{blue}{\frac{-1}{2}}, z\right)\right) \]

   8. +-lowering-+.f64 63.3

      \[\leadsto a + \left(t + \mathsf{fma}\left(\log c, \color{blue}{b + -0.5}, z\right)\right) \]

8. Simplified 63.3%

   \[\leadsto \color{blue}{a + \left(t + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)} \]

9. Taylor expanded in z around inf

   \[\leadsto a + \color{blue}{z} \]
10. Step-by-step derivation

11. Simplified 32.5%

    \[\leadsto a + \color{blue}{z} \]

12. Final simplification 32.5%

    \[\leadsto z + a \]
13. Add Preprocessing

Alternative 26: 16.1% accurate, 234.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a;
}

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 = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a;
}

Python

def code(x, y, z, t, a, b, c, i):
	return a

Julia

function code(x, y, z, t, a, b, c, i)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

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 a around inf

   \[\leadsto \color{blue}{a} \]
4. Step-by-step derivation

5. Simplified 19.0%

   \[\leadsto \color{blue}{a} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024199 
(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)))