FastMath dist4

Percentage Accurate: 88.5% → 100.0%

Time: 11.7s

Alternatives: 12

Speedup: 1.7×

• 33.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Python

def code(d1, d2, d3, d4):
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision]

Initial Program: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Python

def code(d1, d2, d3, d4):
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 (+ d2 (- d4 (+ d1 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * (d2 + (d4 - (d1 + d3)));
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * (d2 + (d4 - (d1 + d3)))
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * (d2 + (d4 - (d1 + d3)));
}

Python

def code(d1, d2, d3, d4):
	return d1 * (d2 + (d4 - (d1 + d3)))

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * Float64(d2 + Float64(d4 - Float64(d1 + d3))))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * (d2 + (d4 - (d1 + d3)));
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * N[(d2 + N[(d4 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.3%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
2. Step-by-step derivation

   1. distribute-lft-out-- N/A

      \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

   2. *-commutative N/A

      \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

   3. distribute-lft-out N/A

      \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

   4. distribute-lft-out-- N/A

      \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

   6. associate-+r- N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

   8. associate-+l+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

   10. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

   11. unsub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

   12. associate--l- N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

   13. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

   16. +-lowering-+.f64 100.0%

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d4 - d3\right)\\ \mathbf{if}\;d2 \leq -3.5 \cdot 10^{+49}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d2 \leq -4.6 \cdot 10^{-77}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d2 \leq 5.8 \cdot 10^{-214}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d4 d3))))
   (if (<= d2 -3.5e+49)
     (* d1 (- d2 d1))
     (if (<= d2 -4.6e-77) t_0 (if (<= d2 5.8e-214) (* d1 (- d4 d1)) t_0)))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d4 - d3);
	double tmp;
	if (d2 <= -3.5e+49) {
		tmp = d1 * (d2 - d1);
	} else if (d2 <= -4.6e-77) {
		tmp = t_0;
	} else if (d2 <= 5.8e-214) {
		tmp = d1 * (d4 - d1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = d1 * (d4 - d3)
    if (d2 <= (-3.5d+49)) then
        tmp = d1 * (d2 - d1)
    else if (d2 <= (-4.6d-77)) then
        tmp = t_0
    else if (d2 <= 5.8d-214) then
        tmp = d1 * (d4 - d1)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d4 - d3);
	double tmp;
	if (d2 <= -3.5e+49) {
		tmp = d1 * (d2 - d1);
	} else if (d2 <= -4.6e-77) {
		tmp = t_0;
	} else if (d2 <= 5.8e-214) {
		tmp = d1 * (d4 - d1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d4 - d3)
	tmp = 0
	if d2 <= -3.5e+49:
		tmp = d1 * (d2 - d1)
	elif d2 <= -4.6e-77:
		tmp = t_0
	elif d2 <= 5.8e-214:
		tmp = d1 * (d4 - d1)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d4 - d3))
	tmp = 0.0
	if (d2 <= -3.5e+49)
		tmp = Float64(d1 * Float64(d2 - d1));
	elseif (d2 <= -4.6e-77)
		tmp = t_0;
	elseif (d2 <= 5.8e-214)
		tmp = Float64(d1 * Float64(d4 - d1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d4 - d3);
	tmp = 0.0;
	if (d2 <= -3.5e+49)
		tmp = d1 * (d2 - d1);
	elseif (d2 <= -4.6e-77)
		tmp = t_0;
	elseif (d2 <= 5.8e-214)
		tmp = d1 * (d4 - d1);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d2, -3.5e+49], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d2, -4.6e-77], t$95$0, If[LessEqual[d2, 5.8e-214], N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -3.49999999999999975e49

   1. Initial program 83.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d2 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 90.3%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 90.3%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d1 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{d1}\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 78.8%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{d1}\right) \]

   if -3.49999999999999975e49 < d2 < -4.59999999999999997e-77 or 5.7999999999999997e-214 < d2

   1. Initial program 85.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto d1 \cdot \left(\left(d4 - \left(d1 + d3\right)\right) + \color{blue}{d2}\right) \]

