FastMath dist3

Percentage Accurate: 98.0% → 100.0%

Time: 3.5s

Alternatives: 6

Speedup: 1.9×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.9× speedup

Math

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

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 96.4%

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

   1. *-commutative 96.4%

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

   2. distribute-lft-out 99.5%

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

   3. distribute-lft-out 100.0%

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

   4. associate-+r+ 100.0%

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

   5. associate-+l+ 100.0%

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

   6. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -38:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -1.85 \cdot 10^{-60} \lor \neg \left(d2 \leq -1.6 \cdot 10^{-72}\right) \land \left(d2 \leq -1.7 \cdot 10^{-227} \lor \neg \left(d2 \leq 8.6 \cdot 10^{-296}\right) \land d2 \leq 1.45 \cdot 10^{-232}\right):\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -38.0)
   (* d1 d2)
   (if (or (<= d2 -1.85e-60)
           (and (not (<= d2 -1.6e-72))
                (or (<= d2 -1.7e-227)
                    (and (not (<= d2 8.6e-296)) (<= d2 1.45e-232)))))
     (* d1 37.0)
     (* d1 d3))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -38.0) {
		tmp = d1 * d2;
	} else if ((d2 <= -1.85e-60) || (!(d2 <= -1.6e-72) && ((d2 <= -1.7e-227) || (!(d2 <= 8.6e-296) && (d2 <= 1.45e-232))))) {
		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 (d2 <= (-38.0d0)) then
        tmp = d1 * d2
    else if ((d2 <= (-1.85d-60)) .or. (.not. (d2 <= (-1.6d-72))) .and. (d2 <= (-1.7d-227)) .or. (.not. (d2 <= 8.6d-296)) .and. (d2 <= 1.45d-232)) 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 (d2 <= -38.0) {
		tmp = d1 * d2;
	} else if ((d2 <= -1.85e-60) || (!(d2 <= -1.6e-72) && ((d2 <= -1.7e-227) || (!(d2 <= 8.6e-296) && (d2 <= 1.45e-232))))) {
		tmp = d1 * 37.0;
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -38.0:
		tmp = d1 * d2
	elif (d2 <= -1.85e-60) or (not (d2 <= -1.6e-72) and ((d2 <= -1.7e-227) or (not (d2 <= 8.6e-296) and (d2 <= 1.45e-232)))):
		tmp = d1 * 37.0
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -38.0)
		tmp = Float64(d1 * d2);
	elseif ((d2 <= -1.85e-60) || (!(d2 <= -1.6e-72) && ((d2 <= -1.7e-227) || (!(d2 <= 8.6e-296) && (d2 <= 1.45e-232)))))
		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 (d2 <= -38.0)
		tmp = d1 * d2;
	elseif ((d2 <= -1.85e-60) || (~((d2 <= -1.6e-72)) && ((d2 <= -1.7e-227) || (~((d2 <= 8.6e-296)) && (d2 <= 1.45e-232)))))
		tmp = d1 * 37.0;
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -38.0], N[(d1 * d2), $MachinePrecision], If[Or[LessEqual[d2, -1.85e-60], And[N[Not[LessEqual[d2, -1.6e-72]], $MachinePrecision], Or[LessEqual[d2, -1.7e-227], And[N[Not[LessEqual[d2, 8.6e-296]], $MachinePrecision], LessEqual[d2, 1.45e-232]]]]], N[(d1 * 37.0), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -38

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. distribute-lft-out 98.5%

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

      3. distribute-lft-out 100.0%

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

      4. associate-+r+ 100.0%

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

      5. associate-+l+ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in d2 around inf 74.5%

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

   if -38 < d2 < -1.85000000000000012e-60 or -1.6e-72 < d2 < -1.69999999999999989e-227 or 8.59999999999999956e-296 < d2 < 1.45e-232

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. distribute-lft-out 99.9%

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

      3. distribute-lft-out 100.0%

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

      4. associate-+r+ 100.0%

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

      5. associate-+l+ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in d2 around 0 98.7%

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

   5. Taylor expanded in d3 around 0 69.1%

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

   if -1.85000000000000012e-60 < d2 < -1.6e-72 or -1.69999999999999989e-227 < d2 < 8.59999999999999956e-296 or 1.45e-232 < d2

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. distribute-lft-out 99.9%

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

      3. distribute-lft-out 100.0%

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

      4. associate-+r+ 100.0%

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

      5. associate-+l+ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in d3 around inf 40.3%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -38:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -1.85 \cdot 10^{-60} \lor \neg \left(d2 \leq -1.6 \cdot 10^{-72}\right) \land \left(d2 \leq -1.7 \cdot 10^{-227} \lor \neg \left(d2 \leq 8.6 \cdot 10^{-296}\right) \land d2 \leq 1.45 \cdot 10^{-232}\right):\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]

