FastMath dist3

Percentage Accurate: 98.0% → 100.0%

Time: 3.6s

Alternatives: 6

Speedup: 1.9×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (+ (+ (* d1 d2) (* (+ d3 5.0) d1)) (* d1 32.0)))

C

double code(double d1, double d2, double d3) {
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = ((d1 * d2) + ((d3 + 5.0d0) * d1)) + (d1 * 32.0d0)
end function

Java

public static double code(double d1, double d2, double d3) {
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
}

Python

def code(d1, d2, d3):
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0)

Julia

function code(d1, d2, d3)
	return Float64(Float64(Float64(d1 * d2) + Float64(Float64(d3 + 5.0) * d1)) + Float64(d1 * 32.0))
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
end

Wolfram

code[d1_, d2_, d3_] := N[(N[(N[(d1 * d2), $MachinePrecision] + N[(N[(d3 + 5.0), $MachinePrecision] * d1), $MachinePrecision]), $MachinePrecision] + N[(d1 * 32.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (+ (+ (* d1 d2) (* (+ d3 5.0) d1)) (* d1 32.0)))

C

double code(double d1, double d2, double d3) {
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = ((d1 * d2) + ((d3 + 5.0d0) * d1)) + (d1 * 32.0d0)
end function

Java

public static double code(double d1, double d2, double d3) {
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
}

Python

def code(d1, d2, d3):
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0)

Julia

function code(d1, d2, d3)
	return Float64(Float64(Float64(d1 * d2) + Float64(Float64(d3 + 5.0) * d1)) + Float64(d1 * 32.0))
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
end

Wolfram

code[d1_, d2_, d3_] := N[(N[(N[(d1 * d2), $MachinePrecision] + N[(N[(d3 + 5.0), $MachinePrecision] * d1), $MachinePrecision]), $MachinePrecision] + N[(d1 * 32.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(d3 + \left(d2 + 37\right)\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3) :precision binary64 (* d1 (+ d3 (+ d2 37.0))))

C

double code(double d1, double d2, double d3) {
	return d1 * (d3 + (d2 + 37.0));
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = d1 * (d3 + (d2 + 37.0d0))
end function

Java

public static double code(double d1, double d2, double d3) {
	return d1 * (d3 + (d2 + 37.0));
}

Python

def code(d1, d2, d3):
	return d1 * (d3 + (d2 + 37.0))

Julia

function code(d1, d2, d3)
	return Float64(d1 * Float64(d3 + Float64(d2 + 37.0)))
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = d1 * (d3 + (d2 + 37.0));
end

Wolfram

code[d1_, d2_, d3_] := N[(d1 * N[(d3 + N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
2. Step-by-step derivation

   1. cancel-sign-sub 98.0%

      \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

   2. +-commutative 98.0%

      \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

   3. *-commutative 98.0%

      \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

   4. distribute-lft-out 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

   5. distribute-lft-neg-out 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

   6. distribute-rgt-neg-in 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

   7. distribute-lft-out-- 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

   8. sub-neg 100.0%

      \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

   9. associate-+r+ 100.0%

      \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

   10. +-commutative 100.0%

       \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

   11. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

   12. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

   13. associate-+r+ 100.0%

       \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

   14. associate-+l+ 100.0%

       \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

   15. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

4. Final simplification 100.0%

   \[\leadsto d1 \cdot \left(d3 + \left(d2 + 37\right)\right) \]