      2. distribute-lft-in N/A

         \[\leadsto d1 \cdot \left(d4 - \left(d1 + d3\right)\right) + \color{blue}{d1 \cdot d2} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\right), \color{blue}{\left(d1 \cdot d2\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \left(d4 - \left(d1 + d3\right)\right)\right), \left(\color{blue}{d1} \cdot d2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \left(d1 + d3\right)\right)\right), \left(d1 \cdot d2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, d3\right)\right)\right), \left(d1 \cdot d2\right)\right) \]

      7. *-lowering-*.f64 93.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, d3\right)\right)\right), \mathsf{*.f64}\left(d1, \color{blue}{d2}\right)\right) \]

   6. Applied egg-rr 93.2%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right) + d1 \cdot d2} \]

   7. Taylor expanded in d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 79.5%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   9. Simplified 79.5%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]

   10. Taylor expanded in d1 around 0

       \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
   11. Step-by-step derivation

       1. remove-double-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(d1 \cdot \left(d4 - d3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{neg}\left(d1 \cdot \left(\mathsf{neg}\left(\left(d4 - d3\right)\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(d1 \cdot \left(-1 \cdot \left(d4 - d3\right)\right)\right) \]

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

          \[\leadsto d1 \cdot \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(d4 - d3\right)\right)\right)} \]

       5. *-rgt-identity N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d4 - d3\right)\right) \cdot 1\right)\right) \]

       6. *-inverses N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d4 - d3\right)\right) \cdot \frac{d1}{d1}\right)\right) \]

       7. associate-/l* N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{\left(-1 \cdot \left(d4 - d3\right)\right) \cdot d1}{d1}\right)\right) \]

       8. associate-*l/ N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{-1 \cdot \left(d4 - d3\right)}{d1} \cdot d1\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \frac{d4 - d3}{d1}\right) \cdot d1\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{d4 - d3}{d1}\right) \cdot d1\right)\right)}\right) \]

       11. neg-sub0 N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \color{blue}{\left(-1 \cdot \frac{d4 - d3}{d1}\right) \cdot d1}\right)\right) \]

       12. associate-*r/ N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \frac{-1 \cdot \left(d4 - d3\right)}{d1} \cdot d1\right)\right) \]

       13. associate-*l/ N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \frac{\left(-1 \cdot \left(d4 - d3\right)\right) \cdot d1}{\color{blue}{d1}}\right)\right) \]

       14. associate-/l* N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \left(-1 \cdot \left(d4 - d3\right)\right) \cdot \color{blue}{\frac{d1}{d1}}\right)\right) \]

       15. *-inverses N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \left(-1 \cdot \left(d4 - d3\right)\right) \cdot 1\right)\right) \]

       16. mul-1-neg N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \left(\mathsf{neg}\left(\left(d4 - d3\right)\right)\right) \cdot 1\right)\right) \]

       17. cancel-sign-sub N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 + \color{blue}{\left(d4 - d3\right) \cdot 1}\right)\right) \]

       18. *-rgt-identity N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 + \left(d4 - \color{blue}{d3}\right)\right)\right) \]

       19. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 + \left(d4 + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

       20. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 + \left(\left(\mathsf{neg}\left(d3\right)\right) + \color{blue}{d4}\right)\right)\right) \]

       21. associate-+l+ N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(0 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \color{blue}{d4}\right)\right) \]

   12. Simplified 59.3%

       \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]

   if -4.59999999999999997e-77 < d2 < 5.7999999999999997e-214

   1. Initial program 82.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(d1 \cdot d4\right)}, \mathsf{*.f64}\left(d1, d1\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 65.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(d1, d4\right), \mathsf{*.f64}\left(\color{blue}{d1}, d1\right)\right) \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{d1 \cdot d4} - d1 \cdot d1 \]
   6. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(d4 - d1\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(d4 - d1\right) \cdot \color{blue}{d1} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(d4 - d1\right), \color{blue}{d1}\right) \]

      4. --lowering--.f64 77.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(d4, d1\right), d1\right) \]

