FastMath dist4

Percentage Accurate: 87.9% → 100.0%

Time: 7.4s

Alternatives: 10

Speedup: 1.7×

• 33.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.9% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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-+l- N/A

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

   7. associate--l- N/A

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

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

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

   9. +-commutative N/A

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

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

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

   11. --lowering--.f64 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto d1 \cdot \left(d2 + \left(\left(d4 - d3\right) - d1\right)\right) \]
6. Add Preprocessing

Alternative 2: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d1 \leq -6.2 \cdot 10^{+69}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d1 \leq 9.2 \cdot 10^{-58}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d1 \leq 5.8 \cdot 10^{+108}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d1 -6.2e+69)
   (* d1 (- d2 d1))
   (if (<= d1 9.2e-58)
     (* d1 (+ d2 d4))
     (if (<= d1 5.8e+108) (* d1 (- d4 d3)) (* d1 (- d4 d1))))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d1 <= -6.2e+69) {
		tmp = d1 * (d2 - d1);
	} else if (d1 <= 9.2e-58) {
		tmp = d1 * (d2 + d4);
	} else if (d1 <= 5.8e+108) {
		tmp = d1 * (d4 - d3);
	} else {
		tmp = d1 * (d4 - d1);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d1 <= (-6.2d+69)) then
        tmp = d1 * (d2 - d1)
    else if (d1 <= 9.2d-58) then
        tmp = d1 * (d2 + d4)
    else if (d1 <= 5.8d+108) then
        tmp = d1 * (d4 - d3)
    else
        tmp = d1 * (d4 - d1)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d1 <= -6.2e+69) {
		tmp = d1 * (d2 - d1);
	} else if (d1 <= 9.2e-58) {
		tmp = d1 * (d2 + d4);
	} else if (d1 <= 5.8e+108) {
		tmp = d1 * (d4 - d3);
	} else {
		tmp = d1 * (d4 - d1);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d1 <= -6.2e+69:
		tmp = d1 * (d2 - d1)
	elif d1 <= 9.2e-58:
		tmp = d1 * (d2 + d4)
	elif d1 <= 5.8e+108:
		tmp = d1 * (d4 - d3)
	else:
		tmp = d1 * (d4 - d1)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d1 <= -6.2e+69)
		tmp = Float64(d1 * Float64(d2 - d1));
	elseif (d1 <= 9.2e-58)
		tmp = Float64(d1 * Float64(d2 + d4));
	elseif (d1 <= 5.8e+108)
		tmp = Float64(d1 * Float64(d4 - d3));
	else
		tmp = Float64(d1 * Float64(d4 - d1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d1 <= -6.2e+69)
		tmp = d1 * (d2 - d1);
	elseif (d1 <= 9.2e-58)
		tmp = d1 * (d2 + d4);
	elseif (d1 <= 5.8e+108)
		tmp = d1 * (d4 - d3);
	else
		tmp = d1 * (d4 - d1);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d1, -6.2e+69], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d1, 9.2e-58], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], If[LessEqual[d1, 5.8e+108], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if d1 < -6.1999999999999997e69

   1. Initial program 76.5%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around inf

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

   7. Simplified 82.5%

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

   if -6.1999999999999997e69 < d1 < 9.1999999999999995e-58

   1. Initial program 100.0%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d3 - d4\right)}\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in d3 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + d4\right)} \]
   9. Step-by-step derivation

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

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

      2. +-lowering-+.f64 77.8%

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

   10. Simplified 77.8%

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

   if 9.1999999999999995e-58 < d1 < 5.80000000000000015e108

   1. Initial program 99.9%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d3 - d4\right)}\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in d2 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 76.5%

