Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A

Percentage Accurate: 99.5% → 99.8%

Time: 8.1s

Alternatives: 18

Speedup: 1.1×

• 55.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))

C

double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
}

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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * 0.5d0) - y) * sqrt((z * 2.0d0))) * exp(((t * t) / 2.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * Math.sqrt((z * 2.0))) * Math.exp(((t * t) / 2.0));
}

Python

def code(x, y, z, t):
	return (((x * 0.5) - y) * math.sqrt((z * 2.0))) * math.exp(((t * t) / 2.0))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0))) * exp(Float64(Float64(t * t) / 2.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))

C

double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
}

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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * 0.5d0) - y) * sqrt((z * 2.0d0))) * exp(((t * t) / 2.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * Math.sqrt((z * 2.0))) * Math.exp(((t * t) / 2.0));
}

Python

def code(x, y, z, t):
	return (((x * 0.5) - y) * math.sqrt((z * 2.0))) * math.exp(((t * t) / 2.0))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0))) * exp(Float64(Float64(t * t) / 2.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.6× speedup

Math

\[\left({\left(e^{0.5 \cdot t}\right)}^{t} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (* (* (pow (exp (* 0.5 t)) t) (- (* 0.5 x) y)) (sqrt (+ z z))))

C

double code(double x, double y, double z, double t) {
	return (pow(exp((0.5 * t)), t) * ((0.5 * x) - y)) * sqrt((z + z));
}

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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((exp((0.5d0 * t)) ** t) * ((0.5d0 * x) - y)) * sqrt((z + z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (Math.pow(Math.exp((0.5 * t)), t) * ((0.5 * x) - y)) * Math.sqrt((z + z));
}

Python

def code(x, y, z, t):
	return (math.pow(math.exp((0.5 * t)), t) * ((0.5 * x) - y)) * math.sqrt((z + z))

Julia

function code(x, y, z, t)
	return Float64(Float64((exp(Float64(0.5 * t)) ^ t) * Float64(Float64(0.5 * x) - y)) * sqrt(Float64(z + z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((exp((0.5 * t)) ^ t) * ((0.5 * x) - y)) * sqrt((z + z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[Power[N[Exp[N[(0.5 * t), $MachinePrecision]], $MachinePrecision], t], $MachinePrecision] * N[(N[(0.5 * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{e^{\frac{t \cdot t}{2}} \cdot \left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto e^{\frac{t \cdot t}{2}} \cdot \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

   4. associate-*r* N/A

      \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

   5. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

   6. lower-*.f64 99.8%

      \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot 0.5 - y\right)\right)} \cdot \sqrt{z \cdot 2} \]

   7. lift-/.f64 N/A

      \[\leadsto \left(e^{\color{blue}{\frac{t \cdot t}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   8. mult-flip N/A

      \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot \frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   9. metadata-eval N/A

      \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \color{blue}{\frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   10. lower-*.f64 99.8%

       \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot 0.5}} \cdot \left(x \cdot 0.5 - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   11. lift-*.f64 N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{x \cdot \frac{1}{2}} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   12. *-commutative N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{\frac{1}{2} \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   13. lower-*.f64 99.8%

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(\color{blue}{0.5 \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   14. lift-*.f64 N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z \cdot 2}} \]

   15. *-commutative N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{2 \cdot z}} \]

   16. count-2-rev N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

   17. lower-+.f64 99.8%

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

3. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z}} \]
4. Step-by-step derivation

   1. lift-exp.f64 N/A

      \[\leadsto \left(\color{blue}{e^{\left(t \cdot t\right) \cdot \frac{1}{2}}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   2. lift-*.f64 N/A

      \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot \frac{1}{2}}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   3. lift-*.f64 N/A

      \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right)} \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   4. associate-*l* N/A

      \[\leadsto \left(e^{\color{blue}{t \cdot \left(t \cdot \frac{1}{2}\right)}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   5. lift-*.f64 N/A

      \[\leadsto \left(e^{t \cdot \color{blue}{\left(t \cdot \frac{1}{2}\right)}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   6. *-commutative N/A

      \[\leadsto \left(e^{\color{blue}{\left(t \cdot \frac{1}{2}\right) \cdot t}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   7. exp-prod N/A

      \[\leadsto \left(\color{blue}{{\left(e^{t \cdot \frac{1}{2}}\right)}^{t}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   8. lower-pow.f64 N/A

      \[\leadsto \left(\color{blue}{{\left(e^{t \cdot \frac{1}{2}}\right)}^{t}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   9. lower-exp.f64 99.8%

      \[\leadsto \left({\color{blue}{\left(e^{t \cdot 0.5}\right)}}^{t} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   10. lift-*.f64 N/A

       \[\leadsto \left({\left(e^{\color{blue}{t \cdot \frac{1}{2}}}\right)}^{t} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   11. *-commutative N/A

       \[\leadsto \left({\left(e^{\color{blue}{\frac{1}{2} \cdot t}}\right)}^{t} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   12. lower-*.f64 99.8%

       \[\leadsto \left({\left(e^{\color{blue}{0.5 \cdot t}}\right)}^{t} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

5. Applied rewrites 99.8%

   \[\leadsto \left(\color{blue}{{\left(e^{0.5 \cdot t}\right)}^{t}} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]
6. Add Preprocessing

Alternative 2: 99.8% accurate, 1.1× speedup

Math

\[\left({1.6487212707001282}^{\left(t \cdot t\right)} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (*
 (* (pow 1.6487212707001282 (* t t)) (- (* 0.5 x) y))
 (sqrt (+ z z))))

C

double code(double x, double y, double z, double t) {
	return (pow(1.6487212707001282, (t * t)) * ((0.5 * x) - y)) * sqrt((z + z));
}

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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((1.6487212707001282d0 ** (t * t)) * ((0.5d0 * x) - y)) * sqrt((z + z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (Math.pow(1.6487212707001282, (t * t)) * ((0.5 * x) - y)) * Math.sqrt((z + z));
}

Python

def code(x, y, z, t):
	return (math.pow(1.6487212707001282, (t * t)) * ((0.5 * x) - y)) * math.sqrt((z + z))

Julia

function code(x, y, z, t)
	return Float64(Float64((1.6487212707001282 ^ Float64(t * t)) * Float64(Float64(0.5 * x) - y)) * sqrt(Float64(z + z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((1.6487212707001282 ^ (t * t)) * ((0.5 * x) - y)) * sqrt((z + z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[Power[1.6487212707001282, N[(t * t), $MachinePrecision]], $MachinePrecision] * N[(N[(0.5 * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{e^{\frac{t \cdot t}{2}} \cdot \left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto e^{\frac{t \cdot t}{2}} \cdot \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

   4. associate-*r* N/A

      \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

   5. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

   6. lower-*.f64 99.8%

      \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot 0.5 - y\right)\right)} \cdot \sqrt{z \cdot 2} \]

   7. lift-/.f64 N/A

      \[\leadsto \left(e^{\color{blue}{\frac{t \cdot t}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   8. mult-flip N/A

      \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot \frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   9. metadata-eval N/A

      \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \color{blue}{\frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   10. lower-*.f64 99.8%

       \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot 0.5}} \cdot \left(x \cdot 0.5 - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   11. lift-*.f64 N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{x \cdot \frac{1}{2}} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   12. *-commutative N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{\frac{1}{2} \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   13. lower-*.f64 99.8%