   7. Applied egg-rr 77.8%

      \[\leadsto \color{blue}{\left(d4 - d1\right) \cdot d1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -3.5 \cdot 10^{+49}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d2 \leq -4.6 \cdot 10^{-77}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \mathbf{elif}\;d2 \leq 5.8 \cdot 10^{-214}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d3\right)\\ \mathbf{if}\;d3 \leq -1.02 \cdot 10^{+89}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq -1.5 \cdot 10^{-141}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d3 \leq 4 \cdot 10^{+46}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d3))))
   (if (<= d3 -1.02e+89)
     t_0
     (if (<= d3 -1.5e-141)
       (* d1 (+ d2 d4))
       (if (<= d3 4e+46) (* d1 (- d2 d1)) t_0)))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d3);
	double tmp;
	if (d3 <= -1.02e+89) {
		tmp = t_0;
	} else if (d3 <= -1.5e-141) {
		tmp = d1 * (d2 + d4);
	} else if (d3 <= 4e+46) {
		tmp = d1 * (d2 - d1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = d1 * (d2 - d3)
    if (d3 <= (-1.02d+89)) then
        tmp = t_0
    else if (d3 <= (-1.5d-141)) then
        tmp = d1 * (d2 + d4)
    else if (d3 <= 4d+46) then
        tmp = d1 * (d2 - d1)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d3);
	double tmp;
	if (d3 <= -1.02e+89) {
		tmp = t_0;
	} else if (d3 <= -1.5e-141) {
		tmp = d1 * (d2 + d4);
	} else if (d3 <= 4e+46) {
		tmp = d1 * (d2 - d1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d3)
	tmp = 0
	if d3 <= -1.02e+89:
		tmp = t_0
	elif d3 <= -1.5e-141:
		tmp = d1 * (d2 + d4)
	elif d3 <= 4e+46:
		tmp = d1 * (d2 - d1)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d3))
	tmp = 0.0
	if (d3 <= -1.02e+89)
		tmp = t_0;
	elseif (d3 <= -1.5e-141)
		tmp = Float64(d1 * Float64(d2 + d4));
	elseif (d3 <= 4e+46)
		tmp = Float64(d1 * Float64(d2 - d1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d3);
	tmp = 0.0;
	if (d3 <= -1.02e+89)
		tmp = t_0;
	elseif (d3 <= -1.5e-141)
		tmp = d1 * (d2 + d4);
	elseif (d3 <= 4e+46)
		tmp = d1 * (d2 - d1);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -1.02e+89], t$95$0, If[LessEqual[d3, -1.5e-141], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], If[LessEqual[d3, 4e+46], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -1.0199999999999999e89 or 4e46 < d3

   1. Initial program 80.6%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d2 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 88.2%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 88.2%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{d3}\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 82.5%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{d3}\right) \]

   if -1.0199999999999999e89 < d3 < -1.49999999999999992e-141

   1. Initial program 91.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 99.9%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{d4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 72.1%

      \[\leadsto d1 \cdot \left(d2 + \color{blue}{d4}\right) \]

   if -1.49999999999999992e-141 < d3 < 4e46

   1. Initial program 83.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d2 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 69.8%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 69.8%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d1 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{d1}\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 67.9%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{d1}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 87.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d1 \leq -1.55 \cdot 10^{+167}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d1 \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;d1 \cdot \left(d4 + \left(d2 - d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d1 -1.55e+167)
   (* d1 (- d2 d1))
   (if (<= d1 2.9e+44) (* d1 (+ d4 (- d2 d3))) (* d1 (- d4 d1)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d1 <= -1.55e+167) {
		tmp = d1 * (d2 - d1);
	} else if (d1 <= 2.9e+44) {
		tmp = d1 * (d4 + (d2 - d3));
	} else {
		tmp = d1 * (d4 - d1);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d1 <= (-1.55d+167)) then
        tmp = d1 * (d2 - d1)
    else if (d1 <= 2.9d+44) then
        tmp = d1 * (d4 + (d2 - d3))
    else
        tmp = d1 * (d4 - d1)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d1 <= -1.55e+167) {
		tmp = d1 * (d2 - d1);
	} else if (d1 <= 2.9e+44) {
		tmp = d1 * (d4 + (d2 - d3));
	} else {
		tmp = d1 * (d4 - d1);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d1 <= -1.55e+167:
		tmp = d1 * (d2 - d1)
	elif d1 <= 2.9e+44:
		tmp = d1 * (d4 + (d2 - d3))
	else:
		tmp = d1 * (d4 - d1)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d1 <= -1.55e+167)
		tmp = Float64(d1 * Float64(d2 - d1));
	elseif (d1 <= 2.9e+44)
		tmp = Float64(d1 * Float64(d4 + Float64(d2 - d3)));
	else
		tmp = Float64(d1 * Float64(d4 - d1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d1 <= -1.55e+167)
		tmp = d1 * (d2 - d1);
	elseif (d1 <= 2.9e+44)
		tmp = d1 * (d4 + (d2 - d3));
	else
		tmp = d1 * (d4 - d1);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d1, -1.55e+167], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d1, 2.9e+44], N[(d1 * N[(d4 + N[(d2 - d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d1 < -1.55e167

