FastMath dist4

Percentage Accurate: 87.6% → 100.0%

Time: 14.9s

Alternatives: 11

Speedup: 1.7×

• 33.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Python

def code(d1, d2, d3, d4):
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision]

Initial Program: 87.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Python

def code(d1, d2, d3, d4):
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 (+ d2 (- d4 (+ d1 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * (d2 + (d4 - (d1 + d3)));
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * (d2 + (d4 - (d1 + d3)))
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * (d2 + (d4 - (d1 + d3)));
}

Python

def code(d1, d2, d3, d4):
	return d1 * (d2 + (d4 - (d1 + d3)))

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * Float64(d2 + Float64(d4 - Float64(d1 + d3))))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * (d2 + (d4 - (d1 + d3)));
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * N[(d2 + N[(d4 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.5%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
2. Step-by-step derivation

   1. distribute-lft-out-- N/A

      \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

   2. *-commutative N/A

      \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

   3. distribute-lft-out N/A

      \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

   4. distribute-lft-out-- N/A

      \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

   6. associate-+r- N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

   8. associate-+l+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

   10. associate-+r- N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

   12. unsub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

   13. associate--l- N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

   14. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

   16. +-lowering-+.f64 100.0%

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 45.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0 - d1 \cdot d3\\ \mathbf{if}\;d3 \leq -1 \cdot 10^{+214}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq -1.5 \cdot 10^{-155}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d3 \leq 3.2 \cdot 10^{+76}:\\ \;\;\;\;d1 \cdot d4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (- 0.0 (* d1 d3))))
   (if (<= d3 -1e+214)
     t_0
     (if (<= d3 -1.5e-155) (* d1 d2) (if (<= d3 3.2e+76) (* d1 d4) t_0)))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = 0.0 - (d1 * d3);
	double tmp;
	if (d3 <= -1e+214) {
		tmp = t_0;
	} else if (d3 <= -1.5e-155) {
		tmp = d1 * d2;
	} else if (d3 <= 3.2e+76) {
		tmp = d1 * d4;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.0d0 - (d1 * d3)
    if (d3 <= (-1d+214)) then
        tmp = t_0
    else if (d3 <= (-1.5d-155)) then
        tmp = d1 * d2
    else if (d3 <= 3.2d+76) then
        tmp = d1 * d4
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = 0.0 - (d1 * d3);
	double tmp;
	if (d3 <= -1e+214) {
		tmp = t_0;
	} else if (d3 <= -1.5e-155) {
		tmp = d1 * d2;
	} else if (d3 <= 3.2e+76) {
		tmp = d1 * d4;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = 0.0 - (d1 * d3)
	tmp = 0
	if d3 <= -1e+214:
		tmp = t_0
	elif d3 <= -1.5e-155:
		tmp = d1 * d2
	elif d3 <= 3.2e+76:
		tmp = d1 * d4
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(0.0 - Float64(d1 * d3))
	tmp = 0.0
	if (d3 <= -1e+214)
		tmp = t_0;
	elseif (d3 <= -1.5e-155)
		tmp = Float64(d1 * d2);
	elseif (d3 <= 3.2e+76)
		tmp = Float64(d1 * d4);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = 0.0 - (d1 * d3);
	tmp = 0.0;
	if (d3 <= -1e+214)
		tmp = t_0;
	elseif (d3 <= -1.5e-155)
		tmp = d1 * d2;
	elseif (d3 <= 3.2e+76)
		tmp = d1 * d4;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(0.0 - N[(d1 * d3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -1e+214], t$95$0, If[LessEqual[d3, -1.5e-155], N[(d1 * d2), $MachinePrecision], If[LessEqual[d3, 3.2e+76], N[(d1 * d4), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -9.9999999999999995e213 or 3.19999999999999976e76 < d3

   1. Initial program 79.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d3 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(d1 \cdot d3\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot d3\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{d1 \cdot d3} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(d1 \cdot d3\right)}\right) \]