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(\color{blue}{0.5 \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

   14. lift-*.f64 N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z \cdot 2}} \]

   15. *-commutative N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{2 \cdot z}} \]

   16. count-2-rev N/A

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

   17. lower-+.f64 99.8%

       \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

3. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z}} \]
4. Step-by-step derivation

   1. lift-exp.f64 N/A

      \[\leadsto \left(\color{blue}{e^{\left(t \cdot t\right) \cdot \frac{1}{2}}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   2. lift-*.f64 N/A

      \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot \frac{1}{2}}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   3. lift-*.f64 N/A

      \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right)} \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   4. associate-*l* N/A

      \[\leadsto \left(e^{\color{blue}{t \cdot \left(t \cdot \frac{1}{2}\right)}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   5. lift-*.f64 N/A

      \[\leadsto \left(e^{t \cdot \color{blue}{\left(t \cdot \frac{1}{2}\right)}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   6. *-commutative N/A

      \[\leadsto \left(e^{\color{blue}{\left(t \cdot \frac{1}{2}\right) \cdot t}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   7. exp-prod N/A

      \[\leadsto \left(\color{blue}{{\left(e^{t \cdot \frac{1}{2}}\right)}^{t}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   8. lower-pow.f64 N/A

      \[\leadsto \left(\color{blue}{{\left(e^{t \cdot \frac{1}{2}}\right)}^{t}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   9. lower-exp.f64 99.8%

      \[\leadsto \left({\color{blue}{\left(e^{t \cdot 0.5}\right)}}^{t} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   10. lift-*.f64 N/A

       \[\leadsto \left({\left(e^{\color{blue}{t \cdot \frac{1}{2}}}\right)}^{t} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   11. *-commutative N/A

       \[\leadsto \left({\left(e^{\color{blue}{\frac{1}{2} \cdot t}}\right)}^{t} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   12. lower-*.f64 99.8%

       \[\leadsto \left({\left(e^{\color{blue}{0.5 \cdot t}}\right)}^{t} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

5. Applied rewrites 99.8%

   \[\leadsto \left(\color{blue}{{\left(e^{0.5 \cdot t}\right)}^{t}} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]
6. Step-by-step derivation

   1. lift-pow.f64 N/A

      \[\leadsto \left(\color{blue}{{\left(e^{\frac{1}{2} \cdot t}\right)}^{t}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   2. lift-exp.f64 N/A

      \[\leadsto \left({\color{blue}{\left(e^{\frac{1}{2} \cdot t}\right)}}^{t} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   3. pow-exp N/A

      \[\leadsto \left(\color{blue}{e^{\left(\frac{1}{2} \cdot t\right) \cdot t}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   4. lift-*.f64 N/A

      \[\leadsto \left(e^{\color{blue}{\left(\frac{1}{2} \cdot t\right)} \cdot t} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   5. associate-*l* N/A

      \[\leadsto \left(e^{\color{blue}{\frac{1}{2} \cdot \left(t \cdot t\right)}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   6. lift-*.f64 N/A

      \[\leadsto \left(e^{\frac{1}{2} \cdot \color{blue}{\left(t \cdot t\right)}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   7. exp-prod N/A

      \[\leadsto \left(\color{blue}{{\left(e^{\frac{1}{2}}\right)}^{\left(t \cdot t\right)}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   8. lower-pow.f64 N/A

      \[\leadsto \left(\color{blue}{{\left(e^{\frac{1}{2}}\right)}^{\left(t \cdot t\right)}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   9. metadata-eval N/A

      \[\leadsto \left({\left(e^{\color{blue}{\frac{1}{2}}}\right)}^{\left(t \cdot t\right)} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   10. exp-sqrt N/A

       \[\leadsto \left({\color{blue}{\left(\sqrt{e^{1}}\right)}}^{\left(t \cdot t\right)} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   11. lower-sqrt.f64 N/A

       \[\leadsto \left({\color{blue}{\left(\sqrt{e^{1}}\right)}}^{\left(t \cdot t\right)} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   12. exp-1-e N/A

       \[\leadsto \left({\left(\sqrt{\color{blue}{\mathsf{E}\left(\right)}}\right)}^{\left(t \cdot t\right)} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

   13. lower-E.f64 99.8%

       \[\leadsto \left({\left(\sqrt{\color{blue}{e}}\right)}^{\left(t \cdot t\right)} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

7. Applied rewrites 99.8%

   \[\leadsto \left(\color{blue}{{\left(\sqrt{e}\right)}^{\left(t \cdot t\right)}} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]

8. Evaluated real constant 99.8%

   \[\leadsto \left({\color{blue}{1.6487212707001282}}^{\left(t \cdot t\right)} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z} \]
9. Add Preprocessing

Alternative 3: 99.8% accurate, 1.1× speedup

Math

\[\left(0.5 \cdot x - y\right) \cdot \sqrt{e^{t \cdot t} \cdot \left(z + z\right)} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (* (- (* 0.5 x) y) (sqrt (* (exp (* t t)) (+ z z)))))

C

double code(double x, double y, double z, double t) {
	return ((0.5 * x) - y) * sqrt((exp((t * t)) * (z + z)));
}

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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((0.5d0 * x) - y) * sqrt((exp((t * t)) * (z + z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((0.5 * x) - y) * Math.sqrt((Math.exp((t * t)) * (z + z)));
}

Python

def code(x, y, z, t):
	return ((0.5 * x) - y) * math.sqrt((math.exp((t * t)) * (z + z)))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(0.5 * x) - y) * sqrt(Float64(exp(Float64(t * t)) * Float64(z + z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((0.5 * x) - y) * sqrt((exp((t * t)) * (z + z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(0.5 * x), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(N[Exp[N[(t * t), $MachinePrecision]], $MachinePrecision] * N[(z + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}} \]

   2. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot e^{\frac{t \cdot t}{2}} \]

   3. associate-*l* N/A

      \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)} \]

   4. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)} \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right) \]

   7. lower-*.f64 N/A

      \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right) \]

   8. lift-sqrt.f64 N/A

      \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \left(\color{blue}{\sqrt{z \cdot 2}} \cdot e^{\frac{t \cdot t}{2}}\right) \]

   9. lift-exp.f64 N/A

      \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \color{blue}{e^{\frac{t \cdot t}{2}}}\right) \]

   10. lift-/.f64 N/A

       \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\color{blue}{\frac{t \cdot t}{2}}}\right) \]

   11. exp-sqrt N/A

       \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \color{blue}{\sqrt{e^{t \cdot t}}}\right) \]

   12. sqrt-unprod N/A

       \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \color{blue}{\sqrt{\left(z \cdot 2\right) \cdot e^{t \cdot t}}} \]

   13. lower-sqrt.f64 N/A

       \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \color{blue}{\sqrt{\left(z \cdot 2\right) \cdot e^{t \cdot t}}} \]

   14. *-commutative N/A

       \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \sqrt{\color{blue}{e^{t \cdot t} \cdot \left(z \cdot 2\right)}} \]

   15. lower-*.f64 N/A

       \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \sqrt{\color{blue}{e^{t \cdot t} \cdot \left(z \cdot 2\right)}} \]

   16. lower-exp.f64 99.8%

       \[\leadsto \left(0.5 \cdot x - y\right) \cdot \sqrt{\color{blue}{e^{t \cdot t}} \cdot \left(z \cdot 2\right)} \]