Alternative 2: 52.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -4.8 \cdot 10^{+28}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -1.35 \cdot 10^{-8} \lor \neg \left(d2 \leq -7 \cdot 10^{-267}\right):\\ \;\;\;\;d1 \cdot d3\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -4.8e+28)
   (* d1 d2)
   (if (or (<= d2 -1.35e-8) (not (<= d2 -7e-267))) (* d1 d3) (* d1 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -4.8e+28) {
		tmp = d1 * d2;
	} else if ((d2 <= -1.35e-8) || !(d2 <= -7e-267)) {
		tmp = d1 * d3;
	} else {
		tmp = d1 * 37.0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8) :: tmp
    if (d2 <= (-4.8d+28)) then
        tmp = d1 * d2
    else if ((d2 <= (-1.35d-8)) .or. (.not. (d2 <= (-7d-267)))) then
        tmp = d1 * d3
    else
        tmp = d1 * 37.0d0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -4.8e+28) {
		tmp = d1 * d2;
	} else if ((d2 <= -1.35e-8) || !(d2 <= -7e-267)) {
		tmp = d1 * d3;
	} else {
		tmp = d1 * 37.0;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -4.8e+28:
		tmp = d1 * d2
	elif (d2 <= -1.35e-8) or not (d2 <= -7e-267):
		tmp = d1 * d3
	else:
		tmp = d1 * 37.0
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -4.8e+28)
		tmp = Float64(d1 * d2);
	elseif ((d2 <= -1.35e-8) || !(d2 <= -7e-267))
		tmp = Float64(d1 * d3);
	else
		tmp = Float64(d1 * 37.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d2 <= -4.8e+28)
		tmp = d1 * d2;
	elseif ((d2 <= -1.35e-8) || ~((d2 <= -7e-267)))
		tmp = d1 * d3;
	else
		tmp = d1 * 37.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -4.8e+28], N[(d1 * d2), $MachinePrecision], If[Or[LessEqual[d2, -1.35e-8], N[Not[LessEqual[d2, -7e-267]], $MachinePrecision]], N[(d1 * d3), $MachinePrecision], N[(d1 * 37.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -4.79999999999999962e28

   1. Initial program 97.0%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 97.0%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 97.0%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 97.0%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. sub-neg 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

      9. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

      10. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

      13. associate-+r+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

   4. Taylor expanded in d2 around inf 79.8%

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

   if -4.79999999999999962e28 < d2 < -1.35000000000000001e-8 or -6.9999999999999999e-267 < d2

   1. Initial program 98.0%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 98.0%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 98.0%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 98.0%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. sub-neg 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

      9. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

      10. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

      13. associate-+r+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

   4. Taylor expanded in d3 around inf 46.7%

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

   if -1.35000000000000001e-8 < d2 < -6.9999999999999999e-267

   1. Initial program 100.0%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 100.0%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. sub-neg 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

      9. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

      10. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

      13. associate-+r+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

   4. Taylor expanded in d2 around 0 99.8%

      \[\leadsto \color{blue}{d1 \cdot \left(37 + d3\right)} \]
   5. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto d1 \cdot \color{blue}{\left(d3 + 37\right)} \]

      2. distribute-lft-in 99.8%

         \[\leadsto \color{blue}{d1 \cdot d3 + d1 \cdot 37} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{d1 \cdot d3 + d1 \cdot 37} \]

   7. Taylor expanded in d3 around 0 52.7%

      \[\leadsto \color{blue}{37 \cdot d1} \]
   8. Step-by-step derivation

      1. *-commutative 52.7%

         \[\leadsto \color{blue}{d1 \cdot 37} \]

   9. Simplified 52.7%

      \[\leadsto \color{blue}{d1 \cdot 37} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -4.8 \cdot 10^{+28}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -1.35 \cdot 10^{-8} \lor \neg \left(d2 \leq -7 \cdot 10^{-267}\right):\\ \;\;\;\;d1 \cdot d3\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \]

Alternative 3: 63.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -13000 \lor \neg \left(d2 \leq 37\right):\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (or (<= d2 -13000.0) (not (<= d2 37.0))) (* d1 d2) (* d1 37.0)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if ((d2 <= -13000.0) || !(d2 <= 37.0)) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * 37.0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8) :: tmp
    if ((d2 <= (-13000.0d0)) .or. (.not. (d2 <= 37.0d0))) then
        tmp = d1 * d2
    else
        tmp = d1 * 37.0d0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if ((d2 <= -13000.0) || !(d2 <= 37.0)) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * 37.0;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if (d2 <= -13000.0) or not (d2 <= 37.0):
		tmp = d1 * d2
	else:
		tmp = d1 * 37.0
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if ((d2 <= -13000.0) || !(d2 <= 37.0))
		tmp = Float64(d1 * d2);
	else
		tmp = Float64(d1 * 37.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if ((d2 <= -13000.0) || ~((d2 <= 37.0)))
		tmp = d1 * d2;
	else
		tmp = d1 * 37.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[Or[LessEqual[d2, -13000.0], N[Not[LessEqual[d2, 37.0]], $MachinePrecision]], N[(d1 * d2), $MachinePrecision], N[(d1 * 37.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -13000 or 37 < d2

