FastMath dist4

Percentage Accurate: 87.1% → 95.7%

Time: 2.8s

Alternatives: 11

Speedup: 1.3×

• 33.5% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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: 87.1% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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: 95.7% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. lift--.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. fp-cancel-sub-sign-inv N/A

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

   7. mul-1-neg N/A

      \[\leadsto \left(\left(d1 \cdot d2 + \color{blue}{\left(-1 \cdot d1\right)} \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

   8. associate-*r* N/A

      \[\leadsto \left(\left(d1 \cdot d2 + \color{blue}{-1 \cdot \left(d1 \cdot d3\right)}\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

   9. +-commutative N/A

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(d1 \cdot d3\right) + d1 \cdot d2\right)} + d4 \cdot d1\right) - d1 \cdot d1 \]

   10. lift-*.f64 N/A

       \[\leadsto \left(\left(-1 \cdot \left(d1 \cdot d3\right) + d1 \cdot d2\right) + \color{blue}{d4 \cdot d1}\right) - d1 \cdot d1 \]

   11. *-commutative N/A

       \[\leadsto \left(\left(-1 \cdot \left(d1 \cdot d3\right) + d1 \cdot d2\right) + \color{blue}{d1 \cdot d4}\right) - d1 \cdot d1 \]

   12. associate-+r+ N/A

       \[\leadsto \color{blue}{\left(-1 \cdot \left(d1 \cdot d3\right) + \left(d1 \cdot d2 + d1 \cdot d4\right)\right)} - d1 \cdot d1 \]

   13. lift-*.f64 N/A

       \[\leadsto \left(-1 \cdot \left(d1 \cdot d3\right) + \left(d1 \cdot d2 + d1 \cdot d4\right)\right) - \color{blue}{d1 \cdot d1} \]

   14. pow2 N/A

       \[\leadsto \left(-1 \cdot \left(d1 \cdot d3\right) + \left(d1 \cdot d2 + d1 \cdot d4\right)\right) - \color{blue}{{d1}^{2}} \]

   15. +-commutative N/A

       \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 + d1 \cdot d4\right) + -1 \cdot \left(d1 \cdot d3\right)\right)} - {d1}^{2} \]

   16. associate-*r* N/A

       \[\leadsto \left(\left(d1 \cdot d2 + d1 \cdot d4\right) + \color{blue}{\left(-1 \cdot d1\right) \cdot d3}\right) - {d1}^{2} \]

   17. mul-1-neg N/A

       \[\leadsto \left(\left(d1 \cdot d2 + d1 \cdot d4\right) + \color{blue}{\left(\mathsf{neg}\left(d1\right)\right)} \cdot d3\right) - {d1}^{2} \]

   18. fp-cancel-sub-sign-inv N/A

       \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 + d1 \cdot d4\right) - d1 \cdot d3\right)} - {d1}^{2} \]

   19. associate--r+ N/A

       \[\leadsto \color{blue}{\left(d1 \cdot d2 + d1 \cdot d4\right) - \left(d1 \cdot d3 + {d1}^{2}\right)} \]

   20. associate--l+ N/A

       \[\leadsto \color{blue}{d1 \cdot d2 + \left(d1 \cdot d4 - \left(d1 \cdot d3 + {d1}^{2}\right)\right)} \]

3. Applied rewrites 95.7%

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

Alternative 2: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \leq -1 \cdot 10^{+112}:\\ \;\;\;\;\left(d2 \cdot d1 + d4 \cdot d1\right) - d1 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(d4 + d2\right) - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)) -1e+112)
   (- (+ (* d2 d1) (* d4 d1)) (* d1 d1))
   (* (- (+ d4 d2) d3) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (((((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= -1e+112) {
		tmp = ((d2 * d1) + (d4 * d1)) - (d1 * d1);
	} else {
		tmp = ((d4 + d2) - d3) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= (-1d+112)) then
        tmp = ((d2 * d1) + (d4 * d1)) - (d1 * d1)
    else
        tmp = ((d4 + d2) - d3) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (((((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= -1e+112) {
		tmp = ((d2 * d1) + (d4 * d1)) - (d1 * d1);
	} else {
		tmp = ((d4 + d2) - d3) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if ((((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= -1e+112:
		tmp = ((d2 * d1) + (d4 * d1)) - (d1 * d1)
	else:
		tmp = ((d4 + d2) - d3) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1)) <= -1e+112)
		tmp = Float64(Float64(Float64(d2 * d1) + Float64(d4 * d1)) - Float64(d1 * d1));
	else
		tmp = Float64(Float64(Float64(d4 + d2) - d3) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (((((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= -1e+112)
		tmp = ((d2 * d1) + (d4 * d1)) - (d1 * d1);
	else
		tmp = ((d4 + d2) - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision], -1e+112], N[(N[(N[(d2 * d1), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(d4 + d2), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1)) (*.f64 d1 d1)) < -9.9999999999999993e111