   17. lift-*.f64 N/A

       \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \sqrt{e^{t \cdot t} \cdot \color{blue}{\left(z \cdot 2\right)}} \]

   18. *-commutative N/A

       \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \sqrt{e^{t \cdot t} \cdot \color{blue}{\left(2 \cdot z\right)}} \]

   19. count-2-rev N/A

       \[\leadsto \left(\frac{1}{2} \cdot x - y\right) \cdot \sqrt{e^{t \cdot t} \cdot \color{blue}{\left(z + z\right)}} \]

   20. lower-+.f64 99.8%

       \[\leadsto \left(0.5 \cdot x - y\right) \cdot \sqrt{e^{t \cdot t} \cdot \color{blue}{\left(z + z\right)}} \]

3. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\left(0.5 \cdot x - y\right) \cdot \sqrt{e^{t \cdot t} \cdot \left(z + z\right)}} \]
4. Add Preprocessing

Alternative 4: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \sqrt{z + z}\\ \mathbf{if}\;\left|t\right| \leq 1.45 \cdot 10^{-12}:\\ \;\;\;\;\left(x \cdot 0.5 - y\right) \cdot \left(t\_1 \cdot 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(e^{\left(\left|t\right| \cdot \left|t\right|\right) \cdot 0.5} \cdot \left(-y\right)\right) \cdot t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (sqrt (+ z z))))
  (if (<= (fabs t) 1.45e-12)
    (* (- (* x 0.5) y) (* t_1 1.0))
    (* (* (exp (* (* (fabs t) (fabs t)) 0.5)) (- y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z + z));
	double tmp;
	if (fabs(t) <= 1.45e-12) {
		tmp = ((x * 0.5) - y) * (t_1 * 1.0);
	} else {
		tmp = (exp(((fabs(t) * fabs(t)) * 0.5)) * -y) * t_1;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt((z + z))
    if (abs(t) <= 1.45d-12) then
        tmp = ((x * 0.5d0) - y) * (t_1 * 1.0d0)
    else
        tmp = (exp(((abs(t) * abs(t)) * 0.5d0)) * -y) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z + z));
	double tmp;
	if (Math.abs(t) <= 1.45e-12) {
		tmp = ((x * 0.5) - y) * (t_1 * 1.0);
	} else {
		tmp = (Math.exp(((Math.abs(t) * Math.abs(t)) * 0.5)) * -y) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z + z))
	tmp = 0
	if math.fabs(t) <= 1.45e-12:
		tmp = ((x * 0.5) - y) * (t_1 * 1.0)
	else:
		tmp = (math.exp(((math.fabs(t) * math.fabs(t)) * 0.5)) * -y) * t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z + z))
	tmp = 0.0
	if (abs(t) <= 1.45e-12)
		tmp = Float64(Float64(Float64(x * 0.5) - y) * Float64(t_1 * 1.0));
	else
		tmp = Float64(Float64(exp(Float64(Float64(abs(t) * abs(t)) * 0.5)) * Float64(-y)) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z + z));
	tmp = 0.0;
	if (abs(t) <= 1.45e-12)
		tmp = ((x * 0.5) - y) * (t_1 * 1.0);
	else
		tmp = (exp(((abs(t) * abs(t)) * 0.5)) * -y) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Abs[t], $MachinePrecision], 1.45e-12], N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[(t$95$1 * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[Exp[N[(N[(N[Abs[t], $MachinePrecision] * N[Abs[t], $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * (-y)), $MachinePrecision] * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 1.4500000000000001e-12

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 1.4500000000000001e-12 < t

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{e^{\frac{t \cdot t}{2}} \cdot \left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto e^{\frac{t \cdot t}{2}} \cdot \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

      6. lower-*.f64 99.8%

         \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot 0.5 - y\right)\right)} \cdot \sqrt{z \cdot 2} \]

      7. lift-/.f64 N/A

         \[\leadsto \left(e^{\color{blue}{\frac{t \cdot t}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      8. mult-flip N/A

         \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot \frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      9. metadata-eval N/A

         \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \color{blue}{\frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      10. lower-*.f64 99.8%

          \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot 0.5}} \cdot \left(x \cdot 0.5 - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{x \cdot \frac{1}{2}} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      12. *-commutative N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{\frac{1}{2} \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      13. lower-*.f64 99.8%

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(\color{blue}{0.5 \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      14. lift-*.f64 N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z \cdot 2}} \]

      15. *-commutative N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{2 \cdot z}} \]

      16. count-2-rev N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

      17. lower-+.f64 99.8%

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \cdot \sqrt{z + z} \]
   5. Step-by-step derivation

      1. lower-*.f64 63.0%

         \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(-1 \cdot \color{blue}{y}\right)\right) \cdot \sqrt{z + z} \]

   6. Applied rewrites 63.0%

      \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \cdot \sqrt{z + z} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(-1 \cdot \color{blue}{y}\right)\right) \cdot \sqrt{z + z} \]

      2. mul-1-neg N/A

         \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\mathsf{neg}\left(y\right)\right)\right) \cdot \sqrt{z + z} \]

      3. lower-neg.f64 63.0%

         \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(-y\right)\right) \cdot \sqrt{z + z} \]

   8. Applied rewrites 63.0%

      \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(-y\right)\right) \cdot \sqrt{z + z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left|t\right| \leq 1.45 \cdot 10^{-12}:\\ \;\;\;\;\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{e^{\left|t\right| \cdot \left|t\right|} \cdot \left(z + z\right)} \cdot \left(-y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= (fabs t) 1.45e-12)
  (* (- (* x 0.5) y) (* (sqrt (+ z z)) 1.0))
  (* (sqrt (* (exp (* (fabs t) (fabs t))) (+ z z))) (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (fabs(t) <= 1.45e-12) {
		tmp = ((x * 0.5) - y) * (sqrt((z + z)) * 1.0);
	} else {
		tmp = sqrt((exp((fabs(t) * fabs(t))) * (z + z))) * -y;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (abs(t) <= 1.45d-12) then
        tmp = ((x * 0.5d0) - y) * (sqrt((z + z)) * 1.0d0)
    else
        tmp = sqrt((exp((abs(t) * abs(t))) * (z + z))) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (Math.abs(t) <= 1.45e-12) {
		tmp = ((x * 0.5) - y) * (Math.sqrt((z + z)) * 1.0);
	} else {
		tmp = Math.sqrt((Math.exp((Math.abs(t) * Math.abs(t))) * (z + z))) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if math.fabs(t) <= 1.45e-12:
		tmp = ((x * 0.5) - y) * (math.sqrt((z + z)) * 1.0)
	else:
		tmp = math.sqrt((math.exp((math.fabs(t) * math.fabs(t))) * (z + z))) * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (abs(t) <= 1.45e-12)
		tmp = Float64(Float64(Float64(x * 0.5) - y) * Float64(sqrt(Float64(z + z)) * 1.0));
	else
		tmp = Float64(sqrt(Float64(exp(Float64(abs(t) * abs(t))) * Float64(z + z))) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (abs(t) <= 1.45e-12)
		tmp = ((x * 0.5) - y) * (sqrt((z + z)) * 1.0);
	else
		tmp = sqrt((exp((abs(t) * abs(t))) * (z + z))) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[Abs[t], $MachinePrecision], 1.45e-12], N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[(N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(N[Exp[N[(N[Abs[t], $MachinePrecision] * N[Abs[t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(z + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.4500000000000001e-12