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

   10. Simplified 76.5%

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

   if 5.80000000000000015e108 < d1

   1. Initial program 65.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around inf

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

      1. *-lowering-*.f64 75.9%

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

   5. Simplified 75.9%

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 86.2%

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

   7. Applied egg-rr 86.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d1 \leq -6.2 \cdot 10^{+69}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d1 \leq 9.2 \cdot 10^{-58}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d1 \leq 5.8 \cdot 10^{+108}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d1\right)\\ \mathbf{if}\;d1 \leq -7 \cdot 10^{+68}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d1 \leq 2.5 \cdot 10^{-60}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d1 \leq 2.45 \cdot 10^{+135}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d1))))
   (if (<= d1 -7e+68)
     t_0
     (if (<= d1 2.5e-60)
       (* d1 (+ d2 d4))
       (if (<= d1 2.45e+135) (* d1 (- d4 d3)) t_0)))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d1);
	double tmp;
	if (d1 <= -7e+68) {
		tmp = t_0;
	} else if (d1 <= 2.5e-60) {
		tmp = d1 * (d2 + d4);
	} else if (d1 <= 2.45e+135) {
		tmp = d1 * (d4 - d3);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = d1 * (d2 - d1)
    if (d1 <= (-7d+68)) then
        tmp = t_0
    else if (d1 <= 2.5d-60) then
        tmp = d1 * (d2 + d4)
    else if (d1 <= 2.45d+135) then
        tmp = d1 * (d4 - d3)
    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 - d1);
	double tmp;
	if (d1 <= -7e+68) {
		tmp = t_0;
	} else if (d1 <= 2.5e-60) {
		tmp = d1 * (d2 + d4);
	} else if (d1 <= 2.45e+135) {
		tmp = d1 * (d4 - d3);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d1)
	tmp = 0
	if d1 <= -7e+68:
		tmp = t_0
	elif d1 <= 2.5e-60:
		tmp = d1 * (d2 + d4)
	elif d1 <= 2.45e+135:
		tmp = d1 * (d4 - d3)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d1))
	tmp = 0.0
	if (d1 <= -7e+68)
		tmp = t_0;
	elseif (d1 <= 2.5e-60)
		tmp = Float64(d1 * Float64(d2 + d4));
	elseif (d1 <= 2.45e+135)
		tmp = Float64(d1 * Float64(d4 - d3));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d1);
	tmp = 0.0;
	if (d1 <= -7e+68)
		tmp = t_0;
	elseif (d1 <= 2.5e-60)
		tmp = d1 * (d2 + d4);
	elseif (d1 <= 2.45e+135)
		tmp = d1 * (d4 - d3);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d1, -7e+68], t$95$0, If[LessEqual[d1, 2.5e-60], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], If[LessEqual[d1, 2.45e+135], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d1 < -6.99999999999999955e68 or 2.4500000000000001e135 < d1

   1. Initial program 68.8%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around inf

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

   7. Simplified 85.4%

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

   if -6.99999999999999955e68 < d1 < 2.5000000000000001e-60

   1. Initial program 100.0%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d3 - d4\right)}\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in d3 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + d4\right)} \]
   9. Step-by-step derivation

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

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

      2. +-lowering-+.f64 77.8%

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

   10. Simplified 77.8%

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

   if 2.5000000000000001e-60 < d1 < 2.4500000000000001e135

   1. Initial program 99.9%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d3 - d4\right)}\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in d2 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 70.4%