   1. Initial program 100.0%

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

   2. Taylor expanded in d2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 86.0

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

   4. Applied rewrites 86.0%

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

   if -9.9999999999999993e111 < (-.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1)) (*.f64 d1 d1))

   1. Initial program 80.8%

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

   2. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 87.0

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

   4. Applied rewrites 87.0%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \leq -1 \cdot 10^{+161}:\\ \;\;\;\;d2 \cdot d1 - d1 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(d4 + d2\right) - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)) -1e+161)
   (- (* d2 d1) (* d1 d1))
   (* (- (+ d4 d2) d3) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (((((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= -1e+161) {
		tmp = (d2 * d1) - (d1 * d1);
	} else {
		tmp = ((d4 + d2) - d3) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= (-1d+161)) then
        tmp = (d2 * d1) - (d1 * d1)
    else
        tmp = ((d4 + d2) - d3) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (((((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= -1e+161) {
		tmp = (d2 * d1) - (d1 * d1);
	} else {
		tmp = ((d4 + d2) - d3) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if ((((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= -1e+161:
		tmp = (d2 * d1) - (d1 * d1)
	else:
		tmp = ((d4 + d2) - d3) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1)) <= -1e+161)
		tmp = Float64(Float64(d2 * d1) - Float64(d1 * d1));
	else
		tmp = Float64(Float64(Float64(d4 + d2) - d3) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (((((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= -1e+161)
		tmp = (d2 * d1) - (d1 * d1);
	else
		tmp = ((d4 + d2) - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision], -1e+161], N[(N[(d2 * d1), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(d4 + d2), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1)) (*.f64 d1 d1)) < -1e161

   1. Initial program 100.0%

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

   2. Taylor expanded in d2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.7

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

   4. Applied rewrites 74.7%

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

   if -1e161 < (-.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1)) (*.f64 d1 d1))

