FastMath dist4

Percentage Accurate: 86.8% → 100.0%

Time: 10.9s

Alternatives: 11

Speedup: 1.7×

• 33.7% 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: 86.8% 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 89.0%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
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. +-commutative N/A

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

   11. unsub-neg N/A

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

   12. associate--l- N/A

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

   13. +-commutative N/A

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

   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: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d3\right)\\ t_1 := d1 \cdot \left(d2 + d4\right)\\ \mathbf{if}\;d3 \leq -2.8 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq -2.1 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;d3 \leq 8.2 \cdot 10^{-19}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \mathbf{elif}\;d3 \leq 1.65 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d3))) (t_1 (* d1 (+ d2 d4))))
   (if (<= d3 -2.8e+43)
     t_0
     (if (<= d3 -2.1e-241)
       t_1
       (if (<= d3 8.2e-19) (* d1 (- d4 d1)) (if (<= d3 1.65e+115) t_1 t_0))))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d3);
	double t_1 = d1 * (d2 + d4);
	double tmp;
	if (d3 <= -2.8e+43) {
		tmp = t_0;
	} else if (d3 <= -2.1e-241) {
		tmp = t_1;
	} else if (d3 <= 8.2e-19) {
		tmp = d1 * (d4 - d1);
	} else if (d3 <= 1.65e+115) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = d1 * (d2 - d3)
    t_1 = d1 * (d2 + d4)
    if (d3 <= (-2.8d+43)) then
        tmp = t_0
    else if (d3 <= (-2.1d-241)) then
        tmp = t_1
    else if (d3 <= 8.2d-19) then
        tmp = d1 * (d4 - d1)
    else if (d3 <= 1.65d+115) then
        tmp = t_1
    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 t_1 = d1 * (d2 + d4);
	double tmp;
	if (d3 <= -2.8e+43) {
		tmp = t_0;
	} else if (d3 <= -2.1e-241) {
		tmp = t_1;
	} else if (d3 <= 8.2e-19) {
		tmp = d1 * (d4 - d1);
	} else if (d3 <= 1.65e+115) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d3)
	t_1 = d1 * (d2 + d4)
	tmp = 0
	if d3 <= -2.8e+43:
		tmp = t_0
	elif d3 <= -2.1e-241:
		tmp = t_1
	elif d3 <= 8.2e-19:
		tmp = d1 * (d4 - d1)
	elif d3 <= 1.65e+115:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d3))
	t_1 = Float64(d1 * Float64(d2 + d4))
	tmp = 0.0
	if (d3 <= -2.8e+43)
		tmp = t_0;
	elseif (d3 <= -2.1e-241)
		tmp = t_1;
	elseif (d3 <= 8.2e-19)
		tmp = Float64(d1 * Float64(d4 - d1));
	elseif (d3 <= 1.65e+115)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d3);
	t_1 = d1 * (d2 + d4);
	tmp = 0.0;
	if (d3 <= -2.8e+43)
		tmp = t_0;
	elseif (d3 <= -2.1e-241)
		tmp = t_1;
	elseif (d3 <= 8.2e-19)
		tmp = d1 * (d4 - d1);
	elseif (d3 <= 1.65e+115)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -2.8e+43], t$95$0, If[LessEqual[d3, -2.1e-241], t$95$1, If[LessEqual[d3, 8.2e-19], N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d3, 1.65e+115], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -2.80000000000000019e43 or 1.65000000000000003e115 < d3

   1. Initial program 87.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   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 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in d1 around 0

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

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

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

      2. --lowering--.f64 82.5%

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

   10. Simplified 82.5%

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

   if -2.80000000000000019e43 < d3 < -2.0999999999999999e-241 or 8.1999999999999997e-19 < d3 < 1.65000000000000003e115