      4. *-lowering-*.f64 77.6%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(d1, \color{blue}{d3}\right)\right) \]

   7. Simplified 77.6%

      \[\leadsto \color{blue}{0 - d1 \cdot d3} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot d3\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(d1 \cdot d3\right)\right) \]

      3. *-lowering-*.f64 77.6%

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

   9. Applied egg-rr 77.6%

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

   if -9.9999999999999995e213 < d3 < -1.49999999999999992e-155

   1. Initial program 87.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around inf

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

      1. *-lowering-*.f64 38.3%

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

   7. Simplified 38.3%

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

   if -1.49999999999999992e-155 < d3 < 3.19999999999999976e76

   1. Initial program 88.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \color{blue}{d1 \cdot d4} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 42.8%

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{d4}\right) \]

   7. Simplified 42.8%

      \[\leadsto \color{blue}{d1 \cdot d4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -1 \cdot 10^{+214}:\\ \;\;\;\;0 - d1 \cdot d3\\ \mathbf{elif}\;d3 \leq -1.5 \cdot 10^{-155}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d3 \leq 3.2 \cdot 10^{+76}:\\ \;\;\;\;d1 \cdot d4\\ \mathbf{else}:\\ \;\;\;\;0 - d1 \cdot d3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -340000000:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d2 \leq 6.4 \cdot 10^{-130}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -340000000.0)
   (* d1 (- d2 d3))
   (if (<= d2 6.4e-130) (* d1 (- d4 d1)) (* d1 (- d4 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -340000000.0) {
		tmp = d1 * (d2 - d3);
	} else if (d2 <= 6.4e-130) {
		tmp = d1 * (d4 - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-340000000.0d0)) then
        tmp = d1 * (d2 - d3)
    else if (d2 <= 6.4d-130) then
        tmp = d1 * (d4 - d1)
    else
        tmp = d1 * (d4 - d3)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -340000000.0) {
		tmp = d1 * (d2 - d3);
	} else if (d2 <= 6.4e-130) {
		tmp = d1 * (d4 - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -340000000.0:
		tmp = d1 * (d2 - d3)
	elif d2 <= 6.4e-130:
		tmp = d1 * (d4 - d1)
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -340000000.0)
		tmp = Float64(d1 * Float64(d2 - d3));
	elseif (d2 <= 6.4e-130)
		tmp = Float64(d1 * Float64(d4 - d1));
	else
		tmp = Float64(d1 * Float64(d4 - d3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -340000000.0)
		tmp = d1 * (d2 - d3);
	elseif (d2 <= 6.4e-130)
		tmp = d1 * (d4 - d1);
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -340000000.0], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], If[LessEqual[d2, 6.4e-130], N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -3.4e8

   1. Initial program 80.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

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

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

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

      2. --lowering--.f64 N/A

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

      3. +-lowering-+.f64 86.7%

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

   7. Simplified 86.7%

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

   8. Taylor expanded in d1 around 0

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

      1. remove-double-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(d1 \cdot \left(d2 - d3\right)\right)\right)\right) \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot \left(\mathsf{neg}\left(\left(d2 - d3\right)\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot \left(-1 \cdot \left(d2 - d3\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(d2 - d3\right)\right)\right)} \]

      5. *-rgt-identity N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot 1\right)\right) \]

      6. *-inverses N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot \frac{d1}{d1}\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{\left(-1 \cdot \left(d2 - d3\right)\right) \cdot d1}{d1}\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{-1 \cdot \left(d2 - d3\right)}{d1} \cdot d1\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \frac{d2 - d3}{d1}\right) \cdot d1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(d1 \cdot \left(-1 \cdot \frac{d2 - d3}{d1}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\mathsf{neg}\left(d1 \cdot \left(-1 \cdot \frac{d2 - d3}{d1}\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot \frac{d2 - d3}{d1}\right) \cdot d1\right)\right)\right) \]

      13. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\frac{-1 \cdot \left(d2 - d3\right)}{d1} \cdot d1\right)\right)\right) \]