Alternative 3: 63.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq -0.0053:\\ \;\;\;\;d1 \cdot d3\\ \mathbf{elif}\;d3 \leq 1450:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 -0.0053) (* d1 d3) (if (<= d3 1450.0) (* d1 37.0) (* d1 d3))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= -0.0053) {
		tmp = d1 * d3;
	} else if (d3 <= 1450.0) {
		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 <= (-0.0053d0)) then
        tmp = d1 * d3
    else if (d3 <= 1450.0d0) 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 <= -0.0053) {
		tmp = d1 * d3;
	} else if (d3 <= 1450.0) {
		tmp = d1 * 37.0;
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= -0.0053:
		tmp = d1 * d3
	elif d3 <= 1450.0:
		tmp = d1 * 37.0
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= -0.0053)
		tmp = Float64(d1 * d3);
	elseif (d3 <= 1450.0)
		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 <= -0.0053)
		tmp = d1 * d3;
	elseif (d3 <= 1450.0)
		tmp = d1 * 37.0;
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, -0.0053], N[(d1 * d3), $MachinePrecision], If[LessEqual[d3, 1450.0], N[(d1 * 37.0), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if d3 < -0.00530000000000000002 or 1450 < d3

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. distribute-lft-out 99.9%

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

      3. distribute-lft-out 99.9%

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

      4. associate-+r+ 99.9%

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

      5. associate-+l+ 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in d3 around inf 70.5%

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

   if -0.00530000000000000002 < d3 < 1450

   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. *-commutative 99.2%

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

      2. distribute-lft-out 99.2%

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

      3. distribute-lft-out 100.0%

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

      4. associate-+r+ 100.0%

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

      5. associate-+l+ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in d2 around 0 51.0%

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

   5. Taylor expanded in d3 around 0 49.7%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -0.0053:\\ \;\;\;\;d1 \cdot d3\\ \mathbf{elif}\;d3 \leq 1450:\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]

Alternative 4: 75.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 3.6 \cdot 10^{+59}:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 3.6e+59) (* d1 (+ d2 37.0)) (* d1 d3)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 3.6e+59) {
		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 <= 3.6d+59) 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 <= 3.6e+59) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= 3.6e+59:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= 3.6e+59)
		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 <= 3.6e+59)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, 3.6e+59], N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d3 < 3.5999999999999999e59

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

      2. distribute-lft-out 99.5%

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

      3. distribute-lft-out 100.0%

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

      4. associate-+r+ 100.0%

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

      5. associate-+l+ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in d3 around 0 75.7%

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

   if 3.5999999999999999e59 < d3

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. distribute-lft-out 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. associate-+r+ 100.0%

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

      5. associate-+l+ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in d3 around inf 85.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 3.6 \cdot 10^{+59}:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]

Alternative 5: 76.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 7200:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d3 7200.0) (* d1 (+ d2 37.0)) (* d1 (+ d3 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 7200.0) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8) :: tmp
    if (d3 <= 7200.0d0) then
        tmp = d1 * (d2 + 37.0d0)
    else
        tmp = d1 * (d3 + 37.0d0)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if (d3 <= 7200.0) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d3 <= 7200.0:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * (d3 + 37.0)
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d3 <= 7200.0)
		tmp = Float64(d1 * Float64(d2 + 37.0));
	else
		tmp = Float64(d1 * Float64(d3 + 37.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d3 <= 7200.0)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * (d3 + 37.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d3, 7200.0], N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d3 + 37.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d3 < 7200

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      2. distribute-lft-out 99.4%

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

      3. distribute-lft-out 100.0%

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

      4. associate-+r+ 100.0%

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

      5. associate-+l+ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in d3 around 0 75.7%

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

   if 7200 < d3

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. distribute-lft-out 100.0%

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

      3. distribute-lft-out 100.0%

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

      4. associate-+r+ 100.0%

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

      5. associate-+l+ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in d2 around 0 72.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 7200:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \]

Alternative 6: 26.6% 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 96.4%

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

   1. *-commutative 96.4%

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

   2. distribute-lft-out 99.5%

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

   3. distribute-lft-out 100.0%

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

   4. associate-+r+ 100.0%

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

   5. associate-+l+ 100.0%

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

   6. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in d2 around 0 60.7%

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

5. Taylor expanded in d3 around 0 26.8%

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

6. Final simplification 26.8%

   \[\leadsto d1 \cdot 37 \]

Developer target: 100.0% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023192 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  :precision binary64

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

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