   1. Initial program 90.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 78.7%

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

   if -2.0999999999999999e-241 < d3 < 8.1999999999999997e-19

   1. Initial program 89.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 74.1%

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

   7. Simplified 74.1%

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

   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 70.5%

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

   10. Simplified 70.5%

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

Alternative 3: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d3\right)\\ t_1 := d1 \cdot \left(d2 + d4\right)\\ \mathbf{if}\;d3 \leq -1.3 \cdot 10^{+48}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq -1.6 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;d3 \leq 3.4 \cdot 10^{-18}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d3 \leq 2.7 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d3))) (t_1 (* d1 (+ d2 d4))))
   (if (<= d3 -1.3e+48)
     t_0
     (if (<= d3 -1.6e-109)
       t_1
       (if (<= d3 3.4e-18) (* d1 (- d2 d1)) (if (<= d3 2.7e+116) t_1 t_0))))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d3);
	double t_1 = d1 * (d2 + d4);
	double tmp;
	if (d3 <= -1.3e+48) {
		tmp = t_0;
	} else if (d3 <= -1.6e-109) {
		tmp = t_1;
	} else if (d3 <= 3.4e-18) {
		tmp = d1 * (d2 - d1);
	} else if (d3 <= 2.7e+116) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = d1 * (d2 - d3)
    t_1 = d1 * (d2 + d4)
    if (d3 <= (-1.3d+48)) then
        tmp = t_0
    else if (d3 <= (-1.6d-109)) then
        tmp = t_1
    else if (d3 <= 3.4d-18) then
        tmp = d1 * (d2 - d1)
    else if (d3 <= 2.7d+116) then
        tmp = t_1
    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 t_1 = d1 * (d2 + d4);
	double tmp;
	if (d3 <= -1.3e+48) {
		tmp = t_0;
	} else if (d3 <= -1.6e-109) {
		tmp = t_1;
	} else if (d3 <= 3.4e-18) {
		tmp = d1 * (d2 - d1);
	} else if (d3 <= 2.7e+116) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d3)
	t_1 = d1 * (d2 + d4)
	tmp = 0
	if d3 <= -1.3e+48:
		tmp = t_0
	elif d3 <= -1.6e-109:
		tmp = t_1
	elif d3 <= 3.4e-18:
		tmp = d1 * (d2 - d1)
	elif d3 <= 2.7e+116:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d3))
	t_1 = Float64(d1 * Float64(d2 + d4))
	tmp = 0.0
	if (d3 <= -1.3e+48)
		tmp = t_0;
	elseif (d3 <= -1.6e-109)
		tmp = t_1;
	elseif (d3 <= 3.4e-18)
		tmp = Float64(d1 * Float64(d2 - d1));
	elseif (d3 <= 2.7e+116)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d3);
	t_1 = d1 * (d2 + d4);
	tmp = 0.0;
	if (d3 <= -1.3e+48)
		tmp = t_0;
	elseif (d3 <= -1.6e-109)
		tmp = t_1;
	elseif (d3 <= 3.4e-18)
		tmp = d1 * (d2 - d1);
	elseif (d3 <= 2.7e+116)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -1.3e+48], t$95$0, If[LessEqual[d3, -1.6e-109], t$95$1, If[LessEqual[d3, 3.4e-18], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d3, 2.7e+116], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -1.29999999999999998e48 or 2.7e116 < d3

   1. Initial program 87.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   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 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in d1 around 0

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

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

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

      2. --lowering--.f64 82.5%

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

   10. Simplified 82.5%

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

   if -1.29999999999999998e48 < d3 < -1.6000000000000001e-109 or 3.40000000000000001e-18 < d3 < 2.7e116

