FastMath dist4

Percentage Accurate: 87.5% → 100.0%

Time: 10.8s

Alternatives: 11

Speedup: 1.7×

• 33.6% 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: 87.5% 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 89.8%

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

Alternative 2: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(0 - d3\right)\\ \mathbf{if}\;d3 \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq 3.8 \cdot 10^{+120}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- 0.0 d3))))
   (if (<= d3 -8.5e+113) t_0 (if (<= d3 3.8e+120) (* d1 (+ d2 d4)) t_0))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (0.0 - d3);
	double tmp;
	if (d3 <= -8.5e+113) {
		tmp = t_0;
	} else if (d3 <= 3.8e+120) {
		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 = d1 * (0.0d0 - d3)
    if (d3 <= (-8.5d+113)) then
        tmp = t_0
    else if (d3 <= 3.8d+120) 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 = d1 * (0.0 - d3);
	double tmp;
	if (d3 <= -8.5e+113) {
		tmp = t_0;
	} else if (d3 <= 3.8e+120) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (0.0 - d3)
	tmp = 0
	if d3 <= -8.5e+113:
		tmp = t_0
	elif d3 <= 3.8e+120:
		tmp = d1 * (d2 + d4)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(0.0 - d3))
	tmp = 0.0
	if (d3 <= -8.5e+113)
		tmp = t_0;
	elseif (d3 <= 3.8e+120)
		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 = d1 * (0.0 - d3);
	tmp = 0.0;
	if (d3 <= -8.5e+113)
		tmp = t_0;
	elseif (d3 <= 3.8e+120)
		tmp = d1 * (d2 + d4);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(0.0 - d3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -8.5e+113], t$95$0, If[LessEqual[d3, 3.8e+120], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d3 < -8.5000000000000001e113 or 3.7999999999999998e120 < d3

   1. Initial program 81.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 72.9%

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

   7. Simplified 72.9%

      \[\leadsto \color{blue}{0 - d1 \cdot d3} \]
   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 72.9%

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

   9. Applied egg-rr 72.9%

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

   if -8.5000000000000001e113 < d3 < 3.7999999999999998e120

   1. Initial program 93.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 69.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;d1 \cdot \left(0 - d3\right)\\ \mathbf{elif}\;d3 \leq 3.8 \cdot 10^{+120}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(0 - d3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 5.5 \cdot 10^{-185}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d4 \leq 1.55 \cdot 10^{+65}:\\ \;\;\;\;d1 \cdot \left(0 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 5.5e-185)
   (* d1 d2)
   (if (<= d4 1.55e+65) (* d1 (- 0.0 d3)) (* d1 d4))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 5.5e-185) {
		tmp = d1 * d2;
	} else if (d4 <= 1.55e+65) {
		tmp = d1 * (0.0 - d3);
	} 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 <= 5.5d-185) then
        tmp = d1 * d2
    else if (d4 <= 1.55d+65) then
        tmp = d1 * (0.0d0 - d3)
    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 <= 5.5e-185) {
		tmp = d1 * d2;
	} else if (d4 <= 1.55e+65) {
		tmp = d1 * (0.0 - d3);
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 5.5e-185:
		tmp = d1 * d2
	elif d4 <= 1.55e+65:
		tmp = d1 * (0.0 - d3)
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 5.5e-185)
		tmp = Float64(d1 * d2);
	elseif (d4 <= 1.55e+65)
		tmp = Float64(d1 * Float64(0.0 - d3));
	else
		tmp = Float64(d1 * d4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 5.5e-185)
		tmp = d1 * d2;
	elseif (d4 <= 1.55e+65)
		tmp = d1 * (0.0 - d3);
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 5.5e-185], N[(d1 * d2), $MachinePrecision], If[LessEqual[d4, 1.55e+65], N[(d1 * N[(0.0 - d3), $MachinePrecision]), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d4 < 5.4999999999999998e-185

