FastMath dist3

Percentage Accurate: 97.7% → 100.0%

Time: 6.3s

Alternatives: 7

Speedup: 1.9×

• 21.6% 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: 97.7% 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 99.2%

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

   1. cancel-sign-sub 99.2%

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

   2. +-commutative 99.2%

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

   3. *-commutative 99.2%

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

   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. associate-+r+ 100.0%

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

   9. +-commutative 100.0%

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

   10. associate--l+ 100.0%

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

   11. sub-neg 100.0%

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

   12. metadata-eval 100.0%

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

   13. metadata-eval 100.0%

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

   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. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto d1 \cdot \left(d3 + \left(d2 + 37\right)\right) \]
6. Add Preprocessing

Alternative 2: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 7.2 \cdot 10^{-260}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d3 \leq 6400000:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 7.2e-260) (* d1 d2) (if (<= d3 6400000.0) (* d1 37.0) (* d1 d3))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 7.2e-260) {
		tmp = d1 * d2;
	} else if (d3 <= 6400000.0) {
		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 <= 7.2d-260) then
        tmp = d1 * d2
    else if (d3 <= 6400000.0d0) 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 <= 7.2e-260) {
		tmp = d1 * d2;
	} else if (d3 <= 6400000.0) {
		tmp = d1 * 37.0;
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= 7.2e-260:
		tmp = d1 * d2
	elif d3 <= 6400000.0:
		tmp = d1 * 37.0
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= 7.2e-260)
		tmp = Float64(d1 * d2);
	elseif (d3 <= 6400000.0)
		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 <= 7.2e-260)
		tmp = d1 * d2;
	elseif (d3 <= 6400000.0)
		tmp = d1 * 37.0;
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, 7.2e-260], N[(d1 * d2), $MachinePrecision], If[LessEqual[d3, 6400000.0], N[(d1 * 37.0), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d3 < 7.2000000000000002e-260

   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. cancel-sign-sub 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-lft-out 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. distribute-lft-out-- 100.0%

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

      8. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d2 around inf 42.3%

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

   if 7.2000000000000002e-260 < d3 < 6.4e6

   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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d3 around inf 73.2%

      \[\leadsto \color{blue}{d3 \cdot \left(d1 + \frac{d1 \cdot \left(37 + d2\right)}{d3}\right)} \]
   6. Step-by-step derivation

      1. +-commutative 73.2%

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

      2. +-commutative 73.2%

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

      3. associate-/l* 67.3%

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

   7. Simplified 67.3%

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

   8. Taylor expanded in d2 around 0 39.0%

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

   9. Taylor expanded in d3 around 0 45.6%

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

   if 6.4e6 < d3

   1. Initial program 96.9%

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

      1. cancel-sign-sub 96.9%

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

      2. +-commutative 96.9%

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

      3. *-commutative 96.9%

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

      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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d3 around inf 78.0%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 7.2 \cdot 10^{-260}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d3 \leq 6400000:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 13200000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 13200000.0) (* d1 (+ d2 37.0)) (* d1 d3)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 13200000.0) {
		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 <= 13200000.0d0) 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 <= 13200000.0) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= 13200000.0:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= 13200000.0)
		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 <= 13200000.0)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, 13200000.0], N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d3 < 1.32e7

   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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d3 around 0 78.1%

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

   if 1.32e7 < d3

   1. Initial program 96.9%

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

      1. cancel-sign-sub 96.9%

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

      2. +-commutative 96.9%

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

      3. *-commutative 96.9%

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

      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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d3 around inf 78.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 13200000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 6.8e-12) (* d1 (+ d2 37.0)) (* d1 (+ d3 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 6.8e-12) {
		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 (d3 <= 6.8d-12) 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 (d3 <= 6.8e-12) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= 6.8e-12:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * (d3 + 37.0)
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= 6.8e-12)
		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 (d3 <= 6.8e-12)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * (d3 + 37.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, 6.8e-12], 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 d3 < 6.8000000000000001e-12

   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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d3 around 0 78.6%