   1. Initial program 38.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d2 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 94.1%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 94.1%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d1 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{d1}\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 91.2%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{d1}\right) \]

   if -1.55e167 < d1 < 2.9000000000000002e44

   1. Initial program 98.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(d2 + d4\right) - d3\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d4 + d2\right) - d3\right)\right) \]

      3. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d4 + \color{blue}{\left(d2 - d3\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d4, \color{blue}{\left(d2 - d3\right)}\right)\right) \]

      5. --lowering--.f64 91.7%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d4, \mathsf{\_.f64}\left(d2, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 91.7%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} \]

   if 2.9000000000000002e44 < d1

   1. Initial program 71.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(d1 \cdot d4\right)}, \mathsf{*.f64}\left(d1, d1\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 65.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(d1, d4\right), \mathsf{*.f64}\left(\color{blue}{d1}, d1\right)\right) \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{d1 \cdot d4} - d1 \cdot d1 \]
   6. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(d4 - d1\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(d4 - d1\right) \cdot \color{blue}{d1} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(d4 - d1\right), \color{blue}{d1}\right) \]

      4. --lowering--.f64 74.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(d4, d1\right), d1\right) \]

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\left(d4 - d1\right) \cdot d1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d1 \leq -1.55 \cdot 10^{+167}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d1 \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;d1 \cdot \left(d4 + \left(d2 - d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq -1.35 \cdot 10^{-250}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d4 \leq 1.6 \cdot 10^{+110}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 -1.35e-250)
   (* d1 (- d2 d3))
   (if (<= d4 1.6e+110) (* d1 (- d2 d1)) (* d1 (- d4 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= -1.35e-250) {
		tmp = d1 * (d2 - d3);
	} else if (d4 <= 1.6e+110) {
		tmp = d1 * (d2 - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= (-1.35d-250)) then
        tmp = d1 * (d2 - d3)
    else if (d4 <= 1.6d+110) then
        tmp = d1 * (d2 - d1)
    else
        tmp = d1 * (d4 - d3)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= -1.35e-250) {
		tmp = d1 * (d2 - d3);
	} else if (d4 <= 1.6e+110) {
		tmp = d1 * (d2 - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= -1.35e-250:
		tmp = d1 * (d2 - d3)
	elif d4 <= 1.6e+110:
		tmp = d1 * (d2 - d1)
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= -1.35e-250)
		tmp = Float64(d1 * Float64(d2 - d3));
	elseif (d4 <= 1.6e+110)
		tmp = Float64(d1 * Float64(d2 - d1));
	else
		tmp = Float64(d1 * Float64(d4 - d3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= -1.35e-250)
		tmp = d1 * (d2 - d3);
	elseif (d4 <= 1.6e+110)
		tmp = d1 * (d2 - d1);
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, -1.35e-250], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], If[LessEqual[d4, 1.6e+110], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d4 < -1.35000000000000001e-250

   1. Initial program 81.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d2 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 73.3%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 73.3%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{d3}\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 58.3%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{d3}\right) \]

   if -1.35000000000000001e-250 < d4 < 1.59999999999999997e110

   1. Initial program 87.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d2 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 95.0%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 95.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d1 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{d1}\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 72.9%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{d1}\right) \]

   if 1.59999999999999997e110 < d4

   1. Initial program 86.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto d1 \cdot \left(\left(d4 - \left(d1 + d3\right)\right) + \color{blue}{d2}\right) \]

      2. distribute-lft-in N/A

         \[\leadsto d1 \cdot \left(d4 - \left(d1 + d3\right)\right) + \color{blue}{d1 \cdot d2} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\right), \color{blue}{\left(d1 \cdot d2\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \left(d4 - \left(d1 + d3\right)\right)\right), \left(\color{blue}{d1} \cdot d2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \left(d1 + d3\right)\right)\right), \left(d1 \cdot d2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, d3\right)\right)\right), \left(d1 \cdot d2\right)\right) \]

