FastMath dist3

Percentage Accurate: 97.9% → 99.9%

Time: 5.4s

Alternatives: 7

Speedup: 1.9×

• 20.9% 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: 97.9% 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: 99.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double d1, double d2, double d3) {
	return (d1 * (d3 + d2)) + (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 * (d3 + d2)) + (d1 * 37.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. +-commutative 97.2%

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

   2. associate-+l+ 97.2%

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

   3. distribute-lft-out 97.2%

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

   4. *-commutative 97.2%

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

   5. distribute-rgt-in 100.0%

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

   6. associate-+r+ 100.0%

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

   7. associate-+l+ 100.0%

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

   8. +-commutative 100.0%

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

   9. distribute-rgt-in 97.2%

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

   10. *-commutative 97.2%

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

   11. cancel-sign-sub 97.2%

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

   12. *-commutative 97.2%

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

   13. distribute-rgt-out-- 100.0%

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

   14. sub-neg 100.0%

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

   15. remove-double-neg 100.0%

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

   16. associate-+l+ 100.0%

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

   17. 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. Step-by-step derivation

   1. associate-+r+ 100.0%

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

   2. distribute-lft-in 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 51.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq -1.52 \cdot 10^{-273}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d3 \leq 2.2 \cdot 10^{-159}:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{elif}\;d3 \leq 1.35 \cdot 10^{-100}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d3 \leq 36:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 -1.52e-273)
   (* d1 d2)
   (if (<= d3 2.2e-159)
     (* d1 37.0)
     (if (<= d3 1.35e-100)
       (* d1 d2)
       (if (<= d3 36.0) (* d1 37.0) (* d1 d3))))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= -1.52e-273) {
		tmp = d1 * d2;
	} else if (d3 <= 2.2e-159) {
		tmp = d1 * 37.0;
	} else if (d3 <= 1.35e-100) {
		tmp = d1 * d2;
	} else if (d3 <= 36.0) {
		tmp = d1 * 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 <= (-1.52d-273)) then
        tmp = d1 * d2
    else if (d3 <= 2.2d-159) then
        tmp = d1 * 37.0d0
    else if (d3 <= 1.35d-100) then
        tmp = d1 * d2
    else if (d3 <= 36.0d0) then
        tmp = d1 * 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 <= -1.52e-273) {
		tmp = d1 * d2;
	} else if (d3 <= 2.2e-159) {
		tmp = d1 * 37.0;
	} else if (d3 <= 1.35e-100) {
		tmp = d1 * d2;
	} else if (d3 <= 36.0) {
		tmp = d1 * 37.0;
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= -1.52e-273:
		tmp = d1 * d2
	elif d3 <= 2.2e-159:
		tmp = d1 * 37.0
	elif d3 <= 1.35e-100:
		tmp = d1 * d2
	elif d3 <= 36.0:
		tmp = d1 * 37.0
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= -1.52e-273)
		tmp = Float64(d1 * d2);
	elseif (d3 <= 2.2e-159)
		tmp = Float64(d1 * 37.0);
	elseif (d3 <= 1.35e-100)
		tmp = Float64(d1 * d2);
	elseif (d3 <= 36.0)
		tmp = Float64(d1 * 37.0);
	else
		tmp = Float64(d1 * d3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d3 <= -1.52e-273)
		tmp = d1 * d2;
	elseif (d3 <= 2.2e-159)
		tmp = d1 * 37.0;
	elseif (d3 <= 1.35e-100)
		tmp = d1 * d2;
	elseif (d3 <= 36.0)
		tmp = d1 * 37.0;
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, -1.52e-273], N[(d1 * d2), $MachinePrecision], If[LessEqual[d3, 2.2e-159], N[(d1 * 37.0), $MachinePrecision], If[LessEqual[d3, 1.35e-100], N[(d1 * d2), $MachinePrecision], If[LessEqual[d3, 36.0], N[(d1 * 37.0), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -1.51999999999999994e-273 or 2.2e-159 < d3 < 1.35000000000000008e-100

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-+l+ 99.1%

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

      3. distribute-lft-out 99.1%

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

      4. *-commutative 99.1%

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

      5. distribute-rgt-in 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-in 99.2%