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

   if 6.8000000000000001e-12 < d3

   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. cancel-sign-sub 97.2%

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

      2. +-commutative 97.2%

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

      3. *-commutative 97.2%

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

      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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d2 around 0 78.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -560:\\ \;\;\;\;d1 \cdot \left(d3 + d2\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -560.0) (* d1 (+ d3 d2)) (* d1 (+ d3 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -560.0) {
		tmp = d1 * (d3 + 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 <= (-560.0d0)) then
        tmp = d1 * (d3 + 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 <= -560.0) {
		tmp = d1 * (d3 + d2);
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -560.0:
		tmp = d1 * (d3 + d2)
	else:
		tmp = d1 * (d3 + 37.0)
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -560.0)
		tmp = Float64(d1 * Float64(d3 + 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 <= -560.0)
		tmp = d1 * (d3 + d2);
	else
		tmp = d1 * (d3 + 37.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -560.0], N[(d1 * N[(d3 + d2), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d3 + 37.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -560

   1. Initial program 96.7%

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

      1. cancel-sign-sub 96.7%

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

      2. +-commutative 96.7%

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

      3. *-commutative 96.7%

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

      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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d3 around inf 86.0%

      \[\leadsto \color{blue}{d3 \cdot \left(d1 + \frac{d1 \cdot \left(37 + d2\right)}{d3}\right)} \]
   6. Step-by-step derivation

      1. +-commutative 86.0%

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

      2. +-commutative 86.0%

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

      3. associate-/l* 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in d2 around inf 86.0%

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

   9. Taylor expanded in d3 around 0 96.7%

      \[\leadsto \color{blue}{d1 \cdot d2 + d1 \cdot d3} \]
   10. Step-by-step derivation

       1. +-commutative 96.7%

          \[\leadsto \color{blue}{d1 \cdot d3 + d1 \cdot d2} \]

       2. distribute-lft-out 100.0%

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

   11. Simplified 100.0%

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

   if -560 < d2

   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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d2 around 0 75.6%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -560:\\ \;\;\;\;d1 \cdot \left(d3 + d2\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -560:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -560.0) (* d1 d2) (* d1 37.0)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -560.0) {
		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 <= (-560.0d0)) 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 <= -560.0) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * 37.0;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -560.0:
		tmp = d1 * d2
	else:
		tmp = d1 * 37.0
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -560.0)
		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 <= -560.0)
		tmp = d1 * d2;
	else
		tmp = d1 * 37.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -560.0], N[(d1 * d2), $MachinePrecision], N[(d1 * 37.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -560

   1. Initial program 96.7%

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

      1. cancel-sign-sub 96.7%

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

      2. +-commutative 96.7%

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

      3. *-commutative 96.7%

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

      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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d2 around inf 85.3%

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

   if -560 < d2

   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. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--l+ 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in d3 around inf 87.4%

      \[\leadsto \color{blue}{d3 \cdot \left(d1 + \frac{d1 \cdot \left(37 + d2\right)}{d3}\right)} \]
   6. Step-by-step derivation

      1. +-commutative 87.4%

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

      2. +-commutative 87.4%

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

      3. associate-/l* 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in d2 around 0 68.6%

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

   9. Taylor expanded in d3 around 0 35.1%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -560:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 27.0% 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 99.2%

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

   1. cancel-sign-sub 99.2%

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

   2. +-commutative 99.2%

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

   3. *-commutative 99.2%

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

   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. associate-+r+ 100.0%

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

   9. +-commutative 100.0%

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

   10. associate--l+ 100.0%

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

   11. sub-neg 100.0%

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

   12. metadata-eval 100.0%

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

   13. metadata-eval 100.0%

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

   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. Add Preprocessing

5. Taylor expanded in d3 around inf 87.1%

   \[\leadsto \color{blue}{d3 \cdot \left(d1 + \frac{d1 \cdot \left(37 + d2\right)}{d3}\right)} \]
6. Step-by-step derivation

   1. +-commutative 87.1%

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

   2. +-commutative 87.1%

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

   3. associate-/l* 82.1%

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

7. Simplified 82.1%

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

8. Taylor expanded in d2 around 0 57.6%

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

9. Taylor expanded in d3 around 0 27.2%

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

10. Final simplification 27.2%

    \[\leadsto d1 \cdot 37 \]
11. Add Preprocessing

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 2024059 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  :precision binary64

  :alt
  (* d1 (+ (+ 37.0 d3) d2))

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