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 1.4500000000000001e-12 < t

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{e^{\frac{t \cdot t}{2}} \cdot \left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto e^{\frac{t \cdot t}{2}} \cdot \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

      6. lower-*.f64 99.8%

         \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot 0.5 - y\right)\right)} \cdot \sqrt{z \cdot 2} \]

      7. lift-/.f64 N/A

         \[\leadsto \left(e^{\color{blue}{\frac{t \cdot t}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      8. mult-flip N/A

         \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot \frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      9. metadata-eval N/A

         \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \color{blue}{\frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      10. lower-*.f64 99.8%

          \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot 0.5}} \cdot \left(x \cdot 0.5 - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{x \cdot \frac{1}{2}} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      12. *-commutative N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{\frac{1}{2} \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      13. lower-*.f64 99.8%

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(\color{blue}{0.5 \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      14. lift-*.f64 N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z \cdot 2}} \]

      15. *-commutative N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{2 \cdot z}} \]

      16. count-2-rev N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

      17. lower-+.f64 99.8%

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \cdot \sqrt{z + z} \]
   5. Step-by-step derivation

      1. lower-*.f64 63.0%

         \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(-1 \cdot \color{blue}{y}\right)\right) \cdot \sqrt{z + z} \]

   6. Applied rewrites 63.0%

      \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \cdot \sqrt{z + z} \]

   8. Applied rewrites 63.0%

      \[\leadsto \color{blue}{\sqrt{e^{t \cdot t} \cdot \left(z + z\right)} \cdot \left(-y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := x \cdot 0.5 - y\\ \mathbf{if}\;\left|t\right| \leq 7.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1 \cdot \left(\sqrt{z + z} \cdot 1\right)\\ \mathbf{elif}\;\left|t\right| \leq 5 \cdot 10^{+79}:\\ \;\;\;\;\left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot t\_1\right)\right) \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(1 + {\left(\left|t\right|\right)}^{2}\right) \cdot \left(z + z\right)} \cdot \left(-y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (- (* x 0.5) y)))
  (if (<= (fabs t) 7.5e+24)
    (* t_1 (* (sqrt (+ z z)) 1.0))
    (if (<= (fabs t) 5e+79)
      (* (* x (* (/ (sqrt (sqrt (* (+ z z) (+ z z)))) x) t_1)) 1.0)
      (* (sqrt (* (+ 1.0 (pow (fabs t) 2.0)) (+ z z))) (- y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * 0.5) - y;
	double tmp;
	if (fabs(t) <= 7.5e+24) {
		tmp = t_1 * (sqrt((z + z)) * 1.0);
	} else if (fabs(t) <= 5e+79) {
		tmp = (x * ((sqrt(sqrt(((z + z) * (z + z)))) / x) * t_1)) * 1.0;
	} else {
		tmp = sqrt(((1.0 + pow(fabs(t), 2.0)) * (z + z))) * -y;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 0.5d0) - y
    if (abs(t) <= 7.5d+24) then
        tmp = t_1 * (sqrt((z + z)) * 1.0d0)
    else if (abs(t) <= 5d+79) then
        tmp = (x * ((sqrt(sqrt(((z + z) * (z + z)))) / x) * t_1)) * 1.0d0
    else
        tmp = sqrt(((1.0d0 + (abs(t) ** 2.0d0)) * (z + z))) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * 0.5) - y;
	double tmp;
	if (Math.abs(t) <= 7.5e+24) {
		tmp = t_1 * (Math.sqrt((z + z)) * 1.0);
	} else if (Math.abs(t) <= 5e+79) {
		tmp = (x * ((Math.sqrt(Math.sqrt(((z + z) * (z + z)))) / x) * t_1)) * 1.0;
	} else {
		tmp = Math.sqrt(((1.0 + Math.pow(Math.abs(t), 2.0)) * (z + z))) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * 0.5) - y
	tmp = 0
	if math.fabs(t) <= 7.5e+24:
		tmp = t_1 * (math.sqrt((z + z)) * 1.0)
	elif math.fabs(t) <= 5e+79:
		tmp = (x * ((math.sqrt(math.sqrt(((z + z) * (z + z)))) / x) * t_1)) * 1.0
	else:
		tmp = math.sqrt(((1.0 + math.pow(math.fabs(t), 2.0)) * (z + z))) * -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * 0.5) - y)
	tmp = 0.0
	if (abs(t) <= 7.5e+24)
		tmp = Float64(t_1 * Float64(sqrt(Float64(z + z)) * 1.0));
	elseif (abs(t) <= 5e+79)
		tmp = Float64(Float64(x * Float64(Float64(sqrt(sqrt(Float64(Float64(z + z) * Float64(z + z)))) / x) * t_1)) * 1.0);
	else
		tmp = Float64(sqrt(Float64(Float64(1.0 + (abs(t) ^ 2.0)) * Float64(z + z))) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * 0.5) - y;
	tmp = 0.0;
	if (abs(t) <= 7.5e+24)
		tmp = t_1 * (sqrt((z + z)) * 1.0);
	elseif (abs(t) <= 5e+79)
		tmp = (x * ((sqrt(sqrt(((z + z) * (z + z)))) / x) * t_1)) * 1.0;
	else
		tmp = sqrt(((1.0 + (abs(t) ^ 2.0)) * (z + z))) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[N[Abs[t], $MachinePrecision], 7.5e+24], N[(t$95$1 * N[(N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Abs[t], $MachinePrecision], 5e+79], N[(N[(x * N[(N[(N[Sqrt[N[Sqrt[N[(N[(z + z), $MachinePrecision] * N[(z + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision], N[(N[Sqrt[N[(N[(1.0 + N[Power[N[Abs[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(z + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < 7.5000000000000001e24

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 7.5000000000000001e24 < t < 5e79

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \color{blue}{-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + -1 \cdot \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      4. mul-1-neg N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \left(\mathsf{neg}\left(\frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right)\right)\right) \cdot 1 \]

      5. sub-flip-reverse N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      6. lift-/.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{y \cdot \sqrt{2 \cdot z}}{\color{blue}{x}}\right)\right) \cdot 1 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      8. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      9. lift-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      10. pow1/2 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      14. count-2-rev N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      15. lift-+.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      16. pow1/2 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      17. lift-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

   9. Applied rewrites 55.1%

      \[\leadsto \left(x \cdot \left(\frac{\sqrt{z + z}}{x} \cdot \color{blue}{\left(x \cdot 0.5 - y\right)}\right)\right) \cdot 1 \]
   10. Step-by-step derivation

       1. rem-square-sqrt N/A

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{z + z} \cdot \sqrt{z + z}}}{x} \cdot \left(x \cdot \frac{1}{2} - y\right)\right)\right) \cdot 1 \]

       2. sqrt-unprod N/A

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot \frac{1}{2} - y\right)\right)\right) \cdot 1 \]

       3. lower-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot \frac{1}{2} - y\right)\right)\right) \cdot 1 \]

       4. lower-*.f64 45.3%

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot 1 \]

   11. Applied rewrites 45.3%

       \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot 1 \]

   if 5e79 < t

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{e^{\frac{t \cdot t}{2}} \cdot \left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto e^{\frac{t \cdot t}{2}} \cdot \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2}} \]