   1. Initial program 91.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 35.1%

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

   7. Simplified 35.1%

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

   if 5.4999999999999998e-185 < d4 < 1.54999999999999995e65

   1. Initial program 94.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 47.3%

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

   7. Simplified 47.3%

      \[\leadsto \color{blue}{0 - d1 \cdot d3} \]
   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 47.3%

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

   9. Applied egg-rr 47.3%

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

   if 1.54999999999999995e65 < d4

   1. Initial program 79.9%

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

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

      1. *-lowering-*.f64 57.3%

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

   7. Simplified 57.3%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d4 \leq 5.5 \cdot 10^{-185}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d4 \leq 1.55 \cdot 10^{+65}:\\ \;\;\;\;d1 \cdot \left(0 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 2.4 \cdot 10^{-26}:\\ \;\;\;\;d1 \cdot \left(d2 - \left(d1 + d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 2.4e-26) (* d1 (- d2 (+ d1 d3))) (* d1 (- d4 (+ d1 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 2.4e-26) {
		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 (d4 <= 2.4d-26) 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 (d4 <= 2.4e-26) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - (d1 + d3));
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 2.4e-26:
		tmp = d1 * (d2 - (d1 + d3))
	else:
		tmp = d1 * (d4 - (d1 + d3))
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 2.4e-26)
		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 (d4 <= 2.4e-26)
		tmp = d1 * (d2 - (d1 + d3));
	else
		tmp = d1 * (d4 - (d1 + d3));
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 2.4e-26], 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 d4 < 2.4000000000000001e-26

   1. Initial program 91.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 82.7%

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

   7. Simplified 82.7%

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

   if 2.4000000000000001e-26 < d4

   1. Initial program 84.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   6. 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 82.4%

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

   7. Simplified 82.4%

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

Alternative 5: 82.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 1.3 \cdot 10^{+71}:\\ \;\;\;\;d1 \cdot \left(d2 - \left(d1 + d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 1.3e+71) (* d1 (- d2 (+ d1 d3))) (* d1 (- d4 d3))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.3e+71) {
		tmp = d1 * (d2 - (d1 + d3));
	} 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 <= 1.3d+71) then
        tmp = d1 * (d2 - (d1 + d3))
    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 <= 1.3e+71) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 1.3e+71:
		tmp = d1 * (d2 - (d1 + d3))
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 1.3e+71)
		tmp = Float64(d1 * Float64(d2 - Float64(d1 + d3)));
	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 <= 1.3e+71)
		tmp = d1 * (d2 - (d1 + d3));
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 1.3e+71], N[(d1 * N[(d2 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 1.29999999999999996e71

   1. Initial program 91.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 83.8%

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

   7. Simplified 83.8%

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

   if 1.29999999999999996e71 < d4

   1. Initial program 81.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   6. 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 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in d1 around 0

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

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

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

      2. --lowering--.f64 74.3%

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

   10. Simplified 74.3%

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

Alternative 6: 62.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 2.65 \cdot 10^{-27}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 2.65e-27) (* d1 (- d2 d3)) (* d1 (- d4 d3))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 2.65e-27) {
		tmp = d1 * (d2 - d3);
	} 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 <= 2.65d-27) then
        tmp = d1 * (d2 - d3)
    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 <= 2.65e-27) {
		tmp = d1 * (d2 - d3);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 2.65e-27:
		tmp = d1 * (d2 - d3)
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 2.65e-27)
		tmp = Float64(d1 * Float64(d2 - d3));
	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 <= 2.65e-27)
		tmp = d1 * (d2 - d3);
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 2.65e-27], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 2.65000000000000003e-27

   1. Initial program 91.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in d1 around 0

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

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

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

      2. --lowering--.f64 61.7%

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

   10. Simplified 61.7%

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

   if 2.65000000000000003e-27 < d4

   1. Initial program 84.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   6. 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 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in d1 around 0