   1. Initial program 96.5%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 96.5%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 96.5%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 96.5%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. sub-neg 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

      9. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

      10. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

      13. associate-+r+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

   4. Taylor expanded in d2 around inf 74.5%

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

   if -13000 < d2 < 37

   1. Initial program 100.0%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 100.0%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. sub-neg 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

      9. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

      10. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

      13. associate-+r+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

   4. Taylor expanded in d2 around 0 98.9%

      \[\leadsto \color{blue}{d1 \cdot \left(37 + d3\right)} \]
   5. Step-by-step derivation

      1. +-commutative 98.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d3 + 37\right)} \]

      2. distribute-lft-in 98.9%

         \[\leadsto \color{blue}{d1 \cdot d3 + d1 \cdot 37} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{d1 \cdot d3 + d1 \cdot 37} \]

   7. Taylor expanded in d3 around 0 48.7%

      \[\leadsto \color{blue}{37 \cdot d1} \]
   8. Step-by-step derivation

      1. *-commutative 48.7%

         \[\leadsto \color{blue}{d1 \cdot 37} \]

   9. Simplified 48.7%

      \[\leadsto \color{blue}{d1 \cdot 37} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -13000 \lor \neg \left(d2 \leq 37\right):\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \]

Alternative 4: 75.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 420000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 420000.0) (* d1 (+ d2 37.0)) (* d1 d3)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 420000.0) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8) :: tmp
    if (d3 <= 420000.0d0) then
        tmp = d1 * (d2 + 37.0d0)
    else
        tmp = d1 * d3
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 420000.0) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= 420000.0:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= 420000.0)
		tmp = Float64(d1 * Float64(d2 + 37.0));
	else
		tmp = Float64(d1 * d3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d3 <= 420000.0)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, 420000.0], N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d3 < 4.2e5

   1. Initial program 98.4%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 98.4%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 98.4%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 98.4%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. sub-neg 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

      9. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

      10. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

      13. associate-+r+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

   4. Taylor expanded in d3 around 0 71.2%

      \[\leadsto \color{blue}{d1 \cdot \left(37 + d2\right)} \]

   if 4.2e5 < d3

   1. Initial program 96.8%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 96.8%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 96.8%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 96.8%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. sub-neg 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

      9. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

      10. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

      13. associate-+r+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

   4. Taylor expanded in d3 around inf 75.1%

      \[\leadsto \color{blue}{d1 \cdot d3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 420000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]

Alternative 5: 76.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -2.8 \cdot 10^{+27}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -2.8e+27) (* d1 d2) (* d1 (+ d3 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -2.8e+27) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8) :: tmp
    if (d2 <= (-2.8d+27)) then
        tmp = d1 * d2
    else
        tmp = d1 * (d3 + 37.0d0)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -2.8e+27) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -2.8e+27:
		tmp = d1 * d2
	else:
		tmp = d1 * (d3 + 37.0)
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -2.8e+27)
		tmp = Float64(d1 * d2);
	else
		tmp = Float64(d1 * Float64(d3 + 37.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d2 <= -2.8e+27)
		tmp = d1 * d2;
	else
		tmp = d1 * (d3 + 37.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -2.8e+27], N[(d1 * d2), $MachinePrecision], N[(d1 * N[(d3 + 37.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -2.7999999999999999e27

   1. Initial program 97.0%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 97.0%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 97.0%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 97.0%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. sub-neg 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