      6. lower-*.f64 99.8%

         \[\leadsto \color{blue}{\left(e^{\frac{t \cdot t}{2}} \cdot \left(x \cdot 0.5 - y\right)\right)} \cdot \sqrt{z \cdot 2} \]

      7. lift-/.f64 N/A

         \[\leadsto \left(e^{\color{blue}{\frac{t \cdot t}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      8. mult-flip N/A

         \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot \frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      9. metadata-eval N/A

         \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \color{blue}{\frac{1}{2}}} \cdot \left(x \cdot \frac{1}{2} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      10. lower-*.f64 99.8%

          \[\leadsto \left(e^{\color{blue}{\left(t \cdot t\right) \cdot 0.5}} \cdot \left(x \cdot 0.5 - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{x \cdot \frac{1}{2}} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      12. *-commutative N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\color{blue}{\frac{1}{2} \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      13. lower-*.f64 99.8%

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(\color{blue}{0.5 \cdot x} - y\right)\right) \cdot \sqrt{z \cdot 2} \]

      14. lift-*.f64 N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z \cdot 2}} \]

      15. *-commutative N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{2 \cdot z}} \]

      16. count-2-rev N/A

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot \frac{1}{2}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

      17. lower-+.f64 99.8%

          \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{\color{blue}{z + z}} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(0.5 \cdot x - y\right)\right) \cdot \sqrt{z + z}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \cdot \sqrt{z + z} \]
   5. Step-by-step derivation

      1. lower-*.f64 63.0%

         \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \left(-1 \cdot \color{blue}{y}\right)\right) \cdot \sqrt{z + z} \]

   6. Applied rewrites 63.0%

      \[\leadsto \left(e^{\left(t \cdot t\right) \cdot 0.5} \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \cdot \sqrt{z + z} \]

   8. Applied rewrites 63.0%

      \[\leadsto \color{blue}{\sqrt{e^{t \cdot t} \cdot \left(z + z\right)} \cdot \left(-y\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \sqrt{\color{blue}{\left(1 + {t}^{2}\right)} \cdot \left(z + z\right)} \cdot \left(-y\right) \]
   10. Step-by-step derivation

       1. lower-+.f64 N/A

          \[\leadsto \sqrt{\left(1 + \color{blue}{{t}^{2}}\right) \cdot \left(z + z\right)} \cdot \left(-y\right) \]

       2. lower-pow.f64 50.9%

          \[\leadsto \sqrt{\left(1 + {t}^{\color{blue}{2}}\right) \cdot \left(z + z\right)} \cdot \left(-y\right) \]

   11. Applied rewrites 50.9%

       \[\leadsto \sqrt{\color{blue}{\left(1 + {t}^{2}\right)} \cdot \left(z + z\right)} \cdot \left(-y\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 67.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{t \cdot t}{2}\\ t_2 := \sqrt{\frac{2}{z}}\\ t_3 := x \cdot 0.5 - y\\ \mathbf{if}\;t\_1 \leq 3.1 \cdot 10^{+49}:\\ \;\;\;\;t\_3 \cdot \left(\sqrt{z + z} \cdot 1\right)\\ \mathbf{elif}\;t\_1 \leq 4.5 \cdot 10^{+157}:\\ \;\;\;\;\left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot t\_3\right)\right) \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot t\_2}{x} + 0.5 \cdot t\_2\right)\right)\right) \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (* t t) 2.0))
       (t_2 (sqrt (/ 2.0 z)))
       (t_3 (- (* x 0.5) y)))
  (if (<= t_1 3.1e+49)
    (* t_3 (* (sqrt (+ z z)) 1.0))
    (if (<= t_1 4.5e+157)
      (* (* x (* (/ (sqrt (sqrt (* (+ z z) (+ z z)))) x) t_3)) 1.0)
      (* (* x (* z (+ (* -1.0 (/ (* y t_2) x)) (* 0.5 t_2)))) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * t) / 2.0;
	double t_2 = sqrt((2.0 / z));
	double t_3 = (x * 0.5) - y;
	double tmp;
	if (t_1 <= 3.1e+49) {
		tmp = t_3 * (sqrt((z + z)) * 1.0);
	} else if (t_1 <= 4.5e+157) {
		tmp = (x * ((sqrt(sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0;
	} else {
		tmp = (x * (z * ((-1.0 * ((y * t_2) / x)) + (0.5 * t_2)))) * 1.0;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t * t) / 2.0d0
    t_2 = sqrt((2.0d0 / z))
    t_3 = (x * 0.5d0) - y
    if (t_1 <= 3.1d+49) then
        tmp = t_3 * (sqrt((z + z)) * 1.0d0)
    else if (t_1 <= 4.5d+157) then
        tmp = (x * ((sqrt(sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0d0
    else
        tmp = (x * (z * (((-1.0d0) * ((y * t_2) / x)) + (0.5d0 * t_2)))) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * t) / 2.0;
	double t_2 = Math.sqrt((2.0 / z));
	double t_3 = (x * 0.5) - y;
	double tmp;
	if (t_1 <= 3.1e+49) {
		tmp = t_3 * (Math.sqrt((z + z)) * 1.0);
	} else if (t_1 <= 4.5e+157) {
		tmp = (x * ((Math.sqrt(Math.sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0;
	} else {
		tmp = (x * (z * ((-1.0 * ((y * t_2) / x)) + (0.5 * t_2)))) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * t) / 2.0
	t_2 = math.sqrt((2.0 / z))
	t_3 = (x * 0.5) - y
	tmp = 0
	if t_1 <= 3.1e+49:
		tmp = t_3 * (math.sqrt((z + z)) * 1.0)
	elif t_1 <= 4.5e+157:
		tmp = (x * ((math.sqrt(math.sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0
	else:
		tmp = (x * (z * ((-1.0 * ((y * t_2) / x)) + (0.5 * t_2)))) * 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * t) / 2.0)
	t_2 = sqrt(Float64(2.0 / z))
	t_3 = Float64(Float64(x * 0.5) - y)
	tmp = 0.0
	if (t_1 <= 3.1e+49)
		tmp = Float64(t_3 * Float64(sqrt(Float64(z + z)) * 1.0));
	elseif (t_1 <= 4.5e+157)
		tmp = Float64(Float64(x * Float64(Float64(sqrt(sqrt(Float64(Float64(z + z) * Float64(z + z)))) / x) * t_3)) * 1.0);
	else
		tmp = Float64(Float64(x * Float64(z * Float64(Float64(-1.0 * Float64(Float64(y * t_2) / x)) + Float64(0.5 * t_2)))) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * t) / 2.0;
	t_2 = sqrt((2.0 / z));
	t_3 = (x * 0.5) - y;
	tmp = 0.0;
	if (t_1 <= 3.1e+49)
		tmp = t_3 * (sqrt((z + z)) * 1.0);
	elseif (t_1 <= 4.5e+157)
		tmp = (x * ((sqrt(sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0;
	else
		tmp = (x * (z * ((-1.0 * ((y * t_2) / x)) + (0.5 * t_2)))) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(2.0 / z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t$95$1, 3.1e+49], N[(t$95$3 * N[(N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4.5e+157], N[(N[(x * N[(N[(N[Sqrt[N[Sqrt[N[(N[(z + z), $MachinePrecision] * N[(z + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision], N[(N[(x * N[(z * N[(N[(-1.0 * N[(N[(y * t$95$2), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(0.5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 t t) #s(literal 2 binary64)) < 3.0999999999999999e49