   1. Initial program 81.9%

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

   2. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 86.4

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

   4. Applied rewrites 86.4%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 65.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-d3\right) \cdot d1\\ t_1 := \left(d4 + d2\right) \cdot d1\\ \mathbf{if}\;d3 \leq -1.05 \cdot 10^{+166}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq -9 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;d3 \leq -1.9 \cdot 10^{-304}:\\ \;\;\;\;\left(-d1\right) \cdot d1\\ \mathbf{elif}\;d3 \leq 8.8 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* (- d3) d1)) (t_1 (* (+ d4 d2) d1)))
   (if (<= d3 -1.05e+166)
     t_0
     (if (<= d3 -9e-221)
       t_1
       (if (<= d3 -1.9e-304) (* (- d1) d1) (if (<= d3 8.8e+82) t_1 t_0))))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = -d3 * d1;
	double t_1 = (d4 + d2) * d1;
	double tmp;
	if (d3 <= -1.05e+166) {
		tmp = t_0;
	} else if (d3 <= -9e-221) {
		tmp = t_1;
	} else if (d3 <= -1.9e-304) {
		tmp = -d1 * d1;
	} else if (d3 <= 8.8e+82) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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 = -d3 * d1
    t_1 = (d4 + d2) * d1
    if (d3 <= (-1.05d+166)) then
        tmp = t_0
    else if (d3 <= (-9d-221)) then
        tmp = t_1
    else if (d3 <= (-1.9d-304)) then
        tmp = -d1 * d1
    else if (d3 <= 8.8d+82) 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 = -d3 * d1;
	double t_1 = (d4 + d2) * d1;
	double tmp;
	if (d3 <= -1.05e+166) {
		tmp = t_0;
	} else if (d3 <= -9e-221) {
		tmp = t_1;
	} else if (d3 <= -1.9e-304) {
		tmp = -d1 * d1;
	} else if (d3 <= 8.8e+82) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = -d3 * d1
	t_1 = (d4 + d2) * d1
	tmp = 0
	if d3 <= -1.05e+166:
		tmp = t_0
	elif d3 <= -9e-221:
		tmp = t_1
	elif d3 <= -1.9e-304:
		tmp = -d1 * d1
	elif d3 <= 8.8e+82:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(Float64(-d3) * d1)
	t_1 = Float64(Float64(d4 + d2) * d1)
	tmp = 0.0
	if (d3 <= -1.05e+166)
		tmp = t_0;
	elseif (d3 <= -9e-221)
		tmp = t_1;
	elseif (d3 <= -1.9e-304)
		tmp = Float64(Float64(-d1) * d1);
	elseif (d3 <= 8.8e+82)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = -d3 * d1;
	t_1 = (d4 + d2) * d1;
	tmp = 0.0;
	if (d3 <= -1.05e+166)
		tmp = t_0;
	elseif (d3 <= -9e-221)
		tmp = t_1;
	elseif (d3 <= -1.9e-304)
		tmp = -d1 * d1;
	elseif (d3 <= 8.8e+82)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[((-d3) * d1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(d4 + d2), $MachinePrecision] * d1), $MachinePrecision]}, If[LessEqual[d3, -1.05e+166], t$95$0, If[LessEqual[d3, -9e-221], t$95$1, If[LessEqual[d3, -1.9e-304], N[((-d1) * d1), $MachinePrecision], If[LessEqual[d3, 8.8e+82], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -1.05e166 or 8.8000000000000005e82 < d3

   1. Initial program 80.7%

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

   2. Taylor expanded in d3 around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot d3\right) \cdot d1 \]

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 70.0

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

   4. Applied rewrites 70.0%

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

   if -1.05e166 < d3 < -9.00000000000000052e-221 or -1.8999999999999998e-304 < d3 < 8.8000000000000005e82

   1. Initial program 89.4%

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

   2. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 75.2

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

   4. Applied rewrites 75.2%

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

   5. Taylor expanded in d3 around 0

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

      1. +-commutative N/A

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

      2. lift-+.f64 65.4

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

   7. Applied rewrites 65.4%

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

   if -9.00000000000000052e-221 < d3 < -1.8999999999999998e-304

   1. Initial program 92.7%

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

   2. Taylor expanded in d1 around inf

      \[\leadsto \color{blue}{-1 \cdot {d1}^{2}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({d1}^{2}\right) \]

      2. pow2 N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot d1\right) \cdot d1 \]

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 41.7

         \[\leadsto \left(-d1\right) \cdot d1 \]