   1. Initial program 90.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 84.6%

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

   if -1.6000000000000001e-109 < d3 < 3.40000000000000001e-18

   1. Initial program 90.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 71.9%

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

   7. Simplified 71.9%

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

   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 69.3%

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

   10. Simplified 69.3%

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

Alternative 4: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d3 \cdot \left(0 - d1\right)\\ \mathbf{if}\;d3 \leq -3.3 \cdot 10^{+108}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d3 \leq 3.6 \cdot 10^{+162}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d3 (- 0.0 d1))))
   (if (<= d3 -3.3e+108)
     t_0
     (if (<= d3 3.8e-18)
       (* d1 (- d2 d1))
       (if (<= d3 3.6e+162) (* d1 (+ d2 d4)) t_0)))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d3 * (0.0 - d1);
	double tmp;
	if (d3 <= -3.3e+108) {
		tmp = t_0;
	} else if (d3 <= 3.8e-18) {
		tmp = d1 * (d2 - d1);
	} else if (d3 <= 3.6e+162) {
		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 = d3 * (0.0d0 - d1)
    if (d3 <= (-3.3d+108)) then
        tmp = t_0
    else if (d3 <= 3.8d-18) then
        tmp = d1 * (d2 - d1)
    else if (d3 <= 3.6d+162) 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 = d3 * (0.0 - d1);
	double tmp;
	if (d3 <= -3.3e+108) {
		tmp = t_0;
	} else if (d3 <= 3.8e-18) {
		tmp = d1 * (d2 - d1);
	} else if (d3 <= 3.6e+162) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d3 * (0.0 - d1)
	tmp = 0
	if d3 <= -3.3e+108:
		tmp = t_0
	elif d3 <= 3.8e-18:
		tmp = d1 * (d2 - d1)
	elif d3 <= 3.6e+162:
		tmp = d1 * (d2 + d4)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d3 * Float64(0.0 - d1))
	tmp = 0.0
	if (d3 <= -3.3e+108)
		tmp = t_0;
	elseif (d3 <= 3.8e-18)
		tmp = Float64(d1 * Float64(d2 - d1));
	elseif (d3 <= 3.6e+162)
		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 = d3 * (0.0 - d1);
	tmp = 0.0;
	if (d3 <= -3.3e+108)
		tmp = t_0;
	elseif (d3 <= 3.8e-18)
		tmp = d1 * (d2 - d1);
	elseif (d3 <= 3.6e+162)
		tmp = d1 * (d2 + d4);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d3 * N[(0.0 - d1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -3.3e+108], t$95$0, If[LessEqual[d3, 3.8e-18], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d3, 3.6e+162], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -3.30000000000000019e108 or 3.59999999999999994e162 < d3

   1. Initial program 92.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 83.1%

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

   7. Simplified 83.1%

      \[\leadsto \color{blue}{0 - d1 \cdot d3} \]
   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 83.1%

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

   9. Applied egg-rr 83.1%

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

   if -3.30000000000000019e108 < d3 < 3.7999999999999998e-18

   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 71.4%

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

   7. Simplified 71.4%

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

   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 66.2%

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

   10. Simplified 66.2%

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

   if 3.7999999999999998e-18 < d3 < 3.59999999999999994e162

   1. Initial program 84.6%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 77.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -3.3 \cdot 10^{+108}:\\ \;\;\;\;d3 \cdot \left(0 - d1\right)\\ \mathbf{elif}\;d3 \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d3 \leq 3.6 \cdot 10^{+162}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;d3 \cdot \left(0 - d1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -3.3 \cdot 10^{+55}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d2 \leq -1.15 \cdot 10^{-184}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -3.3e+55)
   (* d1 (- d2 d3))
   (if (<= d2 -1.15e-184) (* d1 (- d4 d1)) (* d1 (- d4 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -3.3e+55) {
		tmp = d1 * (d2 - d3);
	} else if (d2 <= -1.15e-184) {
		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 <= (-3.3d+55)) then
        tmp = d1 * (d2 - d3)
    else if (d2 <= (-1.15d-184)) 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 <= -3.3e+55) {
		tmp = d1 * (d2 - d3);
	} else if (d2 <= -1.15e-184) {
		tmp = d1 * (d4 - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -3.3e+55:
		tmp = d1 * (d2 - d3)
	elif d2 <= -1.15e-184:
		tmp = d1 * (d4 - d1)
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -3.3e+55)
		tmp = Float64(d1 * Float64(d2 - d3));
	elseif (d2 <= -1.15e-184)
		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 <= -3.3e+55)
		tmp = d1 * (d2 - d3);
	elseif (d2 <= -1.15e-184)
		tmp = d1 * (d4 - d1);
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -3.3e+55], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], If[LessEqual[d2, -1.15e-184], N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -3.3e55

