FastMath dist3

Percentage Accurate: 97.8% → 99.9%

Time: 5.7s

Alternatives: 8

Speedup: 1.9×

• 21.0% 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: 97.8% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. distribute-lft-out N/A

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

   4. distribute-lft-out N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

   6. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

   7. associate-+r+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

   9. associate-+l+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

   11. metadata-eval 100.0%

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

3. Simplified 100.0%

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

   1. associate-+r+ N/A

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

   2. distribute-rgt-in N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(\left(d2 + d3\right) \cdot d1\right), \color{blue}{\left(37 \cdot d1\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(d2 + d3\right), d1\right), \left(\color{blue}{37} \cdot d1\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(d2, d3\right), d1\right), \left(37 \cdot d1\right)\right) \]

   6. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(d2, d3\right), d1\right), \mathsf{*.f64}\left(37, \color{blue}{d1}\right)\right) \]

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 4 \cdot 10^{-289}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{elif}\;d3 \leq 2.2 \cdot 10^{-24}:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{elif}\;d3 \leq 2000:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d3 \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 4e-289)
   (* d2 d1)
   (if (<= d3 2.2e-24) (* d1 37.0) (if (<= d3 2000.0) (* d2 d1) (* d3 d1)))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 4e-289) {
		tmp = d2 * d1;
	} else if (d3 <= 2.2e-24) {
		tmp = d1 * 37.0;
	} else if (d3 <= 2000.0) {
		tmp = d2 * d1;
	} else {
		tmp = d3 * d1;
	}
	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 <= 4d-289) then
        tmp = d2 * d1
    else if (d3 <= 2.2d-24) then
        tmp = d1 * 37.0d0
    else if (d3 <= 2000.0d0) then
        tmp = d2 * d1
    else
        tmp = d3 * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 4e-289) {
		tmp = d2 * d1;
	} else if (d3 <= 2.2e-24) {
		tmp = d1 * 37.0;
	} else if (d3 <= 2000.0) {
		tmp = d2 * d1;
	} else {
		tmp = d3 * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= 4e-289:
		tmp = d2 * d1
	elif d3 <= 2.2e-24:
		tmp = d1 * 37.0
	elif d3 <= 2000.0:
		tmp = d2 * d1
	else:
		tmp = d3 * d1
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= 4e-289)
		tmp = Float64(d2 * d1);
	elseif (d3 <= 2.2e-24)
		tmp = Float64(d1 * 37.0);
	elseif (d3 <= 2000.0)
		tmp = Float64(d2 * d1);
	else
		tmp = Float64(d3 * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d3 <= 4e-289)
		tmp = d2 * d1;
	elseif (d3 <= 2.2e-24)
		tmp = d1 * 37.0;
	elseif (d3 <= 2000.0)
		tmp = d2 * d1;
	else
		tmp = d3 * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, 4e-289], N[(d2 * d1), $MachinePrecision], If[LessEqual[d3, 2.2e-24], N[(d1 * 37.0), $MachinePrecision], If[LessEqual[d3, 2000.0], N[(d2 * d1), $MachinePrecision], N[(d3 * d1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < 4e-289 or 2.20000000000000002e-24 < d3 < 2e3

   1. Initial program 97.7%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d2 around inf

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

      1. *-lowering-*.f64 43.7%

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

   7. Simplified 43.7%

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

   if 4e-289 < d3 < 2.20000000000000002e-24

   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 N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d2 around 0

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(37 + d3\right)}\right) \]

      2. +-lowering-+.f64 55.6%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(37, \color{blue}{d3}\right)\right) \]

   7. Simplified 55.6%

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

   8. Taylor expanded in d3 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{37}\right) \]
   9. Step-by-step derivation

   10. Simplified 55.6%

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

   if 2e3 < d3

   1. Initial program 98.5%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d3 around inf

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

      1. *-lowering-*.f64 77.5%

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

   7. Simplified 77.5%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 4 \cdot 10^{-289}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{elif}\;d3 \leq 2.2 \cdot 10^{-24}:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{elif}\;d3 \leq 2000:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d3 \cdot d1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if d2 < -37 or 37 < d2

   1. Initial program 96.8%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d2 around inf

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

      1. *-lowering-*.f64 78.8%

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

   7. Simplified 78.8%

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

   if -37 < d2 < 37

   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 N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d2 around 0

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(37 + d3\right)}\right) \]

      2. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(37, \color{blue}{d3}\right)\right) \]