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

   10. Simplified 70.4%

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

Alternative 4: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d1\right)\\ \mathbf{if}\;d1 \leq -1.6 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d1 \leq 4.4 \cdot 10^{+14}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d1 \leq 2.9 \cdot 10^{+134}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d1))))
   (if (<= d1 -1.6e+70)
     t_0
     (if (<= d1 4.4e+14)
       (* d1 (+ d2 d4))
       (if (<= d1 2.9e+134) (* d1 (- d2 d3)) t_0)))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d1);
	double tmp;
	if (d1 <= -1.6e+70) {
		tmp = t_0;
	} else if (d1 <= 4.4e+14) {
		tmp = d1 * (d2 + d4);
	} else if (d1 <= 2.9e+134) {
		tmp = d1 * (d2 - d3);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = d1 * (d2 - d1)
    if (d1 <= (-1.6d+70)) then
        tmp = t_0
    else if (d1 <= 4.4d+14) then
        tmp = d1 * (d2 + d4)
    else if (d1 <= 2.9d+134) then
        tmp = d1 * (d2 - d3)
    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 - d1);
	double tmp;
	if (d1 <= -1.6e+70) {
		tmp = t_0;
	} else if (d1 <= 4.4e+14) {
		tmp = d1 * (d2 + d4);
	} else if (d1 <= 2.9e+134) {
		tmp = d1 * (d2 - d3);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d1)
	tmp = 0
	if d1 <= -1.6e+70:
		tmp = t_0
	elif d1 <= 4.4e+14:
		tmp = d1 * (d2 + d4)
	elif d1 <= 2.9e+134:
		tmp = d1 * (d2 - d3)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d1))
	tmp = 0.0
	if (d1 <= -1.6e+70)
		tmp = t_0;
	elseif (d1 <= 4.4e+14)
		tmp = Float64(d1 * Float64(d2 + d4));
	elseif (d1 <= 2.9e+134)
		tmp = Float64(d1 * Float64(d2 - d3));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d1);
	tmp = 0.0;
	if (d1 <= -1.6e+70)
		tmp = t_0;
	elseif (d1 <= 4.4e+14)
		tmp = d1 * (d2 + d4);
	elseif (d1 <= 2.9e+134)
		tmp = d1 * (d2 - d3);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d1, -1.6e+70], t$95$0, If[LessEqual[d1, 4.4e+14], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], If[LessEqual[d1, 2.9e+134], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d1 < -1.6000000000000001e70 or 2.90000000000000012e134 < d1

   1. Initial program 68.8%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around inf

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

   7. Simplified 85.4%

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

   if -1.6000000000000001e70 < d1 < 4.4e14

   1. Initial program 100.0%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d3 - d4\right)}\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in d3 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + d4\right)} \]
   9. Step-by-step derivation

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

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

      2. +-lowering-+.f64 76.4%

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

   10. Simplified 76.4%

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

   if 4.4e14 < d1 < 2.90000000000000012e134

   1. Initial program 99.9%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in d3 around inf

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

   7. Simplified 70.7%

      \[\leadsto d1 \cdot \left(d2 - \color{blue}{d3}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 90.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d1 \leq -1.9 \cdot 10^{+88}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d1 \leq 3900:\\ \;\;\;\;d1 \cdot \left(d2 + \left(d4 - d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d1 -1.9e+88)
   (* d1 (- d2 d1))
   (if (<= d1 3900.0) (* d1 (+ d2 (- d4 d3))) (* d1 (- d4 (+ d1 d3))))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d1 <= -1.9e+88) {
		tmp = d1 * (d2 - d1);
	} else if (d1 <= 3900.0) {
		tmp = d1 * (d2 + (d4 - 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 (d1 <= (-1.9d+88)) then
        tmp = d1 * (d2 - d1)
    else if (d1 <= 3900.0d0) then
        tmp = d1 * (d2 + (d4 - 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 (d1 <= -1.9e+88) {
		tmp = d1 * (d2 - d1);
	} else if (d1 <= 3900.0) {
		tmp = d1 * (d2 + (d4 - d3));
	} else {
		tmp = d1 * (d4 - (d1 + d3));
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d1 <= -1.9e+88:
		tmp = d1 * (d2 - d1)
	elif d1 <= 3900.0:
		tmp = d1 * (d2 + (d4 - d3))
	else:
		tmp = d1 * (d4 - (d1 + d3))
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d1 <= -1.9e+88)
		tmp = Float64(d1 * Float64(d2 - d1));
	elseif (d1 <= 3900.0)
		tmp = Float64(d1 * Float64(d2 + Float64(d4 - 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 (d1 <= -1.9e+88)
		tmp = d1 * (d2 - d1);
	elseif (d1 <= 3900.0)
		tmp = d1 * (d2 + (d4 - d3));
	else
		tmp = d1 * (d4 - (d1 + d3));
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d1, -1.9e+88], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d1, 3900.0], N[(d1 * N[(d2 + N[(d4 - d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - N[(d1 + d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d1 < -1.8999999999999998e88