      7. *-lowering-*.f64 95.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, d3\right)\right)\right), \mathsf{*.f64}\left(d1, \color{blue}{d2}\right)\right) \]

   6. Applied egg-rr 95.6%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right) + d1 \cdot d2} \]

   7. Taylor expanded in d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 91.8%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   9. Simplified 91.8%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]

   10. Taylor expanded in d1 around 0

       \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
   11. Step-by-step derivation

       1. remove-double-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(d1 \cdot \left(d4 - d3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{neg}\left(d1 \cdot \left(\mathsf{neg}\left(\left(d4 - d3\right)\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(d1 \cdot \left(-1 \cdot \left(d4 - d3\right)\right)\right) \]

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

          \[\leadsto d1 \cdot \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(d4 - d3\right)\right)\right)} \]

       5. *-rgt-identity N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d4 - d3\right)\right) \cdot 1\right)\right) \]

       6. *-inverses N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d4 - d3\right)\right) \cdot \frac{d1}{d1}\right)\right) \]

       7. associate-/l* N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{\left(-1 \cdot \left(d4 - d3\right)\right) \cdot d1}{d1}\right)\right) \]

       8. associate-*l/ N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{-1 \cdot \left(d4 - d3\right)}{d1} \cdot d1\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \frac{d4 - d3}{d1}\right) \cdot d1\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{d4 - d3}{d1}\right) \cdot d1\right)\right)}\right) \]

       11. neg-sub0 N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \color{blue}{\left(-1 \cdot \frac{d4 - d3}{d1}\right) \cdot d1}\right)\right) \]

       12. associate-*r/ N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \frac{-1 \cdot \left(d4 - d3\right)}{d1} \cdot d1\right)\right) \]

       13. associate-*l/ N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \frac{\left(-1 \cdot \left(d4 - d3\right)\right) \cdot d1}{\color{blue}{d1}}\right)\right) \]

       14. associate-/l* N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \left(-1 \cdot \left(d4 - d3\right)\right) \cdot \color{blue}{\frac{d1}{d1}}\right)\right) \]

       15. *-inverses N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \left(-1 \cdot \left(d4 - d3\right)\right) \cdot 1\right)\right) \]

       16. mul-1-neg N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 - \left(\mathsf{neg}\left(\left(d4 - d3\right)\right)\right) \cdot 1\right)\right) \]

       17. cancel-sign-sub N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 + \color{blue}{\left(d4 - d3\right) \cdot 1}\right)\right) \]

       18. *-rgt-identity N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 + \left(d4 - \color{blue}{d3}\right)\right)\right) \]

       19. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 + \left(d4 + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

       20. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(0 + \left(\left(\mathsf{neg}\left(d3\right)\right) + \color{blue}{d4}\right)\right)\right) \]

       21. associate-+l+ N/A

           \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(0 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \color{blue}{d4}\right)\right) \]

   12. Simplified 80.6%

       \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0 - d1 \cdot d3\\ \mathbf{if}\;d3 \leq -3.3 \cdot 10^{+89}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq 4.4 \cdot 10^{+178}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (- 0.0 (* d1 d3))))
   (if (<= d3 -3.3e+89) t_0 (if (<= d3 4.4e+178) (* d1 (+ d2 d4)) t_0))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = 0.0 - (d1 * d3);
	double tmp;
	if (d3 <= -3.3e+89) {
		tmp = t_0;
	} else if (d3 <= 4.4e+178) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.0d0 - (d1 * d3)
    if (d3 <= (-3.3d+89)) then
        tmp = t_0
    else if (d3 <= 4.4d+178) then
        tmp = d1 * (d2 + d4)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = 0.0 - (d1 * d3);
	double tmp;
	if (d3 <= -3.3e+89) {
		tmp = t_0;
	} else if (d3 <= 4.4e+178) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = 0.0 - (d1 * d3)
	tmp = 0
	if d3 <= -3.3e+89:
		tmp = t_0
	elif d3 <= 4.4e+178:
		tmp = d1 * (d2 + d4)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(0.0 - Float64(d1 * d3))
	tmp = 0.0
	if (d3 <= -3.3e+89)
		tmp = t_0;
	elseif (d3 <= 4.4e+178)
		tmp = Float64(d1 * Float64(d2 + d4));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = 0.0 - (d1 * d3);
	tmp = 0.0;
	if (d3 <= -3.3e+89)
		tmp = t_0;
	elseif (d3 <= 4.4e+178)
		tmp = d1 * (d2 + d4);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(0.0 - N[(d1 * d3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -3.3e+89], t$95$0, If[LessEqual[d3, 4.4e+178], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d3 < -3.29999999999999974e89 or 4.39999999999999994e178 < d3