   7. Simplified 100.0%

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

   8. Taylor expanded in d3 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{37}\right) \]
   9. Step-by-step derivation

   10. Simplified 44.4%

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

4. Final simplification 61.3%

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

Alternative 4: 80.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 2.6 \cdot 10^{-18}:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;\left(d2 + d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 2.6e-18) (* d1 (+ d2 37.0)) (* (+ d2 d3) d1)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 2.6e-18) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = (d2 + d3) * d1;
	}
	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 <= 2.6d-18) then
        tmp = d1 * (d2 + 37.0d0)
    else
        tmp = (d2 + d3) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 2.6e-18) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = (d2 + d3) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= 2.6e-18:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = (d2 + d3) * d1
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= 2.6e-18)
		tmp = Float64(d1 * Float64(d2 + 37.0));
	else
		tmp = Float64(Float64(d2 + d3) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d3 <= 2.6e-18)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = (d2 + d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, 2.6e-18], N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision], N[(N[(d2 + d3), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d3 < 2.6e-18

   1. Initial program 98.3%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d3 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{37}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 72.4%

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

   if 2.6e-18 < d3

   1. Initial program 98.5%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d3 around inf

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

   7. Simplified 98.6%

      \[\leadsto d1 \cdot \left(d2 + \color{blue}{d3}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 2.6 \cdot 10^{-18}:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;\left(d2 + d3\right) \cdot d1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -0.012:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -0.012) (* d1 (+ d2 37.0)) (* d1 (+ d3 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -0.012) {
		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 <= (-0.012d0)) 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 <= -0.012) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -0.012:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * (d3 + 37.0)
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -0.012)
		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 <= -0.012)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * (d3 + 37.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -0.012], 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 < -0.012

   1. Initial program 98.1%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d3 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{37}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 83.6%

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

   if -0.012 < d2

   1. Initial program 98.4%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d2 around 0

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(37 + d3\right)}\right) \]

      2. +-lowering-+.f64 75.1%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(37, \color{blue}{d3}\right)\right) \]

   7. Simplified 75.1%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -0.012:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -29000:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -29000.0) (* d2 d1) (* d1 (+ d3 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -29000.0) {
		tmp = d2 * d1;
	} 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 <= (-29000.0d0)) then
        tmp = d2 * d1
    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 <= -29000.0) {
		tmp = d2 * d1;
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -29000.0:
		tmp = d2 * d1
	else:
		tmp = d1 * (d3 + 37.0)
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -29000.0)
		tmp = Float64(d2 * d1);
	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 <= -29000.0)
		tmp = d2 * d1;
	else
		tmp = d1 * (d3 + 37.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -29000.0], N[(d2 * d1), $MachinePrecision], N[(d1 * N[(d3 + 37.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -29000

   1. Initial program 98.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d2 around inf

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

      1. *-lowering-*.f64 87.1%

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

   7. Simplified 87.1%

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

   if -29000 < d2

   1. Initial program 98.5%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

      9. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in d2 around 0

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

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(37 + d3\right)}\right) \]

      2. +-lowering-+.f64 75.5%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(37, \color{blue}{d3}\right)\right) \]

   7. Simplified 75.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -29000:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. distribute-lft-out N/A

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

   4. distribute-lft-out N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

   6. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

   7. associate-+r+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

   9. associate-+l+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

   11. metadata-eval 100.0%

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d3 + 37\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 8: 26.5% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. distribute-lft-out N/A

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

   4. distribute-lft-out N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(32 + \left(d2 + \left(d3 + 5\right)\right)\right)}\right) \]

   6. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(d3 + 5\right)\right) + \color{blue}{32}\right)\right) \]

   7. associate-+r+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(d3 + 5\right) + 32\right)}\right)\right) \]

   9. associate-+l+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d3 + \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, \color{blue}{\left(5 + 32\right)}\right)\right)\right) \]

   11. metadata-eval 100.0%

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{+.f64}\left(d3, 37\right)\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in d2 around 0

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

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

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(37 + d3\right)}\right) \]

   2. +-lowering-+.f64 63.2%

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(37, \color{blue}{d3}\right)\right) \]

7. Simplified 63.2%

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

8. Taylor expanded in d3 around 0

   \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{37}\right) \]
9. Step-by-step derivation

10. Simplified 24.2%

    \[\leadsto d1 \cdot \color{blue}{37} \]
11. Add Preprocessing

Developer Target 1: 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 2024155 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  :precision binary64

  :alt
  (! :herbie-platform default (* d1 (+ 37 d3 d2)))

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