      14. associate-*l/ N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\frac{\left(-1 \cdot \left(d2 - d3\right)\right) \cdot d1}{d1}\right)\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot \frac{d1}{d1}\right)\right)\right) \]

      16. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot 1\right)\right)\right) \]

      17. *-rgt-identity N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(-1 \cdot \left(d2 - d3\right)\right)\right)\right) \]

      18. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(-1 \cdot \left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right)\right)\right)\right) \]

      19. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot d2 + -1 \cdot \left(\mathsf{neg}\left(d3\right)\right)\right)\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot d2 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(d3\right)\right)\right)\right)\right)\right)\right)\right) \]

      21. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot d2 + d3\right)\right)\right)\right) \]

   10. Simplified 71.0%

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

   if -3.4e8 < d2 < 6.3999999999999999e-130

   1. Initial program 88.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - \left(d1 + d3\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 98.0%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 98.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d3 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - d1\right)}\right) \]

      2. --lowering--.f64 75.7%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{d1}\right)\right) \]

   10. Simplified 75.7%

       \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} \]

   if 6.3999999999999999e-130 < d2

   1. Initial program 85.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - \left(d1 + d3\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 71.5%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - d3\right)}\right) \]

      2. --lowering--.f64 53.8%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{d3}\right)\right) \]

   10. Simplified 53.8%

       \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d3\right)\\ \mathbf{if}\;d3 \leq -4.7 \cdot 10^{+55}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq 7 \cdot 10^{+77}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d3))))
   (if (<= d3 -4.7e+55) t_0 (if (<= d3 7e+77) (* d1 (+ d2 d4)) t_0))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d3);
	double tmp;
	if (d3 <= -4.7e+55) {
		tmp = t_0;
	} else if (d3 <= 7e+77) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = d1 * (d2 - d3)
    if (d3 <= (-4.7d+55)) then
        tmp = t_0
    else if (d3 <= 7d+77) then
        tmp = d1 * (d2 + d4)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d3);
	double tmp;
	if (d3 <= -4.7e+55) {
		tmp = t_0;
	} else if (d3 <= 7e+77) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d3)
	tmp = 0
	if d3 <= -4.7e+55:
		tmp = t_0
	elif d3 <= 7e+77:
		tmp = d1 * (d2 + d4)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d3))
	tmp = 0.0
	if (d3 <= -4.7e+55)
		tmp = t_0;
	elseif (d3 <= 7e+77)
		tmp = Float64(d1 * Float64(d2 + d4));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d3);
	tmp = 0.0;
	if (d3 <= -4.7e+55)
		tmp = t_0;
	elseif (d3 <= 7e+77)
		tmp = d1 * (d2 + d4);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -4.7e+55], t$95$0, If[LessEqual[d3, 7e+77], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d3 < -4.7000000000000001e55 or 7.0000000000000003e77 < d3

   1. Initial program 81.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

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

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

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

      2. --lowering--.f64 N/A

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

      3. +-lowering-+.f64 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in d1 around 0

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

      1. remove-double-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(d1 \cdot \left(d2 - d3\right)\right)\right)\right) \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot \left(\mathsf{neg}\left(\left(d2 - d3\right)\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot \left(-1 \cdot \left(d2 - d3\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(d2 - d3\right)\right)\right)} \]

      5. *-rgt-identity N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot 1\right)\right) \]

      6. *-inverses N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot \frac{d1}{d1}\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{\left(-1 \cdot \left(d2 - d3\right)\right) \cdot d1}{d1}\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{-1 \cdot \left(d2 - d3\right)}{d1} \cdot d1\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \frac{d2 - d3}{d1}\right) \cdot d1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(d1 \cdot \left(-1 \cdot \frac{d2 - d3}{d1}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\mathsf{neg}\left(d1 \cdot \left(-1 \cdot \frac{d2 - d3}{d1}\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot \frac{d2 - d3}{d1}\right) \cdot d1\right)\right)\right) \]