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 3.0999999999999999e49 < (/.f64 (*.f64 t t) #s(literal 2 binary64)) < 4.4999999999999998e157

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \color{blue}{-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + -1 \cdot \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      4. mul-1-neg N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \left(\mathsf{neg}\left(\frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right)\right)\right) \cdot 1 \]

      5. sub-flip-reverse N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      6. lift-/.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{y \cdot \sqrt{2 \cdot z}}{\color{blue}{x}}\right)\right) \cdot 1 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      8. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      9. lift-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      10. pow1/2 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      14. count-2-rev N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      15. lift-+.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      16. pow1/2 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      17. lift-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

   9. Applied rewrites 55.1%

      \[\leadsto \left(x \cdot \left(\frac{\sqrt{z + z}}{x} \cdot \color{blue}{\left(x \cdot 0.5 - y\right)}\right)\right) \cdot 1 \]
   10. Step-by-step derivation

       1. rem-square-sqrt N/A

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{z + z} \cdot \sqrt{z + z}}}{x} \cdot \left(x \cdot \frac{1}{2} - y\right)\right)\right) \cdot 1 \]

       2. sqrt-unprod N/A

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot \frac{1}{2} - y\right)\right)\right) \cdot 1 \]

       3. lower-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot \frac{1}{2} - y\right)\right)\right) \cdot 1 \]

       4. lower-*.f64 45.3%

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot 1 \]

   11. Applied rewrites 45.3%

       \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot 1 \]

   if 4.4999999999999998e157 < (/.f64 (*.f64 t t) #s(literal 2 binary64))

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]

   8. Taylor expanded in z around inf

      \[\leadsto \left(x \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \frac{1}{2} \cdot \sqrt{\frac{2}{z}}\right)}\right)\right) \cdot 1 \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{\frac{2}{z}}}\right)\right)\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{\frac{2}{z}}}\right)\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \frac{1}{2} \cdot \sqrt{\color{blue}{\frac{2}{z}}}\right)\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \frac{1}{2} \cdot \sqrt{\frac{2}{\color{blue}{z}}}\right)\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \frac{1}{2} \cdot \sqrt{\frac{2}{z}}\right)\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \frac{1}{2} \cdot \sqrt{\frac{2}{z}}\right)\right)\right) \cdot 1 \]

      7. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \frac{1}{2} \cdot \sqrt{\frac{2}{z}}\right)\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \frac{1}{2} \cdot \sqrt{\frac{2}{z}}\right)\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + \frac{1}{2} \cdot \sqrt{\frac{2}{z}}\right)\right)\right) \cdot 1 \]

      10. lower-/.f64 57.5%

          \[\leadsto \left(x \cdot \left(z \cdot \left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + 0.5 \cdot \sqrt{\frac{2}{z}}\right)\right)\right) \cdot 1 \]

   10. Applied rewrites 57.5%

       \[\leadsto \left(x \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{\frac{2}{z}}}{x} + 0.5 \cdot \sqrt{\frac{2}{z}}\right)}\right)\right) \cdot 1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 67.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := \sqrt{z + z}\\ t_2 := \frac{t \cdot t}{2}\\ t_3 := x \cdot 0.5 - y\\ \mathbf{if}\;t\_2 \leq 3.1 \cdot 10^{+49}:\\ \;\;\;\;t\_3 \cdot \left(t\_1 \cdot 1\right)\\ \mathbf{elif}\;t\_2 \leq 4.5 \cdot 10^{+157}:\\ \;\;\;\;\left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot t\_3\right)\right) \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{\left(t\_3 \cdot x\right) \cdot t\_1}} \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (sqrt (+ z z)))
       (t_2 (/ (* t t) 2.0))
       (t_3 (- (* x 0.5) y)))
  (if (<= t_2 3.1e+49)
    (* t_3 (* t_1 1.0))
    (if (<= t_2 4.5e+157)
      (* (* x (* (/ (sqrt (sqrt (* (+ z z) (+ z z)))) x) t_3)) 1.0)
      (* (/ 1.0 (/ x (* (* t_3 x) t_1))) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z + z));
	double t_2 = (t * t) / 2.0;
	double t_3 = (x * 0.5) - y;
	double tmp;
	if (t_2 <= 3.1e+49) {
		tmp = t_3 * (t_1 * 1.0);
	} else if (t_2 <= 4.5e+157) {
		tmp = (x * ((sqrt(sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0;
	} else {
		tmp = (1.0 / (x / ((t_3 * x) * t_1))) * 1.0;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = sqrt((z + z))
    t_2 = (t * t) / 2.0d0
    t_3 = (x * 0.5d0) - y
    if (t_2 <= 3.1d+49) then
        tmp = t_3 * (t_1 * 1.0d0)
    else if (t_2 <= 4.5d+157) then
        tmp = (x * ((sqrt(sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0d0
    else
        tmp = (1.0d0 / (x / ((t_3 * x) * t_1))) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z + z));
	double t_2 = (t * t) / 2.0;
	double t_3 = (x * 0.5) - y;
	double tmp;
	if (t_2 <= 3.1e+49) {
		tmp = t_3 * (t_1 * 1.0);
	} else if (t_2 <= 4.5e+157) {
		tmp = (x * ((Math.sqrt(Math.sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0;
	} else {
		tmp = (1.0 / (x / ((t_3 * x) * t_1))) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z + z))
	t_2 = (t * t) / 2.0
	t_3 = (x * 0.5) - y
	tmp = 0
	if t_2 <= 3.1e+49:
		tmp = t_3 * (t_1 * 1.0)
	elif t_2 <= 4.5e+157:
		tmp = (x * ((math.sqrt(math.sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0
	else:
		tmp = (1.0 / (x / ((t_3 * x) * t_1))) * 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z + z))
	t_2 = Float64(Float64(t * t) / 2.0)
	t_3 = Float64(Float64(x * 0.5) - y)
	tmp = 0.0
	if (t_2 <= 3.1e+49)
		tmp = Float64(t_3 * Float64(t_1 * 1.0));
	elseif (t_2 <= 4.5e+157)
		tmp = Float64(Float64(x * Float64(Float64(sqrt(sqrt(Float64(Float64(z + z) * Float64(z + z)))) / x) * t_3)) * 1.0);
	else
		tmp = Float64(Float64(1.0 / Float64(x / Float64(Float64(t_3 * x) * t_1))) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z + z));
	t_2 = (t * t) / 2.0;
	t_3 = (x * 0.5) - y;
	tmp = 0.0;
	if (t_2 <= 3.1e+49)
		tmp = t_3 * (t_1 * 1.0);
	elseif (t_2 <= 4.5e+157)
		tmp = (x * ((sqrt(sqrt(((z + z) * (z + z)))) / x) * t_3)) * 1.0;
	else
		tmp = (1.0 / (x / ((t_3 * x) * t_1))) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t$95$2, 3.1e+49], N[(t$95$3 * N[(t$95$1 * 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4.5e+157], N[(N[(x * N[(N[(N[Sqrt[N[Sqrt[N[(N[(z + z), $MachinePrecision] * N[(z + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision], N[(N[(1.0 / N[(x / N[(N[(t$95$3 * x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 t t) #s(literal 2 binary64)) < 3.0999999999999999e49