   4. Applied rewrites 41.7%

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

Alternative 5: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -6.5 \cdot 10^{+142}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{elif}\;d2 \leq -3.35 \cdot 10^{-32}:\\ \;\;\;\;\left(-d3\right) \cdot d1\\ \mathbf{elif}\;d2 \leq 6.7 \cdot 10^{-140}:\\ \;\;\;\;\left(-d1\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -6.5e+142)
   (* d2 d1)
   (if (<= d2 -3.35e-32)
     (* (- d3) d1)
     (if (<= d2 6.7e-140) (* (- d1) d1) (* d4 d1)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -6.5e+142) {
		tmp = d2 * d1;
	} else if (d2 <= -3.35e-32) {
		tmp = -d3 * d1;
	} else if (d2 <= 6.7e-140) {
		tmp = -d1 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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 <= (-6.5d+142)) then
        tmp = d2 * d1
    else if (d2 <= (-3.35d-32)) then
        tmp = -d3 * d1
    else if (d2 <= 6.7d-140) then
        tmp = -d1 * d1
    else
        tmp = d4 * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -6.5e+142) {
		tmp = d2 * d1;
	} else if (d2 <= -3.35e-32) {
		tmp = -d3 * d1;
	} else if (d2 <= 6.7e-140) {
		tmp = -d1 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -6.5e+142:
		tmp = d2 * d1
	elif d2 <= -3.35e-32:
		tmp = -d3 * d1
	elif d2 <= 6.7e-140:
		tmp = -d1 * d1
	else:
		tmp = d4 * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -6.5e+142)
		tmp = Float64(d2 * d1);
	elseif (d2 <= -3.35e-32)
		tmp = Float64(Float64(-d3) * d1);
	elseif (d2 <= 6.7e-140)
		tmp = Float64(Float64(-d1) * d1);
	else
		tmp = Float64(d4 * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -6.5e+142)
		tmp = d2 * d1;
	elseif (d2 <= -3.35e-32)
		tmp = -d3 * d1;
	elseif (d2 <= 6.7e-140)
		tmp = -d1 * d1;
	else
		tmp = d4 * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -6.5e+142], N[(d2 * d1), $MachinePrecision], If[LessEqual[d2, -3.35e-32], N[((-d3) * d1), $MachinePrecision], If[LessEqual[d2, 6.7e-140], N[((-d1) * d1), $MachinePrecision], N[(d4 * d1), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if d2 < -6.4999999999999997e142

   1. Initial program 82.4%

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

   2. Taylor expanded in d2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 73.0

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

   4. Applied rewrites 73.0%

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

   if -6.4999999999999997e142 < d2 < -3.35e-32

   1. Initial program 88.3%

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

   2. Taylor expanded in d3 around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot d3\right) \cdot d1 \]

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 30.5

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

   4. Applied rewrites 30.5%

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

   if -3.35e-32 < d2 < 6.7e-140

   1. Initial program 89.8%

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

   2. Taylor expanded in d1 around inf

      \[\leadsto \color{blue}{-1 \cdot {d1}^{2}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({d1}^{2}\right) \]

      2. pow2 N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot d1\right) \cdot d1 \]

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 40.2

         \[\leadsto \left(-d1\right) \cdot d1 \]

   4. Applied rewrites 40.2%

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

   if 6.7e-140 < d2

   1. Initial program 85.6%

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

   2. Taylor expanded in d4 around inf

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

      1. *-commutative N/A

         \[\leadsto d4 \cdot \color{blue}{d1} \]

      2. lift-*.f64 27.3

         \[\leadsto d4 \cdot \color{blue}{d1} \]

   4. Applied rewrites 27.3%

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

Alternative 6: 85.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-d1\right) \cdot d1\\ \mathbf{if}\;d1 \leq -1.46 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(d2, d1, t\_0\right)\\ \mathbf{elif}\;d1 \leq 4.4 \cdot 10^{+264}:\\ \;\;\;\;\left(\left(d4 + d2\right) - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* (- d1) d1)))
   (if (<= d1 -1.46e+91)
     (fma d2 d1 t_0)
     (if (<= d1 4.4e+264) (* (- (+ d4 d2) d3) d1) t_0))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = -d1 * d1;
	double tmp;
	if (d1 <= -1.46e+91) {
		tmp = fma(d2, d1, t_0);
	} else if (d1 <= 4.4e+264) {
		tmp = ((d4 + d2) - d3) * d1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(Float64(-d1) * d1)
	tmp = 0.0
	if (d1 <= -1.46e+91)
		tmp = fma(d2, d1, t_0);
	elseif (d1 <= 4.4e+264)
		tmp = Float64(Float64(Float64(d4 + d2) - d3) * d1);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[((-d1) * d1), $MachinePrecision]}, If[LessEqual[d1, -1.46e+91], N[(d2 * d1 + t$95$0), $MachinePrecision], If[LessEqual[d1, 4.4e+264], N[(N[(N[(d4 + d2), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if d1 < -1.45999999999999999e91

   1. Initial program 64.5%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. mul-1-neg N/A

         \[\leadsto \left(\left(d1 \cdot d2 + \color{blue}{\left(-1 \cdot d1\right)} \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      8. associate-*r* N/A

         \[\leadsto \left(\left(d1 \cdot d2 + \color{blue}{-1 \cdot \left(d1 \cdot d3\right)}\right) + d4 \cdot d1\right) - d1 \cdot d1 \]