      13. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\frac{-1 \cdot \left(d2 - d3\right)}{d1} \cdot d1\right)\right)\right) \]

      14. associate-*l/ N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\frac{\left(-1 \cdot \left(d2 - d3\right)\right) \cdot d1}{d1}\right)\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot \frac{d1}{d1}\right)\right)\right) \]

      16. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot 1\right)\right)\right) \]

      17. *-rgt-identity N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(-1 \cdot \left(d2 - d3\right)\right)\right)\right) \]

      18. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(-1 \cdot \left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right)\right)\right)\right) \]

      19. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot d2 + -1 \cdot \left(\mathsf{neg}\left(d3\right)\right)\right)\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot d2 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(d3\right)\right)\right)\right)\right)\right)\right)\right) \]

      21. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot d2 + d3\right)\right)\right)\right) \]

   10. Simplified 78.5%

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

   if -4.7000000000000001e55 < d3 < 7.0000000000000003e77

   1. Initial program 88.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{d4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 70.6%

      \[\leadsto d1 \cdot \left(d2 + \color{blue}{d4}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0 - d1 \cdot d3\\ \mathbf{if}\;d3 \leq -1 \cdot 10^{+214}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq 3.9 \cdot 10^{+90}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (- 0.0 (* d1 d3))))
   (if (<= d3 -1e+214) t_0 (if (<= d3 3.9e+90) (* d1 (+ d2 d4)) t_0))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = 0.0 - (d1 * d3);
	double tmp;
	if (d3 <= -1e+214) {
		tmp = t_0;
	} else if (d3 <= 3.9e+90) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.0d0 - (d1 * d3)
    if (d3 <= (-1d+214)) then
        tmp = t_0
    else if (d3 <= 3.9d+90) then
        tmp = d1 * (d2 + d4)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = 0.0 - (d1 * d3);
	double tmp;
	if (d3 <= -1e+214) {
		tmp = t_0;
	} else if (d3 <= 3.9e+90) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = 0.0 - (d1 * d3)
	tmp = 0
	if d3 <= -1e+214:
		tmp = t_0
	elif d3 <= 3.9e+90:
		tmp = d1 * (d2 + d4)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(0.0 - Float64(d1 * d3))
	tmp = 0.0
	if (d3 <= -1e+214)
		tmp = t_0;
	elseif (d3 <= 3.9e+90)
		tmp = Float64(d1 * Float64(d2 + d4));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = 0.0 - (d1 * d3);
	tmp = 0.0;
	if (d3 <= -1e+214)
		tmp = t_0;
	elseif (d3 <= 3.9e+90)
		tmp = d1 * (d2 + d4);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(0.0 - N[(d1 * d3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -1e+214], t$95$0, If[LessEqual[d3, 3.9e+90], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d3 < -9.9999999999999995e213 or 3.9000000000000002e90 < d3

   1. Initial program 78.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d3 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(d1 \cdot d3\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot d3\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{d1 \cdot d3} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(d1 \cdot d3\right)}\right) \]

      4. *-lowering-*.f64 79.5%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(d1, \color{blue}{d3}\right)\right) \]

   7. Simplified 79.5%

      \[\leadsto \color{blue}{0 - d1 \cdot d3} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot d3\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(d1 \cdot d3\right)\right) \]

      3. *-lowering-*.f64 79.5%

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

   9. Applied egg-rr 79.5%

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

   if -9.9999999999999995e213 < d3 < 3.9000000000000002e90

   1. Initial program 88.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{d4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 69.3%