   1. Initial program 72.7%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around inf

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

   7. Simplified 86.5%

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

   if -1.8999999999999998e88 < d1 < 3900

   1. Initial program 100.0%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d3 - d4\right)}\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 98.6%

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

   7. Simplified 98.6%

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

   if 3900 < d1

   1. Initial program 75.0%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + \left(d3 - d4\right)\right)\right)} \]
   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 92.4%

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

   7. Simplified 92.4%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d1 \leq -1.9 \cdot 10^{+88}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d1 \leq 3900:\\ \;\;\;\;d1 \cdot \left(d2 + \left(d4 - d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d1 \leq -4.6 \cdot 10^{+88}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d1 \leq 3.6 \cdot 10^{+109}:\\ \;\;\;\;d1 \cdot \left(d2 + \left(d4 - d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d1 -4.6e+88)
   (* d1 (- d2 d1))
   (if (<= d1 3.6e+109) (* d1 (+ d2 (- d4 d3))) (* d1 (- d4 d1)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d1 <= -4.6e+88) {
		tmp = d1 * (d2 - d1);
	} else if (d1 <= 3.6e+109) {
		tmp = d1 * (d2 + (d4 - d3));
	} else {
		tmp = d1 * (d4 - d1);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d1 <= (-4.6d+88)) then
        tmp = d1 * (d2 - d1)
    else if (d1 <= 3.6d+109) then
        tmp = d1 * (d2 + (d4 - d3))
    else
        tmp = d1 * (d4 - d1)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d1 <= -4.6e+88) {
		tmp = d1 * (d2 - d1);
	} else if (d1 <= 3.6e+109) {
		tmp = d1 * (d2 + (d4 - d3));
	} else {
		tmp = d1 * (d4 - d1);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d1 <= -4.6e+88:
		tmp = d1 * (d2 - d1)
	elif d1 <= 3.6e+109:
		tmp = d1 * (d2 + (d4 - d3))
	else:
		tmp = d1 * (d4 - d1)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d1 <= -4.6e+88)
		tmp = Float64(d1 * Float64(d2 - d1));
	elseif (d1 <= 3.6e+109)
		tmp = Float64(d1 * Float64(d2 + Float64(d4 - d3)));
	else
		tmp = Float64(d1 * Float64(d4 - d1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d1 <= -4.6e+88)
		tmp = d1 * (d2 - d1);
	elseif (d1 <= 3.6e+109)
		tmp = d1 * (d2 + (d4 - d3));
	else
		tmp = d1 * (d4 - d1);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d1, -4.6e+88], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d1, 3.6e+109], N[(d1 * N[(d2 + N[(d4 - d3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d1 < -4.6000000000000003e88

   1. Initial program 72.7%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around inf

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

   7. Simplified 86.5%

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

   if -4.6000000000000003e88 < d1 < 3.6e109

   1. Initial program 100.0%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d3 - d4\right)}\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 96.4%