      9. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(d1 \cdot d3\right) + d1 \cdot d2\right)} + d4 \cdot d1\right) - d1 \cdot d1 \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(-1 \cdot \left(d1 \cdot d3\right) + d1 \cdot d2\right) + \color{blue}{d4 \cdot d1}\right) - d1 \cdot d1 \]

      11. *-commutative N/A

          \[\leadsto \left(\left(-1 \cdot \left(d1 \cdot d3\right) + d1 \cdot d2\right) + \color{blue}{d1 \cdot d4}\right) - d1 \cdot d1 \]

      12. associate-+r+ N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(d1 \cdot d3\right) + \left(d1 \cdot d2 + d1 \cdot d4\right)\right)} - d1 \cdot d1 \]

      13. lift-*.f64 N/A

          \[\leadsto \left(-1 \cdot \left(d1 \cdot d3\right) + \left(d1 \cdot d2 + d1 \cdot d4\right)\right) - \color{blue}{d1 \cdot d1} \]

      14. pow2 N/A

          \[\leadsto \left(-1 \cdot \left(d1 \cdot d3\right) + \left(d1 \cdot d2 + d1 \cdot d4\right)\right) - \color{blue}{{d1}^{2}} \]

      15. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 + d1 \cdot d4\right) + -1 \cdot \left(d1 \cdot d3\right)\right)} - {d1}^{2} \]

      16. associate-*r* N/A

          \[\leadsto \left(\left(d1 \cdot d2 + d1 \cdot d4\right) + \color{blue}{\left(-1 \cdot d1\right) \cdot d3}\right) - {d1}^{2} \]

      17. mul-1-neg N/A

          \[\leadsto \left(\left(d1 \cdot d2 + d1 \cdot d4\right) + \color{blue}{\left(\mathsf{neg}\left(d1\right)\right)} \cdot d3\right) - {d1}^{2} \]

      18. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 + d1 \cdot d4\right) - d1 \cdot d3\right)} - {d1}^{2} \]

      19. associate--r+ N/A

          \[\leadsto \color{blue}{\left(d1 \cdot d2 + d1 \cdot d4\right) - \left(d1 \cdot d3 + {d1}^{2}\right)} \]

      20. associate--l+ N/A

          \[\leadsto \color{blue}{d1 \cdot d2 + \left(d1 \cdot d4 - \left(d1 \cdot d3 + {d1}^{2}\right)\right)} \]

   3. Applied rewrites 87.7%

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

   4. Taylor expanded in d1 around inf

      \[\leadsto \mathsf{fma}\left(d2, d1, \color{blue}{-1 \cdot {d1}^{2}}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(d2, d1, \mathsf{neg}\left({d1}^{2}\right)\right) \]

      2. pow2 N/A

         \[\leadsto \mathsf{fma}\left(d2, d1, \mathsf{neg}\left(d1 \cdot d1\right)\right) \]

      3. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(d2, d1, \left(\mathsf{neg}\left(d1\right)\right) \cdot \color{blue}{d1}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(d2, d1, \left(\mathsf{neg}\left(d1\right)\right) \cdot \color{blue}{d1}\right) \]

      5. lift-neg.f64 77.3

         \[\leadsto \mathsf{fma}\left(d2, d1, \left(-d1\right) \cdot d1\right) \]

   6. Applied rewrites 77.3%

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

   if -1.45999999999999999e91 < d1 < 4.4e264

   1. Initial program 94.3%

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

   2. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 86.9

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

   4. Applied rewrites 86.9%

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

   if 4.4e264 < d1

   1. Initial program 39.4%

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

   2. Taylor expanded in d1 around inf

      \[\leadsto \color{blue}{-1 \cdot {d1}^{2}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({d1}^{2}\right) \]

      2. pow2 N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot d1\right) \cdot d1 \]

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 92.4

         \[\leadsto \left(-d1\right) \cdot d1 \]