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 3.0999999999999999e49 < (/.f64 (*.f64 t t) #s(literal 2 binary64)) < 4.4999999999999998e157

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \color{blue}{-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + -1 \cdot \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      4. mul-1-neg N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \left(\mathsf{neg}\left(\frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right)\right)\right) \cdot 1 \]

      5. sub-flip-reverse N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      6. lift-/.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{y \cdot \sqrt{2 \cdot z}}{\color{blue}{x}}\right)\right) \cdot 1 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      8. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      9. lift-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      10. pow1/2 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      14. count-2-rev N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      15. lift-+.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      16. pow1/2 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      17. lift-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

   9. Applied rewrites 55.1%

      \[\leadsto \left(x \cdot \left(\frac{\sqrt{z + z}}{x} \cdot \color{blue}{\left(x \cdot 0.5 - y\right)}\right)\right) \cdot 1 \]
   10. Step-by-step derivation

       1. rem-square-sqrt N/A

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{z + z} \cdot \sqrt{z + z}}}{x} \cdot \left(x \cdot \frac{1}{2} - y\right)\right)\right) \cdot 1 \]

       2. sqrt-unprod N/A

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot \frac{1}{2} - y\right)\right)\right) \cdot 1 \]

       3. lower-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot \frac{1}{2} - y\right)\right)\right) \cdot 1 \]

       4. lower-*.f64 45.3%

          \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot 1 \]

   11. Applied rewrites 45.3%

       \[\leadsto \left(x \cdot \left(\frac{\sqrt{\sqrt{\left(z + z\right) \cdot \left(z + z\right)}}}{x} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot 1 \]

   if 4.4999999999999998e157 < (/.f64 (*.f64 t t) #s(literal 2 binary64))

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]

   9. Applied rewrites 51.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{x}{\left(\left(x \cdot 0.5 - y\right) \cdot x\right) \cdot \sqrt{z + z}}}} \cdot 1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 66.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} t_1 := \sqrt{z + z}\\ t_2 := x \cdot 0.5 - y\\ \mathbf{if}\;\left|t\right| \leq 46000000:\\ \;\;\;\;t\_2 \cdot \left(t\_1 \cdot 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t\_2 \cdot x\right) \cdot t\_1}{x} \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (sqrt (+ z z))) (t_2 (- (* x 0.5) y)))
  (if (<= (fabs t) 46000000.0)
    (* t_2 (* t_1 1.0))
    (* (/ (* (* t_2 x) t_1) x) 1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z + z));
	double t_2 = (x * 0.5) - y;
	double tmp;
	if (fabs(t) <= 46000000.0) {
		tmp = t_2 * (t_1 * 1.0);
	} else {
		tmp = (((t_2 * x) * t_1) / x) * 1.0;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = sqrt((z + z))
    t_2 = (x * 0.5d0) - y
    if (abs(t) <= 46000000.0d0) then
        tmp = t_2 * (t_1 * 1.0d0)
    else
        tmp = (((t_2 * x) * t_1) / x) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z + z));
	double t_2 = (x * 0.5) - y;
	double tmp;
	if (Math.abs(t) <= 46000000.0) {
		tmp = t_2 * (t_1 * 1.0);
	} else {
		tmp = (((t_2 * x) * t_1) / x) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z + z))
	t_2 = (x * 0.5) - y
	tmp = 0
	if math.fabs(t) <= 46000000.0:
		tmp = t_2 * (t_1 * 1.0)
	else:
		tmp = (((t_2 * x) * t_1) / x) * 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z + z))
	t_2 = Float64(Float64(x * 0.5) - y)
	tmp = 0.0
	if (abs(t) <= 46000000.0)
		tmp = Float64(t_2 * Float64(t_1 * 1.0));
	else
		tmp = Float64(Float64(Float64(Float64(t_2 * x) * t_1) / x) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z + z));
	t_2 = (x * 0.5) - y;
	tmp = 0.0;
	if (abs(t) <= 46000000.0)
		tmp = t_2 * (t_1 * 1.0);
	else
		tmp = (((t_2 * x) * t_1) / x) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[N[Abs[t], $MachinePrecision], 46000000.0], N[(t$95$2 * N[(t$95$1 * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t$95$2 * x), $MachinePrecision] * t$95$1), $MachinePrecision] / x), $MachinePrecision] * 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if t < 4.6e7

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 4.6e7 < t

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]

   9. Applied rewrites 51.7%

      \[\leadsto \frac{\left(\left(x \cdot 0.5 - y\right) \cdot x\right) \cdot \sqrt{z + z}}{\color{blue}{x}} \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 65.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} t_1 := \sqrt{z + z}\\ t_2 := x \cdot 0.5 - y\\ \mathbf{if}\;\left|t\right| \leq 46000000:\\ \;\;\;\;t\_2 \cdot \left(t\_1 \cdot 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{\left(t\_2 \cdot x\right) \cdot t\_1}} \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (sqrt (+ z z))) (t_2 (- (* x 0.5) y)))
  (if (<= (fabs t) 46000000.0)
    (* t_2 (* t_1 1.0))
    (* (/ 1.0 (/ x (* (* t_2 x) t_1))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z + z));
	double t_2 = (x * 0.5) - y;
	double tmp;
	if (fabs(t) <= 46000000.0) {
		tmp = t_2 * (t_1 * 1.0);
	} else {
		tmp = (1.0 / (x / ((t_2 * x) * t_1))) * 1.0;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = sqrt((z + z))
    t_2 = (x * 0.5d0) - y
    if (abs(t) <= 46000000.0d0) then
        tmp = t_2 * (t_1 * 1.0d0)
    else
        tmp = (1.0d0 / (x / ((t_2 * x) * t_1))) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z + z));
	double t_2 = (x * 0.5) - y;
	double tmp;
	if (Math.abs(t) <= 46000000.0) {
		tmp = t_2 * (t_1 * 1.0);
	} else {
		tmp = (1.0 / (x / ((t_2 * x) * t_1))) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z + z))
	t_2 = (x * 0.5) - y
	tmp = 0
	if math.fabs(t) <= 46000000.0:
		tmp = t_2 * (t_1 * 1.0)
	else:
		tmp = (1.0 / (x / ((t_2 * x) * t_1))) * 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z + z))
	t_2 = Float64(Float64(x * 0.5) - y)
	tmp = 0.0
	if (abs(t) <= 46000000.0)
		tmp = Float64(t_2 * Float64(t_1 * 1.0));
	else
		tmp = Float64(Float64(1.0 / Float64(x / Float64(Float64(t_2 * x) * t_1))) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z + z));
	t_2 = (x * 0.5) - y;
	tmp = 0.0;
	if (abs(t) <= 46000000.0)
		tmp = t_2 * (t_1 * 1.0);
	else
		tmp = (1.0 / (x / ((t_2 * x) * t_1))) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[N[Abs[t], $MachinePrecision], 46000000.0], N[(t$95$2 * N[(t$95$1 * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(x / N[(N[(t$95$2 * x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if t < 4.6e7

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 4.6e7 < t

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]