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

   7. Simplified 96.4%

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

   if 3.6e109 < d1

   1. Initial program 65.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around inf

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

      1. *-lowering-*.f64 75.9%

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

   5. Simplified 75.9%

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 86.2%

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

   7. Applied egg-rr 86.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d1 \leq -4.6 \cdot 10^{+88}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d1 \leq 3.6 \cdot 10^{+109}:\\ \;\;\;\;d1 \cdot \left(d2 + \left(d4 - d3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d1\right)\\ \mathbf{if}\;d1 \leq -2 \cdot 10^{+68}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d1 \leq 2.1 \cdot 10^{+134}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d1))))
   (if (<= d1 -2e+68) t_0 (if (<= d1 2.1e+134) (* d1 (+ d2 d4)) t_0))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d1);
	double tmp;
	if (d1 <= -2e+68) {
		tmp = t_0;
	} else if (d1 <= 2.1e+134) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = d1 * (d2 - d1)
    if (d1 <= (-2d+68)) then
        tmp = t_0
    else if (d1 <= 2.1d+134) then
        tmp = d1 * (d2 + d4)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d1);
	double tmp;
	if (d1 <= -2e+68) {
		tmp = t_0;
	} else if (d1 <= 2.1e+134) {
		tmp = d1 * (d2 + d4);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d1)
	tmp = 0
	if d1 <= -2e+68:
		tmp = t_0
	elif d1 <= 2.1e+134:
		tmp = d1 * (d2 + d4)
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d1))
	tmp = 0.0
	if (d1 <= -2e+68)
		tmp = t_0;
	elseif (d1 <= 2.1e+134)
		tmp = Float64(d1 * Float64(d2 + d4));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d1);
	tmp = 0.0;
	if (d1 <= -2e+68)
		tmp = t_0;
	elseif (d1 <= 2.1e+134)
		tmp = d1 * (d2 + d4);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d1, -2e+68], t$95$0, If[LessEqual[d1, 2.1e+134], N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d1 < -1.99999999999999991e68 or 2.1000000000000001e134 < d1

   1. Initial program 69.1%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around inf

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

   7. Simplified 84.6%

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

   if -1.99999999999999991e68 < d1 < 2.1000000000000001e134

   1. Initial program 100.0%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d1 around 0

      \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d3 - d4\right)}\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in d3 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + d4\right)} \]
   9. Step-by-step derivation

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

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

      2. +-lowering-+.f64 70.6%

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

   10. Simplified 70.6%

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

Alternative 8: 38.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 3 \cdot 10^{+14}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 3e+14) (* d1 d2) (* d1 d4)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 3e+14) {
		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 (d4 <= 3d+14) 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 (d4 <= 3e+14) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 3e+14:
		tmp = d1 * d2
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 3e+14)
		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 (d4 <= 3e+14)
		tmp = d1 * d2;
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 3e+14], N[(d1 * d2), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 3e14

   1. Initial program 88.7%

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

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d2 around inf

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

      1. *-lowering-*.f64 33.0%

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

   7. Simplified 33.0%

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

   if 3e14 < d4

   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-+l- N/A

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

      7. associate--l- N/A

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

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

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

      9. +-commutative N/A

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

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

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

      11. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in d4 around inf

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

      1. *-lowering-*.f64 62.0%

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

   7. Simplified 62.0%

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

Alternative 9: 56.0% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

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)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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-+l- N/A

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

   7. associate--l- N/A

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

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

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

   9. +-commutative N/A

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

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

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

   11. --lowering--.f64 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in d1 around 0

   \[\leadsto \mathsf{*.f64}\left(d1, \mathsf{\_.f64}\left(d2, \color{blue}{\left(d3 - d4\right)}\right)\right) \]
6. Step-by-step derivation

   1. --lowering--.f64 81.2%

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

7. Simplified 81.2%

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

8. Taylor expanded in d3 around 0

   \[\leadsto \color{blue}{d1 \cdot \left(d2 + d4\right)} \]
9. Step-by-step derivation

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

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

   2. +-lowering-+.f64 59.6%

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

10. Simplified 59.6%

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

Alternative 10: 30.5% 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 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-+l- N/A

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

   7. associate--l- N/A

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

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

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

   9. +-commutative N/A

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

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

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

   11. --lowering--.f64 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in d2 around inf

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

   1. *-lowering-*.f64 29.8%

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

7. Simplified 29.8%

   \[\leadsto \color{blue}{d1 \cdot d2} \]
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 2024164 
(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)))