   4. Applied rewrites 92.4%

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

Alternative 7: 84.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-d1\right) \cdot d1\\ \mathbf{if}\;d1 \leq -2.05 \cdot 10^{+195}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d1 \leq 4.4 \cdot 10^{+264}:\\ \;\;\;\;\left(\left(d4 + d2\right) - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* (- d1) d1)))
   (if (<= d1 -2.05e+195)
     t_0
     (if (<= d1 4.4e+264) (* (- (+ d4 d2) d3) d1) t_0))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = -d1 * d1;
	double tmp;
	if (d1 <= -2.05e+195) {
		tmp = t_0;
	} else if (d1 <= 4.4e+264) {
		tmp = ((d4 + d2) - d3) * d1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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 * d1
    if (d1 <= (-2.05d+195)) then
        tmp = t_0
    else if (d1 <= 4.4d+264) then
        tmp = ((d4 + d2) - d3) * d1
    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 * d1;
	double tmp;
	if (d1 <= -2.05e+195) {
		tmp = t_0;
	} else if (d1 <= 4.4e+264) {
		tmp = ((d4 + d2) - d3) * d1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = -d1 * d1
	tmp = 0
	if d1 <= -2.05e+195:
		tmp = t_0
	elif d1 <= 4.4e+264:
		tmp = ((d4 + d2) - d3) * d1
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(Float64(-d1) * d1)
	tmp = 0.0
	if (d1 <= -2.05e+195)
		tmp = t_0;
	elseif (d1 <= 4.4e+264)
		tmp = Float64(Float64(Float64(d4 + d2) - d3) * d1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = -d1 * d1;
	tmp = 0.0;
	if (d1 <= -2.05e+195)
		tmp = t_0;
	elseif (d1 <= 4.4e+264)
		tmp = ((d4 + d2) - d3) * d1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[((-d1) * d1), $MachinePrecision]}, If[LessEqual[d1, -2.05e+195], t$95$0, If[LessEqual[d1, 4.4e+264], N[(N[(N[(d4 + d2), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d1 < -2.05e195 or 4.4e264 < d1

   1. Initial program 46.4%

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

   2. Taylor expanded in d1 around inf

      \[\leadsto \color{blue}{-1 \cdot {d1}^{2}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({d1}^{2}\right) \]

      2. pow2 N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot d1\right) \cdot d1 \]

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 89.0

         \[\leadsto \left(-d1\right) \cdot d1 \]

   4. Applied rewrites 89.0%

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

   if -2.05e195 < d1 < 4.4e264

   1. Initial program 92.9%

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

   2. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 84.3

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

   4. Applied rewrites 84.3%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 38.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -1.8 \cdot 10^{+139}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{elif}\;d2 \leq 6.7 \cdot 10^{-140}:\\ \;\;\;\;\left(-d1\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -1.8e+139)
   (* d2 d1)
   (if (<= d2 6.7e-140) (* (- d1) d1) (* d4 d1))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.8e+139) {
		tmp = d2 * d1;
	} else if (d2 <= 6.7e-140) {
		tmp = -d1 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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 <= (-1.8d+139)) then
        tmp = d2 * d1
    else if (d2 <= 6.7d-140) then
        tmp = -d1 * d1
    else
        tmp = d4 * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.8e+139) {
		tmp = d2 * d1;
	} else if (d2 <= 6.7e-140) {
		tmp = -d1 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -1.8e+139:
		tmp = d2 * d1
	elif d2 <= 6.7e-140:
		tmp = -d1 * d1
	else:
		tmp = d4 * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -1.8e+139)
		tmp = Float64(d2 * d1);
	elseif (d2 <= 6.7e-140)
		tmp = Float64(Float64(-d1) * d1);
	else
		tmp = Float64(d4 * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -1.8e+139)
		tmp = d2 * d1;
	elseif (d2 <= 6.7e-140)
		tmp = -d1 * d1;
	else
		tmp = d4 * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -1.8e+139], N[(d2 * d1), $MachinePrecision], If[LessEqual[d2, 6.7e-140], N[((-d1) * d1), $MachinePrecision], N[(d4 * d1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -1.79999999999999993e139

   1. Initial program 82.6%

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

   2. Taylor expanded in d2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 72.1

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

   4. Applied rewrites 72.1%

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

   if -1.79999999999999993e139 < d2 < 6.7e-140

   1. Initial program 89.4%

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

   2. Taylor expanded in d1 around inf

      \[\leadsto \color{blue}{-1 \cdot {d1}^{2}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({d1}^{2}\right) \]