      \[\leadsto d1 \cdot \left(d2 + \color{blue}{d4}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -1 \cdot 10^{+214}:\\ \;\;\;\;0 - d1 \cdot d3\\ \mathbf{elif}\;d3 \leq 3.9 \cdot 10^{+90}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;0 - d1 \cdot d3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -6500000:\\ \;\;\;\;d1 \cdot \left(d2 - \left(d1 + d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -6500000.0) (* d1 (- d2 (+ d1 d3))) (* d1 (- d4 (+ d1 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -6500000.0) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - (d1 + d3));
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-6500000.0d0)) then
        tmp = d1 * (d2 - (d1 + d3))
    else
        tmp = d1 * (d4 - (d1 + d3))
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -6500000.0) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - (d1 + d3));
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -6500000.0:
		tmp = d1 * (d2 - (d1 + d3))
	else:
		tmp = d1 * (d4 - (d1 + d3))
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -6500000.0)
		tmp = Float64(d1 * Float64(d2 - Float64(d1 + d3)));
	else
		tmp = Float64(d1 * Float64(d4 - Float64(d1 + d3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -6500000.0)
		tmp = d1 * (d2 - (d1 + d3));
	else
		tmp = d1 * (d4 - (d1 + d3));
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -6500000.0], N[(d1 * N[(d2 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -6.5e6

   1. Initial program 81.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

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

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

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

      2. --lowering--.f64 N/A

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

      3. +-lowering-+.f64 85.3%

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

   7. Simplified 85.3%

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

   if -6.5e6 < d2

   1. Initial program 86.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - \left(d1 + d3\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 83.7%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 83.7%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 82.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 7.2 \cdot 10^{+132}:\\ \;\;\;\;d1 \cdot \left(d2 - \left(d1 + d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 7.2e+132) (* d1 (- d2 (+ d1 d3))) (* d1 (- d4 d3))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 7.2e+132) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= 7.2d+132) then
        tmp = d1 * (d2 - (d1 + d3))
    else
        tmp = d1 * (d4 - d3)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 7.2e+132) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 7.2e+132:
		tmp = d1 * (d2 - (d1 + d3))
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 7.2e+132)
		tmp = Float64(d1 * Float64(d2 - Float64(d1 + d3)));
	else
		tmp = Float64(d1 * Float64(d4 - d3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 7.2e+132)
		tmp = d1 * (d2 - (d1 + d3));
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 7.2e+132], N[(d1 * N[(d2 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 7.20000000000000031e132

   1. Initial program 85.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

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

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

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

      2. --lowering--.f64 N/A

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

      3. +-lowering-+.f64 84.3%

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

   7. Simplified 84.3%

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

   if 7.20000000000000031e132 < d4

   1. Initial program 87.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - \left(d1 + d3\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 95.0%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 95.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - d3\right)}\right) \]

      2. --lowering--.f64 92.5%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{d3}\right)\right) \]

   10. Simplified 92.5%

       \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 62.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -1300000000:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -1300000000.0) (* d1 (- d2 d3)) (* d1 (- d4 d1))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1300000000.0) {
		tmp = d1 * (d2 - d3);
	} else {
		tmp = d1 * (d4 - d1);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-1300000000.0d0)) then
        tmp = d1 * (d2 - d3)
    else
        tmp = d1 * (d4 - d1)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1300000000.0) {
		tmp = d1 * (d2 - d3);
	} else {
		tmp = d1 * (d4 - d1);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -1300000000.0:
		tmp = d1 * (d2 - d3)
	else:
		tmp = d1 * (d4 - d1)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -1300000000.0)
		tmp = Float64(d1 * Float64(d2 - d3));
	else
		tmp = Float64(d1 * Float64(d4 - d1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -1300000000.0)
		tmp = d1 * (d2 - d3);
	else
		tmp = d1 * (d4 - d1);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -1300000000.0], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -1.3e9

   1. Initial program 80.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

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

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

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

      2. --lowering--.f64 N/A

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

      3. +-lowering-+.f64 86.7%

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

   7. Simplified 86.7%

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

   8. Taylor expanded in d1 around 0

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

      1. remove-double-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(d1 \cdot \left(d2 - d3\right)\right)\right)\right) \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot \left(\mathsf{neg}\left(\left(d2 - d3\right)\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot \left(-1 \cdot \left(d2 - d3\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(d2 - d3\right)\right)\right)} \]