      9. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

      10. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

      13. associate-+r+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

   4. Taylor expanded in d2 around inf 79.8%

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

   if -2.7999999999999999e27 < d2

   1. Initial program 98.4%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 98.4%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 98.4%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 98.4%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. sub-neg 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

      9. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

      10. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

      13. associate-+r+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

   4. Taylor expanded in d2 around 0 75.9%

      \[\leadsto \color{blue}{d1 \cdot \left(37 + d3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -2.8 \cdot 10^{+27}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \]

Alternative 6: 26.8% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ d1 \cdot 37 \end{array} \]

FPCore

(FPCore (d1 d2 d3) :precision binary64 (* d1 37.0))

C

double code(double d1, double d2, double d3) {
	return d1 * 37.0;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = d1 * 37.0d0
end function

Java

public static double code(double d1, double d2, double d3) {
	return d1 * 37.0;
}

Python

def code(d1, d2, d3):
	return d1 * 37.0

Julia

function code(d1, d2, d3)
	return Float64(d1 * 37.0)
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = d1 * 37.0;
end

Wolfram

code[d1_, d2_, d3_] := N[(d1 * 37.0), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
2. Step-by-step derivation

   1. cancel-sign-sub 98.0%

      \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

   2. +-commutative 98.0%

      \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

   3. *-commutative 98.0%

      \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

   4. distribute-lft-out 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

   5. distribute-lft-neg-out 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

   6. distribute-rgt-neg-in 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

   7. distribute-lft-out-- 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

   8. sub-neg 100.0%

      \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d3 + 5\right) + d2\right) + \left(-\left(-32\right)\right)\right)} \]

   9. associate-+r+ 100.0%

      \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} + \left(-\left(-32\right)\right)\right) \]

   10. +-commutative 100.0%

       \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) + \left(-\left(-32\right)\right)\right) \]

   11. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \left(-\color{blue}{-32}\right)\right) \]

   12. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(\left(d3 + \left(d2 + 5\right)\right) + \color{blue}{32}\right) \]

   13. associate-+r+ 100.0%

       \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) + 32\right)\right)} \]

   14. associate-+l+ 100.0%

       \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

   15. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]

4. Taylor expanded in d2 around 0 62.8%

   \[\leadsto \color{blue}{d1 \cdot \left(37 + d3\right)} \]
5. Step-by-step derivation

   1. +-commutative 62.8%

      \[\leadsto d1 \cdot \color{blue}{\left(d3 + 37\right)} \]

   2. distribute-lft-in 62.7%

      \[\leadsto \color{blue}{d1 \cdot d3 + d1 \cdot 37} \]

6. Applied egg-rr 62.7%

   \[\leadsto \color{blue}{d1 \cdot d3 + d1 \cdot 37} \]

7. Taylor expanded in d3 around 0 23.7%

   \[\leadsto \color{blue}{37 \cdot d1} \]
8. Step-by-step derivation

   1. *-commutative 23.7%

      \[\leadsto \color{blue}{d1 \cdot 37} \]

9. Simplified 23.7%

   \[\leadsto \color{blue}{d1 \cdot 37} \]

10. Final simplification 23.7%

    \[\leadsto d1 \cdot 37 \]

Developer target: 100.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(\left(37 + d3\right) + d2\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3) :precision binary64 (* d1 (+ (+ 37.0 d3) d2)))

C

double code(double d1, double d2, double d3) {
	return d1 * ((37.0 + d3) + d2);
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = d1 * ((37.0d0 + d3) + d2)
end function

Java

public static double code(double d1, double d2, double d3) {
	return d1 * ((37.0 + d3) + d2);
}

Python

def code(d1, d2, d3):
	return d1 * ((37.0 + d3) + d2)

Julia

function code(d1, d2, d3)
	return Float64(d1 * Float64(Float64(37.0 + d3) + d2))
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = d1 * ((37.0 + d3) + d2);
end

Wolfram

code[d1_, d2_, d3_] := N[(d1 * N[(N[(37.0 + d3), $MachinePrecision] + d2), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023334 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  :precision binary64

  :herbie-target
  (* d1 (+ (+ 37.0 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5.0) d1)) (* d1 32.0)))