   1. Initial program 90.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   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 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in d1 around 0

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

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

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

      2. --lowering--.f64 77.6%

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

   10. Simplified 77.6%

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

   if -3.3e55 < d2 < -1.15e-184

   1. Initial program 92.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 96.2%

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

   7. Simplified 96.2%

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

   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 76.4%

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

   10. Simplified 76.4%

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

   if -1.15e-184 < d2

   1. Initial program 87.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 80.6%

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

   7. Simplified 80.6%

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

   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 59.4%

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

   10. Simplified 59.4%

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

Alternative 6: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d3 \cdot \left(0 - d1\right)\\ \mathbf{if}\;d3 \leq -2.55 \cdot 10^{+100}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq 6.2 \cdot 10^{+160}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d3 (- 0.0 d1))))
   (if (<= d3 -2.55e+100) t_0 (if (<= d3 6.2e+160) (* d1 (+ d2 d4)) t_0))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d3 * (0.0 - d1);
	double tmp;
	if (d3 <= -2.55e+100) {
		tmp = t_0;
	} else if (d3 <= 6.2e+160) {
		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 = d3 * (0.0d0 - d1)
    if (d3 <= (-2.55d+100)) then
        tmp = t_0
    else if (d3 <= 6.2d+160) 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 = d3 * (0.0 - d1);
	double tmp;
	if (d3 <= -2.55e+100) {
		tmp = t_0;
	} else if (d3 <= 6.2e+160) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d3 * (0.0 - d1)
	tmp = 0
	if d3 <= -2.55e+100:
		tmp = t_0
	elif d3 <= 6.2e+160:
		tmp = d1 * (d2 + d4)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d3 * Float64(0.0 - d1))
	tmp = 0.0
	if (d3 <= -2.55e+100)
		tmp = t_0;
	elseif (d3 <= 6.2e+160)
		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 = d3 * (0.0 - d1);
	tmp = 0.0;
	if (d3 <= -2.55e+100)
		tmp = t_0;
	elseif (d3 <= 6.2e+160)
		tmp = d1 * (d2 + d4);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d3 * N[(0.0 - d1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -2.55e+100], t$95$0, If[LessEqual[d3, 6.2e+160], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d3 < -2.55000000000000005e100 or 6.1999999999999996e160 < d3

   1. Initial program 91.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 82.3%

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

   7. Simplified 82.3%

      \[\leadsto \color{blue}{0 - d1 \cdot d3} \]
   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 82.3%

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

   9. Applied egg-rr 82.3%

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

   if -2.55000000000000005e100 < d3 < 6.1999999999999996e160

   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 63.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -2.55 \cdot 10^{+100}:\\ \;\;\;\;d3 \cdot \left(0 - d1\right)\\ \mathbf{elif}\;d3 \leq 6.2 \cdot 10^{+160}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;d3 \cdot \left(0 - d1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -1.4 \cdot 10^{+108}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -7 \cdot 10^{-276}:\\ \;\;\;\;d3 \cdot \left(0 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -1.4e+108)
   (* d1 d2)
   (if (<= d2 -7e-276) (* d3 (- 0.0 d1)) (* d1 d4))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.4e+108) {
		tmp = d1 * d2;
	} else if (d2 <= -7e-276) {
		tmp = d3 * (0.0 - d1);
	} 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 <= (-1.4d+108)) then
        tmp = d1 * d2
    else if (d2 <= (-7d-276)) then
        tmp = d3 * (0.0d0 - d1)
    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 <= -1.4e+108) {
		tmp = d1 * d2;
	} else if (d2 <= -7e-276) {
		tmp = d3 * (0.0 - d1);
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -1.4e+108:
		tmp = d1 * d2
	elif d2 <= -7e-276:
		tmp = d3 * (0.0 - d1)
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -1.4e+108)
		tmp = Float64(d1 * d2);
	elseif (d2 <= -7e-276)
		tmp = Float64(d3 * Float64(0.0 - d1));
	else
		tmp = Float64(d1 * d4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -1.4e+108)
		tmp = d1 * d2;
	elseif (d2 <= -7e-276)
		tmp = d3 * (0.0 - d1);
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -1.4e+108], N[(d1 * d2), $MachinePrecision], If[LessEqual[d2, -7e-276], N[(d3 * N[(0.0 - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -1.3999999999999999e108