      5. *-rgt-identity N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot 1\right)\right) \]

      6. *-inverses N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot \frac{d1}{d1}\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{\left(-1 \cdot \left(d2 - d3\right)\right) \cdot d1}{d1}\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\frac{-1 \cdot \left(d2 - d3\right)}{d1} \cdot d1\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto d1 \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \frac{d2 - d3}{d1}\right) \cdot d1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto d1 \cdot \left(\mathsf{neg}\left(d1 \cdot \left(-1 \cdot \frac{d2 - d3}{d1}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\mathsf{neg}\left(d1 \cdot \left(-1 \cdot \frac{d2 - d3}{d1}\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot \frac{d2 - d3}{d1}\right) \cdot d1\right)\right)\right) \]

      13. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\frac{-1 \cdot \left(d2 - d3\right)}{d1} \cdot d1\right)\right)\right) \]

      14. associate-*l/ N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\frac{\left(-1 \cdot \left(d2 - d3\right)\right) \cdot d1}{d1}\right)\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot \frac{d1}{d1}\right)\right)\right) \]

      16. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot \left(d2 - d3\right)\right) \cdot 1\right)\right)\right) \]

      17. *-rgt-identity N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(-1 \cdot \left(d2 - d3\right)\right)\right)\right) \]

      18. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(-1 \cdot \left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right)\right)\right)\right) \]

      19. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot d2 + -1 \cdot \left(\mathsf{neg}\left(d3\right)\right)\right)\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot d2 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(d3\right)\right)\right)\right)\right)\right)\right)\right) \]

      21. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \left(\mathsf{neg}\left(\left(-1 \cdot d2 + d3\right)\right)\right)\right) \]

   10. Simplified 71.0%

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

   if -1.3e9 < d2

   1. Initial program 86.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - \left(d1 + d3\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d1 + d3\right)}\right)\right) \]

      3. +-lowering-+.f64 83.4%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right) \]

   7. Simplified 83.4%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]

   8. Taylor expanded in d3 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(d4 - d1\right)}\right) \]

      2. --lowering--.f64 61.9%

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d4, \color{blue}{d1}\right)\right) \]

   10. Simplified 61.9%

       \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 62.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 1.02 \cdot 10^{+62}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 1.02e+62) (* d1 (- d2 d1)) (* d1 (+ d2 d4))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.02e+62) {
		tmp = d1 * (d2 - d1);
	} else {
		tmp = d1 * (d2 + d4);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= 1.02d+62) then
        tmp = d1 * (d2 - d1)
    else
        tmp = d1 * (d2 + d4)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.02e+62) {
		tmp = d1 * (d2 - d1);
	} else {
		tmp = d1 * (d2 + d4);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 1.02e+62:
		tmp = d1 * (d2 - d1)
	else:
		tmp = d1 * (d2 + d4)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 1.02e+62)
		tmp = Float64(d1 * Float64(d2 - d1));
	else
		tmp = Float64(d1 * Float64(d2 + d4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 1.02e+62)
		tmp = d1 * (d2 - d1);
	else
		tmp = d1 * (d2 + d4);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 1.02e+62], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 1.02000000000000002e62

   1. Initial program 86.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around 0

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

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

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

      2. --lowering--.f64 N/A

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

      3. +-lowering-+.f64 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in d3 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - d1\right)} \]
   9. Step-by-step derivation

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

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

      2. --lowering--.f64 60.9%

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

   10. Simplified 60.9%

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

   if 1.02000000000000002e62 < d4

   1. Initial program 83.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{d4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 76.3%

      \[\leadsto d1 \cdot \left(d2 + \color{blue}{d4}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 39.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -0.00136:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -0.00136) (* d1 d2) (* d1 d4)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -0.00136) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-0.00136d0)) then
        tmp = d1 * d2
    else
        tmp = d1 * d4
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -0.00136) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -0.00136:
		tmp = d1 * d2
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -0.00136)
		tmp = Float64(d1 * d2);
	else
		tmp = Float64(d1 * d4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -0.00136)
		tmp = d1 * d2;
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -0.00136], N[(d1 * d2), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -0.00136