   1. Initial program 77.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d3 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(d1 \cdot d3\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot d3\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{d1 \cdot d3} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(d1 \cdot d3\right)}\right) \]

      4. *-lowering-*.f64 83.8%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(d1, \color{blue}{d3}\right)\right) \]

   7. Simplified 83.8%

      \[\leadsto \color{blue}{0 - d1 \cdot d3} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot d3\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(d1 \cdot d3\right)\right) \]

      3. *-lowering-*.f64 83.8%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(d1, d3\right)\right) \]

   9. Applied egg-rr 83.8%

      \[\leadsto \color{blue}{-d1 \cdot d3} \]

   if -3.29999999999999974e89 < d3 < 4.39999999999999994e178

   1. Initial program 86.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{d4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 66.3%

      \[\leadsto d1 \cdot \left(d2 + \color{blue}{d4}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -3.3 \cdot 10^{+89}:\\ \;\;\;\;0 - d1 \cdot d3\\ \mathbf{elif}\;d3 \leq 4.4 \cdot 10^{+178}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;0 - d1 \cdot d3\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -8.2 \cdot 10^{+92}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq 1.72 \cdot 10^{-252}:\\ \;\;\;\;0 - d1 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -8.2e+92)
   (* d1 d2)
   (if (<= d2 1.72e-252) (- 0.0 (* d1 d1)) (* d1 d4))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -8.2e+92) {
		tmp = d1 * d2;
	} else if (d2 <= 1.72e-252) {
		tmp = 0.0 - (d1 * d1);
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-8.2d+92)) then
        tmp = d1 * d2
    else if (d2 <= 1.72d-252) then
        tmp = 0.0d0 - (d1 * d1)
    else
        tmp = d1 * d4
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -8.2e+92) {
		tmp = d1 * d2;
	} else if (d2 <= 1.72e-252) {
		tmp = 0.0 - (d1 * d1);
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -8.2e+92:
		tmp = d1 * d2
	elif d2 <= 1.72e-252:
		tmp = 0.0 - (d1 * d1)
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -8.2e+92)
		tmp = Float64(d1 * d2);
	elseif (d2 <= 1.72e-252)
		tmp = Float64(0.0 - Float64(d1 * d1));
	else
		tmp = Float64(d1 * d4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -8.2e+92)
		tmp = d1 * d2;
	elseif (d2 <= 1.72e-252)
		tmp = 0.0 - (d1 * d1);
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -8.2e+92], N[(d1 * d2), $MachinePrecision], If[LessEqual[d2, 1.72e-252], N[(0.0 - N[(d1 * d1), $MachinePrecision]), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -8.20000000000000047e92

   1. Initial program 81.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around inf

      \[\leadsto \color{blue}{d1 \cdot d2} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.6%

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{d2}\right) \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{d1 \cdot d2} \]

   if -8.20000000000000047e92 < d2 < 1.7200000000000001e-252

   1. Initial program 85.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d1 around inf

      \[\leadsto \color{blue}{-1 \cdot {d1}^{2}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({d1}^{2}\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{{d1}^{2}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left({d1}^{2}\right)}\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(d1 \cdot \color{blue}{d1}\right)\right) \]

      5. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(d1, \color{blue}{d1}\right)\right) \]

   7. Simplified 43.2%

      \[\leadsto \color{blue}{0 - d1 \cdot d1} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot d1\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(d1 \cdot d1\right)\right) \]

      3. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(d1, d1\right)\right) \]