      2. pow2 N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot d1\right) \cdot d1 \]

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 37.9

         \[\leadsto \left(-d1\right) \cdot d1 \]

   4. Applied rewrites 37.9%

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

   if 6.7e-140 < d2

   1. Initial program 85.6%

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

   2. Taylor expanded in d4 around inf

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

      1. *-commutative N/A

         \[\leadsto d4 \cdot \color{blue}{d1} \]

      2. lift-*.f64 27.3

         \[\leadsto d4 \cdot \color{blue}{d1} \]

   4. Applied rewrites 27.3%

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

Alternative 9: 63.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 2.1 \cdot 10^{+124}:\\ \;\;\;\;\left(d2 - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 + d2\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 2.1e+124) (* (- d2 d3) d1) (* (+ d4 d2) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 2.1e+124) {
		tmp = (d2 - d3) * d1;
	} else {
		tmp = (d4 + d2) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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 <= 2.1d+124) then
        tmp = (d2 - d3) * d1
    else
        tmp = (d4 + d2) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 2.1e+124) {
		tmp = (d2 - d3) * d1;
	} else {
		tmp = (d4 + d2) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 2.1e+124:
		tmp = (d2 - d3) * d1
	else:
		tmp = (d4 + d2) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 2.1e+124)
		tmp = Float64(Float64(d2 - d3) * d1);
	else
		tmp = Float64(Float64(d4 + d2) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 2.1e+124)
		tmp = (d2 - d3) * d1;
	else
		tmp = (d4 + d2) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 2.1e+124], N[(N[(d2 - d3), $MachinePrecision] * d1), $MachinePrecision], N[(N[(d4 + d2), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 2.10000000000000011e124

   1. Initial program 88.2%

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

   2. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 77.6

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

   4. Applied rewrites 77.6%

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

   5. Taylor expanded in d2 around inf

      \[\leadsto \left(d2 - d3\right) \cdot d1 \]
   6. Step-by-step derivation

   7. Applied rewrites 60.6%

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

   if 2.10000000000000011e124 < d4

   1. Initial program 81.1%

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

   2. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 92.8

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

   4. Applied rewrites 92.8%

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

   5. Taylor expanded in d3 around 0

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

      1. +-commutative N/A

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

      2. lift-+.f64 82.1

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

   7. Applied rewrites 82.1%

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

Alternative 10: 38.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -9.5 \cdot 10^{-15}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -9.5e-15) (* d2 d1) (* d4 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -9.5e-15) {
		tmp = d2 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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 <= (-9.5d-15)) then
        tmp = d2 * d1
    else
        tmp = d4 * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -9.5e-15) {
		tmp = d2 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -9.5e-15:
		tmp = d2 * d1
	else:
		tmp = d4 * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -9.5e-15)
		tmp = Float64(d2 * d1);
	else
		tmp = Float64(d4 * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -9.5e-15)
		tmp = d2 * d1;
	else
		tmp = d4 * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -9.5e-15], N[(d2 * d1), $MachinePrecision], N[(d4 * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -9.5000000000000005e-15

   1. Initial program 85.4%

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

   2. Taylor expanded in d2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 51.9

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

   4. Applied rewrites 51.9%

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

   if -9.5000000000000005e-15 < d2

   1. Initial program 87.7%

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

   2. Taylor expanded in d4 around inf

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

      1. *-commutative N/A

         \[\leadsto d4 \cdot \color{blue}{d1} \]

      2. lift-*.f64 33.3

         \[\leadsto d4 \cdot \color{blue}{d1} \]

   4. Applied rewrites 33.3%

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

Alternative 11: 31.2% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ d2 \cdot d1 \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

2. Taylor expanded in d2 around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 31.2

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

4. Applied rewrites 31.2%

   \[\leadsto \color{blue}{d2 \cdot d1} \]
5. Add Preprocessing

Developer Target 1: 100.0% accurate, 2.0× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(d1, d2, d3, d4)
use fmin_fmax_functions
    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 2025095 
(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)))