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

      10. *-commutative 99.2%

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

      11. cancel-sign-sub 99.2%

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

      12. *-commutative 99.2%

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

      13. distribute-rgt-out-- 100.0%

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

      14. sub-neg 100.0%

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

      15. remove-double-neg 100.0%

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

      16. associate-+l+ 100.0%

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

      17. 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 45.3%

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

   if -1.51999999999999994e-273 < d3 < 2.2e-159 or 1.35000000000000008e-100 < d3 < 36

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. distribute-lft-out 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-rgt-in 99.9%

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

      10. *-commutative 99.9%

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

      11. cancel-sign-sub 99.9%

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

      12. *-commutative 99.9%

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

      13. distribute-rgt-out-- 99.9%

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

      14. sub-neg 99.9%

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

      15. remove-double-neg 99.9%

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

      16. associate-+l+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in d3 around 0 98.1%

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

   5. Taylor expanded in d2 around 0 54.6%

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

      1. *-commutative 54.6%

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

   7. Simplified 54.6%

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

   if 36 < d3

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-+l+ 90.6%

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

      3. distribute-lft-out 90.6%

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

      4. *-commutative 90.6%

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

      5. distribute-rgt-in 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-in 90.6%

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

      10. *-commutative 90.6%

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

      11. cancel-sign-sub 90.6%

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

      12. *-commutative 90.6%

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

      13. distribute-rgt-out-- 100.0%

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

      14. sub-neg 100.0%

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

      15. remove-double-neg 100.0%

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

      16. associate-+l+ 100.0%

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

      17. 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 76.3%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -1.52 \cdot 10^{-273}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d3 \leq 2.2 \cdot 10^{-159}:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{elif}\;d3 \leq 1.35 \cdot 10^{-100}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d3 \leq 36:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]

Alternative 3: 75.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 5300000000000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 5300000000000.0) (* d1 (+ d2 37.0)) (* d1 d3)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 5300000000000.0) {
		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 <= 5300000000000.0d0) 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 <= 5300000000000.0) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= 5300000000000.0:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= 5300000000000.0)
		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 <= 5300000000000.0)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, 5300000000000.0], N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d3 < 5.3e12

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-+l+ 99.4%

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

      3. distribute-lft-out 99.4%

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

      4. *-commutative 99.4%

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

      5. distribute-rgt-in 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-in 99.4%

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

      10. *-commutative 99.4%

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

      11. cancel-sign-sub 99.4%

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

      12. *-commutative 99.4%

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

      13. distribute-rgt-out-- 100.0%

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

      14. sub-neg 100.0%

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

      15. remove-double-neg 100.0%

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

      16. associate-+l+ 100.0%

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

      17. 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 75.5%

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

   if 5.3e12 < d3

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-+l+ 90.0%

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

      3. distribute-lft-out 90.0%

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

      4. *-commutative 90.0%

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

      5. distribute-rgt-in 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-in 90.0%

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

      10. *-commutative 90.0%

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

      11. cancel-sign-sub 90.0%

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

      12. *-commutative 90.0%

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

      13. distribute-rgt-out-- 100.0%

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

      14. sub-neg 100.0%

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

      15. remove-double-neg 100.0%

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

      16. associate-+l+ 100.0%

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

      17. 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 78.7%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 5300000000000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]

Alternative 4: 76.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -4600000000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -4600000000.0) (* d1 (+ d2 37.0)) (* d1 (+ d3 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -4600000000.0) {
		tmp = d1 * (d2 + 37.0);
	} 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 <= (-4600000000.0d0)) then
        tmp = d1 * (d2 + 37.0d0)
    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 <= -4600000000.0) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -4600000000.0:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * (d3 + 37.0)
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -4600000000.0)
		tmp = Float64(d1 * Float64(d2 + 37.0));
	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 <= -4600000000.0)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * (d3 + 37.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -4600000000.0], N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d3 + 37.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -4.6e9

   1. Initial program 91.0%

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

      1. +-commutative 91.0%

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

      2. associate-+l+ 91.0%

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

      3. distribute-lft-out 91.0%

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

      4. *-commutative 91.0%

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

      5. distribute-rgt-in 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-in 91.0%

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

      10. *-commutative 91.0%

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

      11. cancel-sign-sub 91.0%

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

      12. *-commutative 91.0%

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

      13. distribute-rgt-out-- 100.0%

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

      14. sub-neg 100.0%

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

      15. remove-double-neg 100.0%

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

      16. associate-+l+ 100.0%

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

      17. 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 79.7%

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

   if -4.6e9 < d2

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-+l+ 99.4%

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

      3. distribute-lft-out 99.4%

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

      4. *-commutative 99.4%

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

      5. distribute-rgt-in 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-in 99.4%