   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in d2 around inf

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

      1. *-lowering-*.f64 70.0%

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

   7. Simplified 70.0%

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

   if -1.3999999999999999e108 < d2 < -6.99999999999999986e-276

   1. Initial program 93.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 38.3%

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

   7. Simplified 38.3%

      \[\leadsto \color{blue}{0 - d1 \cdot d3} \]
   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 38.3%

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

   9. Applied egg-rr 38.3%

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

   if -6.99999999999999986e-276 < d2

   1. Initial program 86.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 29.7%

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

   7. Simplified 29.7%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -1.4 \cdot 10^{+108}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -7 \cdot 10^{-276}:\\ \;\;\;\;d3 \cdot \left(0 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -3.6 \cdot 10^{+76}:\\ \;\;\;\;d1 \cdot \left(d2 - \left(d1 + d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -3.6e+76) (* d1 (- d2 (+ d1 d3))) (* d1 (- d4 (+ d1 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -3.6e+76) {
		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 <= (-3.6d+76)) 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 <= -3.6e+76) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - (d1 + d3));
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -3.6e+76:
		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 <= -3.6e+76)
		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 <= -3.6e+76)
		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, -3.6e+76], 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 < -3.6000000000000003e76

   1. Initial program 91.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d4 - \left(d1 + d3\right)\right)\right)} \]
   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 90.0%

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

   7. Simplified 90.0%

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

   if -3.6000000000000003e76 < d2

   1. Initial program 88.6%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 85.0%

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

   7. Simplified 85.0%

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

Alternative 9: 82.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 5.2 \cdot 10^{+60}:\\ \;\;\;\;d1 \cdot \left(d2 - \left(d1 + d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 5.2e+60) (* d1 (- d2 (+ d1 d3))) (* d1 (- d4 d3))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 5.2e+60) {
		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 <= 5.2d+60) 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 <= 5.2e+60) {
		tmp = d1 * (d2 - (d1 + d3));
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 5.2e+60:
		tmp = d1 * (d2 - (d1 + d3))
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 5.2e+60)
		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 <= 5.2e+60)
		tmp = d1 * (d2 - (d1 + d3));
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 5.2e+60], 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 < 5.20000000000000016e60

   1. Initial program 90.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 83.5%

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

   7. Simplified 83.5%

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

   if 5.20000000000000016e60 < d4

   1. Initial program 82.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 86.4%

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

   7. Simplified 86.4%

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

   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 74.9%

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

   10. Simplified 74.9%

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

Alternative 10: 39.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -1.36 \cdot 10^{+76}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -1.36e+76) (* d1 d2) (* d1 d4)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.36e+76) {
		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 <= (-1.36d+76)) 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 <= -1.36e+76) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -1.36e+76:
		tmp = d1 * d2
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -1.36e+76)
		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 <= -1.36e+76)
		tmp = d1 * d2;
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -1.36e+76], N[(d1 * d2), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -1.36000000000000004e76

   1. Initial program 91.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in d2 around inf

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

      1. *-lowering-*.f64 60.4%

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

   7. Simplified 60.4%

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

   if -1.36000000000000004e76 < d2

   1. Initial program 88.6%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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. +-commutative N/A

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

      11. unsub-neg N/A

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

      12. associate--l- N/A

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

      13. +-commutative N/A

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

      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 31.2%

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

   7. Simplified 31.2%

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

Alternative 11: 30.6% 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 89.0%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
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. +-commutative N/A

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

   11. unsub-neg N/A

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

   12. associate--l- N/A

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

   13. +-commutative N/A

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

   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 26.3%

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

7. Simplified 26.3%

   \[\leadsto \color{blue}{d1 \cdot d2} \]
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 2024160 
(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)))