   9. Applied egg-rr 43.2%

      \[\leadsto \color{blue}{-d1 \cdot d1} \]

   if 1.7200000000000001e-252 < d2

   1. Initial program 85.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \color{blue}{d1 \cdot d4} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 30.9%

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{d4}\right) \]

   7. Simplified 30.9%

      \[\leadsto \color{blue}{d1 \cdot d4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -8.2 \cdot 10^{+92}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq 1.72 \cdot 10^{-252}:\\ \;\;\;\;0 - d1 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -1.35 \cdot 10^{-39}:\\ \;\;\;\;d1 \cdot \left(d2 - \left(d1 + d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -1.35e-39) (* d1 (- d2 (+ d1 d3))) (* d1 (- d4 (+ d1 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.35e-39) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - (d1 + d3));
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-1.35d-39)) then
        tmp = d1 * (d2 - (d1 + d3))
    else
        tmp = d1 * (d4 - (d1 + d3))
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.35e-39) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - (d1 + d3));
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -1.35e-39:
		tmp = d1 * (d2 - (d1 + d3))
	else:
		tmp = d1 * (d4 - (d1 + d3))
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -1.35e-39)
		tmp = Float64(d1 * Float64(d2 - Float64(d1 + d3)));
	else
		tmp = Float64(d1 * Float64(d4 - Float64(d1 + d3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -1.35e-39)
		tmp = d1 * (d2 - (d1 + d3));
	else
		tmp = d1 * (d4 - (d1 + d3));
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -1.35e-39], N[(d1 * N[(d2 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -1.35e-39

   1. Initial program 85.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d2 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 88.5%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 88.5%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]

   if -1.35e-39 < d2

   1. Initial program 84.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto d1 \cdot \left(\left(d4 - \left(d1 + d3\right)\right) + \color{blue}{d2}\right) \]

      2. distribute-lft-in N/A

         \[\leadsto d1 \cdot \left(d4 - \left(d1 + d3\right)\right) + \color{blue}{d1 \cdot d2} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\right), \color{blue}{\left(d1 \cdot d2\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \left(d4 - \left(d1 + d3\right)\right)\right), \left(\color{blue}{d1} \cdot d2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \left(d1 + d3\right)\right)\right), \left(d1 \cdot d2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, d3\right)\right)\right), \left(d1 \cdot d2\right)\right) \]

      7. *-lowering-*.f64 95.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, d3\right)\right)\right), \mathsf{*.f64}\left(d1, \color{blue}{d2}\right)\right) \]

   6. Applied egg-rr 95.6%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right) + d1 \cdot d2} \]

   7. Taylor expanded in d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 86.7%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   9. Simplified 86.7%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 84.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 4 \cdot 10^{+116}:\\ \;\;\;\;d1 \cdot \left(d2 - \left(d1 + d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 + \left(d2 - d3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 4e+116) (* d1 (- d2 (+ d1 d3))) (* d1 (+ d4 (- d2 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 4e+116) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 + (d2 - d3));
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= 4d+116) then
        tmp = d1 * (d2 - (d1 + d3))
    else
        tmp = d1 * (d4 + (d2 - d3))
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 4e+116) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 + (d2 - d3));
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 4e+116:
		tmp = d1 * (d2 - (d1 + d3))
	else:
		tmp = d1 * (d4 + (d2 - d3))
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 4e+116)
		tmp = Float64(d1 * Float64(d2 - Float64(d1 + d3)));
	else
		tmp = Float64(d1 * Float64(d4 + Float64(d2 - d3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 4e+116)
		tmp = d1 * (d2 - (d1 + d3));
	else
		tmp = d1 * (d4 + (d2 - d3));
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 4e+116], N[(d1 * N[(d2 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 + N[(d2 - d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 4.00000000000000006e116

   1. Initial program 84.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d2 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 81.9%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 81.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]

   if 4.00000000000000006e116 < d4

   1. Initial program 86.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(d2 + d4\right) - d3\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d4 + d2\right) - d3\right)\right) \]

      3. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d4 + \color{blue}{\left(d2 - d3\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d4, \color{blue}{\left(d2 - d3\right)}\right)\right) \]