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

      10. *-commutative 99.4%

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

      11. cancel-sign-sub 99.4%

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

      12. *-commutative 99.4%

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

      13. distribute-rgt-out-- 100.0%

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

      14. sub-neg 100.0%

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

      15. remove-double-neg 100.0%

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

      16. associate-+l+ 100.0%

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

      17. 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 76.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -4600000000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \]

Alternative 5: 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 97.2%

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

   1. +-commutative 97.2%

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

   2. associate-+l+ 97.2%

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

   3. distribute-lft-out 97.2%

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

   4. *-commutative 97.2%

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

   5. distribute-rgt-in 100.0%

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

   6. associate-+r+ 100.0%

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

   7. associate-+l+ 100.0%

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

   8. +-commutative 100.0%

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

   9. distribute-rgt-in 97.2%

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

   10. *-commutative 97.2%

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

   11. cancel-sign-sub 97.2%

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

   12. *-commutative 97.2%

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

   13. distribute-rgt-out-- 100.0%

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

   14. sub-neg 100.0%

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

   15. remove-double-neg 100.0%

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

   16. associate-+l+ 100.0%

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

   17. 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 6: 45.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -9000000:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -9000000.0) (* d1 d2) (* d1 37.0)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -9000000.0) {
		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 <= (-9000000.0d0)) 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 <= -9000000.0) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * 37.0;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -9000000.0:
		tmp = d1 * d2
	else:
		tmp = d1 * 37.0
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -9000000.0)
		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 <= -9000000.0)
		tmp = d1 * d2;
	else
		tmp = d1 * 37.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -9000000.0], N[(d1 * d2), $MachinePrecision], N[(d1 * 37.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -9e6

   1. Initial program 91.0%

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

      1. +-commutative 91.0%

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

      2. associate-+l+ 91.0%

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

      3. distribute-lft-out 91.0%

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

      4. *-commutative 91.0%

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

      5. distribute-rgt-in 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-in 91.0%

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

      10. *-commutative 91.0%

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

      11. cancel-sign-sub 91.0%

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

      12. *-commutative 91.0%

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

      13. distribute-rgt-out-- 100.0%

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

      14. sub-neg 100.0%

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

      15. remove-double-neg 100.0%

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

      16. associate-+l+ 100.0%

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

      17. 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 79.2%

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

   if -9e6 < d2

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-+l+ 99.4%

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

      3. distribute-lft-out 99.4%

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

      4. *-commutative 99.4%

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

      5. distribute-rgt-in 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-in 99.4%

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

      10. *-commutative 99.4%

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

      11. cancel-sign-sub 99.4%

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

      12. *-commutative 99.4%

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

      13. distribute-rgt-out-- 100.0%

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

      14. sub-neg 100.0%

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

      15. remove-double-neg 100.0%

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

      16. associate-+l+ 100.0%

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

      17. 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 59.1%

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

   5. Taylor expanded in d2 around 0 35.1%

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

      1. *-commutative 35.1%

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

   7. Simplified 35.1%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -9000000:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \]

Alternative 7: 26.9% 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 97.2%

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

   1. +-commutative 97.2%

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

   2. associate-+l+ 97.2%

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

   3. distribute-lft-out 97.2%

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

   4. *-commutative 97.2%

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

   5. distribute-rgt-in 100.0%

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

   6. associate-+r+ 100.0%

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

   7. associate-+l+ 100.0%

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

   8. +-commutative 100.0%

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

   9. distribute-rgt-in 97.2%

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

   10. *-commutative 97.2%

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

   11. cancel-sign-sub 97.2%

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

   12. *-commutative 97.2%

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

   13. distribute-rgt-out-- 100.0%

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

   14. sub-neg 100.0%

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

   15. remove-double-neg 100.0%

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

   16. associate-+l+ 100.0%

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

   17. 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 64.5%

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

5. Taylor expanded in d2 around 0 26.3%

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

   1. *-commutative 26.3%

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

7. Simplified 26.3%

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

8. Final simplification 26.3%

   \[\leadsto d1 \cdot 37 \]

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 2023297 
(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)))