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

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

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

      2. --lowering--.f64 69.8%

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

   10. Simplified 69.8%

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

Alternative 7: 62.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 4.9 \cdot 10^{+68}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 4.9e+68) (* d1 (- d2 d3)) (* d1 (- d4 d1))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 4.9e+68) {
		tmp = d1 * (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 (d4 <= 4.9d+68) then
        tmp = d1 * (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 (d4 <= 4.9e+68) {
		tmp = d1 * (d2 - d3);
	} else {
		tmp = d1 * (d4 - d1);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 4.9e+68:
		tmp = d1 * (d2 - d3)
	else:
		tmp = d1 * (d4 - d1)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 4.9e+68)
		tmp = Float64(d1 * 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 (d4 <= 4.9e+68)
		tmp = d1 * (d2 - d3);
	else
		tmp = d1 * (d4 - d1);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 4.9e+68], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 4.89999999999999978e68

   1. Initial program 91.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in d1 around 0

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

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

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

      2. --lowering--.f64 63.3%

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

   10. Simplified 63.3%

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

   if 4.89999999999999978e68 < d4

   1. Initial program 81.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   6. 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 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in d3 around 0

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

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

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

      2. --lowering--.f64 70.0%

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

   10. Simplified 70.0%

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

Alternative 8: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 6 \cdot 10^{+67}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 6e+67) (* d1 (- d2 d3)) (* d1 (+ d2 d4))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 6e+67) {
		tmp = d1 * (d2 - d3);
	} 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 <= 6d+67) then
        tmp = d1 * (d2 - d3)
    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 <= 6e+67) {
		tmp = d1 * (d2 - d3);
	} else {
		tmp = d1 * (d2 + d4);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 6e+67:
		tmp = d1 * (d2 - d3)
	else:
		tmp = d1 * (d2 + d4)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 6e+67)
		tmp = Float64(d1 * Float64(d2 - d3));
	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 <= 6e+67)
		tmp = d1 * (d2 - d3);
	else
		tmp = d1 * (d2 + d4);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 6e+67], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 6.0000000000000002e67

   1. Initial program 91.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in d1 around 0

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

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

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

      2. --lowering--.f64 63.2%

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

   10. Simplified 63.2%

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

   if 6.0000000000000002e67 < d4

   1. Initial program 79.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 73.6%

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

Alternative 9: 62.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 1.6 \cdot 10^{+68}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 1.6e+68) (* d1 (- d2 d1)) (* d1 (+ d2 d4))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.6e+68) {
		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 <= 1.6d+68) 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 <= 1.6e+68) {
		tmp = d1 * (d2 - d1);
	} else {
		tmp = d1 * (d2 + d4);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 1.6e+68:
		tmp = d1 * (d2 - d1)
	else:
		tmp = d1 * (d2 + d4)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 1.6e+68)
		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 <= 1.6e+68)
		tmp = d1 * (d2 - d1);
	else
		tmp = d1 * (d2 + d4);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 1.6e+68], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 1.59999999999999997e68

   1. Initial program 91.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in d3 around 0

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

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

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

      2. --lowering--.f64 57.1%

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

   10. Simplified 57.1%

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

   if 1.59999999999999997e68 < d4

   1. Initial program 79.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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 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 73.6%

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

Alternative 10: 37.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 3.8 \cdot 10^{-21}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 3.8e-21) (* d1 d2) (* d1 d4)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 3.8e-21) {
		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 <= 3.8d-21) 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 <= 3.8e-21) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 3.8e-21:
		tmp = d1 * d2
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 3.8e-21)
		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 <= 3.8e-21)
		tmp = d1 * d2;
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 3.8e-21], N[(d1 * d2), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 3.7999999999999998e-21

   1. Initial program 91.7%

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

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

      1. *-lowering-*.f64 35.8%

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

   7. Simplified 35.8%

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

   if 3.7999999999999998e-21 < d4

   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 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

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

      1. *-lowering-*.f64 43.9%

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

   7. Simplified 43.9%

      \[\leadsto \color{blue}{d1 \cdot d4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 30.3% 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 89.8%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
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 32.5%

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

7. Simplified 32.5%

   \[\leadsto \color{blue}{d1 \cdot d2} \]
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 2024155 
(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)))