      5. --lowering--.f64 90.7%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d4, \mathsf{\_.f64}\left(d2, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 90.7%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 61.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 8.5 \cdot 10^{+116}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 8.5e+116) (* d1 (- d2 d1)) (* d1 (+ d2 d4))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 8.5e+116) {
		tmp = d1 * (d2 - d1);
	} else {
		tmp = d1 * (d2 + d4);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= 8.5d+116) then
        tmp = d1 * (d2 - d1)
    else
        tmp = d1 * (d2 + d4)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 8.5e+116) {
		tmp = d1 * (d2 - d1);
	} else {
		tmp = d1 * (d2 + d4);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 8.5e+116:
		tmp = d1 * (d2 - d1)
	else:
		tmp = d1 * (d2 + d4)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 8.5e+116)
		tmp = Float64(d1 * Float64(d2 - d1));
	else
		tmp = Float64(d1 * Float64(d2 + d4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 8.5e+116)
		tmp = d1 * (d2 - d1);
	else
		tmp = d1 * (d2 + d4);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 8.5e+116], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 8.5000000000000002e116

   1. Initial program 84.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d2 - \left(d1 + d3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 81.9%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 81.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d1 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{d1}\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 60.2%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{d1}\right) \]

   if 8.5000000000000002e116 < d4

   1. Initial program 86.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{d4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 75.1%

      \[\leadsto d1 \cdot \left(d2 + \color{blue}{d4}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 38.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 1.1 \cdot 10^{-13}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 1.1e-13) (* d1 d2) (* d1 d4)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.1e-13) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= 1.1d-13) then
        tmp = d1 * d2
    else
        tmp = d1 * d4
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.1e-13) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 1.1e-13:
		tmp = d1 * d2
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 1.1e-13)
		tmp = Float64(d1 * d2);
	else
		tmp = Float64(d1 * d4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 1.1e-13)
		tmp = d1 * d2;
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 1.1e-13], N[(d1 * d2), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 1.09999999999999998e-13

   1. Initial program 83.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around inf

      \[\leadsto \color{blue}{d1 \cdot d2} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 33.4%

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{d2}\right) \]

   7. Simplified 33.4%

      \[\leadsto \color{blue}{d1 \cdot d2} \]

   if 1.09999999999999998e-13 < d4

   1. Initial program 85.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

      12. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \color{blue}{d1 \cdot d4} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 53.0%

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{d4}\right) \]

   7. Simplified 53.0%

      \[\leadsto \color{blue}{d1 \cdot d4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 30.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ d1 \cdot d2 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 d2))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * d2;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * d2
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * d2;
}

Python

def code(d1, d2, d3, d4):
	return d1 * d2

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * d2)
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * d2;
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * d2), $MachinePrecision]

Derivation

1. Initial program 84.3%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
2. Step-by-step derivation

   1. distribute-lft-out-- N/A

      \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

   2. *-commutative N/A

      \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

   3. distribute-lft-out N/A

      \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

   4. distribute-lft-out-- N/A

      \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

   6. associate-+r- N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

   8. associate-+l+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

   10. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) + \color{blue}{\left(\mathsf{neg}\left(d3\right)\right)}\right)\right)\right) \]

   11. unsub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d1\right) - \color{blue}{d3}\right)\right)\right) \]

   12. associate--l- N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d1 + d3\right)}\right)\right)\right) \]

   13. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \left(d3 + \color{blue}{d1}\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

   16. +-lowering-+.f64 100.0%

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in d2 around inf

   \[\leadsto \color{blue}{d1 \cdot d2} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 30.3%

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{d2}\right) \]

7. Simplified 30.3%

   \[\leadsto \color{blue}{d1 \cdot d2} \]
8. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(\left(\left(d2 - d3\right) + d4\right) - d1\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 (- (+ (- d2 d3) d4) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * (((d2 - d3) + d4) - d1);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * (((d2 - d3) + d4) - d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * (((d2 - d3) + d4) - d1);
}

Python

def code(d1, d2, d3, d4):
	return d1 * (((d2 - d3) + d4) - d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * Float64(Float64(Float64(d2 - d3) + d4) - d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * (((d2 - d3) + d4) - d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * N[(N[(N[(d2 - d3), $MachinePrecision] + d4), $MachinePrecision] - d1), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024156 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  :precision binary64

  :alt
  (! :herbie-platform default (* d1 (- (+ (- d2 d3) d4) d1)))

  (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))