   1. Initial program 81.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around inf

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

      1. *-lowering-*.f64 53.1%

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

   7. Simplified 53.1%

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

   if -0.00136 < d2

   1. Initial program 86.6%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      2. *-commutative N/A

         \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

      3. distribute-lft-out N/A

         \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

      4. distribute-lft-out-- N/A

         \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

      6. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

      10. associate-+r- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

      16. +-lowering-+.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d4 around inf

      \[\leadsto \color{blue}{d1 \cdot d4} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 34.8%

         \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{d4}\right) \]

   7. Simplified 34.8%

      \[\leadsto \color{blue}{d1 \cdot d4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 30.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ d1 \cdot d2 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 d2))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * d2;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * d2
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * d2;
}

Python

def code(d1, d2, d3, d4):
	return d1 * d2

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * d2)
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * d2;
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * d2), $MachinePrecision]

Derivation

1. Initial program 85.5%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
2. Step-by-step derivation

   1. distribute-lft-out-- N/A

      \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

   2. *-commutative N/A

      \[\leadsto \left(d1 \cdot \left(d2 - d3\right) + d1 \cdot d4\right) - d1 \cdot d1 \]

   3. distribute-lft-out N/A

      \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + d4\right) - \color{blue}{d1} \cdot d1 \]

   4. distribute-lft-out-- N/A

      \[\leadsto d1 \cdot \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)} \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \color{blue}{\left(\left(\left(d2 - d3\right) + d4\right) - d1\right)}\right) \]

   6. associate-+r- N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 - d3\right) + \color{blue}{\left(d4 - d1\right)}\right)\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(\left(d2 + \left(\mathsf{neg}\left(d3\right)\right)\right) + \left(\color{blue}{d4} - d1\right)\right)\right) \]

   8. associate-+l+ N/A

      \[\leadsto \mathsf{*.f64}\left(d1, \left(d2 + \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \color{blue}{\left(\left(\mathsf{neg}\left(d3\right)\right) + \left(d4 - d1\right)\right)}\right)\right) \]

   10. associate-+r- N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(\left(\mathsf{neg}\left(d3\right)\right) + d4\right) - \color{blue}{d1}\right)\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 + \left(\mathsf{neg}\left(d3\right)\right)\right) - d1\right)\right)\right) \]

   12. unsub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(\left(d4 - d3\right) - d1\right)\right)\right) \]

   13. associate--l- N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \left(d4 - \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

   14. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \color{blue}{\left(d3 + d1\right)}\right)\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \left(d1 + \color{blue}{d3}\right)\right)\right)\right) \]

   16. +-lowering-+.f64 100.0%

       \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{+.f64}\left(d2, \mathsf{\_.f64}\left(d4, \mathsf{+.f64}\left(d1, \color{blue}{d3}\right)\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in d2 around inf

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

   1. *-lowering-*.f64 31.5%

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

7. Simplified 31.5%

   \[\leadsto \color{blue}{d1 \cdot d2} \]
8. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(\left(\left(d2 - d3\right) + d4\right) - d1\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 (- (+ (- d2 d3) d4) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * (((d2 - d3) + d4) - d1);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * (((d2 - d3) + d4) - d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * (((d2 - d3) + d4) - d1);
}

Python

def code(d1, d2, d3, d4):
	return d1 * (((d2 - d3) + d4) - d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * Float64(Float64(Float64(d2 - d3) + d4) - d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * (((d2 - d3) + d4) - d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * N[(N[(N[(d2 - d3), $MachinePrecision] + d4), $MachinePrecision] - d1), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024144 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  :precision binary64

  :alt
  (! :herbie-platform default (* d1 (- (+ (- d2 d3) d4) d1)))

  (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))