   9. Applied rewrites 51.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{x}{\left(\left(x \cdot 0.5 - y\right) \cdot x\right) \cdot \sqrt{z + z}}}} \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 64.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} t_1 := \sqrt{z + z}\\ t_2 := x \cdot 0.5 - y\\ t_3 := \frac{t\_1}{x}\\ \mathbf{if}\;\left|t\right| \leq 8 \cdot 10^{+21}:\\ \;\;\;\;t\_2 \cdot \left(t\_1 \cdot 1\right)\\ \mathbf{elif}\;\left|t\right| \leq 2.7 \cdot 10^{+165}:\\ \;\;\;\;\left(x \cdot \left(t\_3 \cdot t\_2\right)\right) \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\left(t\_3 \cdot \left(t\_2 \cdot x\right)\right) \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (sqrt (+ z z))) (t_2 (- (* x 0.5) y)) (t_3 (/ t_1 x)))
  (if (<= (fabs t) 8e+21)
    (* t_2 (* t_1 1.0))
    (if (<= (fabs t) 2.7e+165)
      (* (* x (* t_3 t_2)) 1.0)
      (* (* t_3 (* t_2 x)) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z + z));
	double t_2 = (x * 0.5) - y;
	double t_3 = t_1 / x;
	double tmp;
	if (fabs(t) <= 8e+21) {
		tmp = t_2 * (t_1 * 1.0);
	} else if (fabs(t) <= 2.7e+165) {
		tmp = (x * (t_3 * t_2)) * 1.0;
	} else {
		tmp = (t_3 * (t_2 * x)) * 1.0;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = sqrt((z + z))
    t_2 = (x * 0.5d0) - y
    t_3 = t_1 / x
    if (abs(t) <= 8d+21) then
        tmp = t_2 * (t_1 * 1.0d0)
    else if (abs(t) <= 2.7d+165) then
        tmp = (x * (t_3 * t_2)) * 1.0d0
    else
        tmp = (t_3 * (t_2 * x)) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z + z));
	double t_2 = (x * 0.5) - y;
	double t_3 = t_1 / x;
	double tmp;
	if (Math.abs(t) <= 8e+21) {
		tmp = t_2 * (t_1 * 1.0);
	} else if (Math.abs(t) <= 2.7e+165) {
		tmp = (x * (t_3 * t_2)) * 1.0;
	} else {
		tmp = (t_3 * (t_2 * x)) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z + z))
	t_2 = (x * 0.5) - y
	t_3 = t_1 / x
	tmp = 0
	if math.fabs(t) <= 8e+21:
		tmp = t_2 * (t_1 * 1.0)
	elif math.fabs(t) <= 2.7e+165:
		tmp = (x * (t_3 * t_2)) * 1.0
	else:
		tmp = (t_3 * (t_2 * x)) * 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z + z))
	t_2 = Float64(Float64(x * 0.5) - y)
	t_3 = Float64(t_1 / x)
	tmp = 0.0
	if (abs(t) <= 8e+21)
		tmp = Float64(t_2 * Float64(t_1 * 1.0));
	elseif (abs(t) <= 2.7e+165)
		tmp = Float64(Float64(x * Float64(t_3 * t_2)) * 1.0);
	else
		tmp = Float64(Float64(t_3 * Float64(t_2 * x)) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z + z));
	t_2 = (x * 0.5) - y;
	t_3 = t_1 / x;
	tmp = 0.0;
	if (abs(t) <= 8e+21)
		tmp = t_2 * (t_1 * 1.0);
	elseif (abs(t) <= 2.7e+165)
		tmp = (x * (t_3 * t_2)) * 1.0;
	else
		tmp = (t_3 * (t_2 * x)) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / x), $MachinePrecision]}, If[LessEqual[N[Abs[t], $MachinePrecision], 8e+21], N[(t$95$2 * N[(t$95$1 * 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Abs[t], $MachinePrecision], 2.7e+165], N[(N[(x * N[(t$95$3 * t$95$2), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision], N[(N[(t$95$3 * N[(t$95$2 * x), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 8e21

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 8e21 < t < 2.7e165

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \color{blue}{-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + -1 \cdot \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      4. mul-1-neg N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \left(\mathsf{neg}\left(\frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right)\right)\right) \cdot 1 \]

      5. sub-flip-reverse N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      6. lift-/.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{y \cdot \sqrt{2 \cdot z}}{\color{blue}{x}}\right)\right) \cdot 1 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      8. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      9. lift-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      10. pow1/2 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      14. count-2-rev N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      15. lift-+.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      16. pow1/2 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      17. lift-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

   9. Applied rewrites 55.1%

      \[\leadsto \left(x \cdot \left(\frac{\sqrt{z + z}}{x} \cdot \color{blue}{\left(x \cdot 0.5 - y\right)}\right)\right) \cdot 1 \]

   if 2.7e165 < t

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lift-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \color{blue}{-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      4. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + -1 \cdot \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      5. mul-1-neg N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \left(\mathsf{neg}\left(\frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right)\right)\right) \cdot 1 \]

      6. sub-flip-reverse N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      7. lift-/.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{y \cdot \sqrt{2 \cdot z}}{\color{blue}{x}}\right)\right) \cdot 1 \]

      8. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      9. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      10. lift-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      11. pow1/2 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      12. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      14. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      15. count-2-rev N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      16. lift-+.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      17. pow1/2 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      18. lift-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

   9. Applied rewrites 50.9%

      \[\leadsto \left(\frac{\sqrt{z + z}}{x} \cdot \color{blue}{\left(\left(x \cdot 0.5 - y\right) \cdot x\right)}\right) \cdot 1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 63.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} t_1 := \sqrt{z + z}\\ t_2 := x \cdot 0.5 - y\\ \mathbf{if}\;\frac{t \cdot t}{2} \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;t\_2 \cdot \left(t\_1 \cdot 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\frac{t\_1}{x} \cdot t\_2\right)\right) \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (sqrt (+ z z))) (t_2 (- (* x 0.5) y)))
  (if (<= (/ (* t t) 2.0) 3.6e+48)
    (* t_2 (* t_1 1.0))
    (* (* x (* (/ t_1 x) t_2)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z + z));
	double t_2 = (x * 0.5) - y;
	double tmp;
	if (((t * t) / 2.0) <= 3.6e+48) {
		tmp = t_2 * (t_1 * 1.0);
	} else {
		tmp = (x * ((t_1 / x) * t_2)) * 1.0;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = sqrt((z + z))
    t_2 = (x * 0.5d0) - y
    if (((t * t) / 2.0d0) <= 3.6d+48) then
        tmp = t_2 * (t_1 * 1.0d0)
    else
        tmp = (x * ((t_1 / x) * t_2)) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z + z));
	double t_2 = (x * 0.5) - y;
	double tmp;
	if (((t * t) / 2.0) <= 3.6e+48) {
		tmp = t_2 * (t_1 * 1.0);
	} else {
		tmp = (x * ((t_1 / x) * t_2)) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z + z))
	t_2 = (x * 0.5) - y
	tmp = 0
	if ((t * t) / 2.0) <= 3.6e+48:
		tmp = t_2 * (t_1 * 1.0)
	else:
		tmp = (x * ((t_1 / x) * t_2)) * 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z + z))
	t_2 = Float64(Float64(x * 0.5) - y)
	tmp = 0.0
	if (Float64(Float64(t * t) / 2.0) <= 3.6e+48)
		tmp = Float64(t_2 * Float64(t_1 * 1.0));
	else
		tmp = Float64(Float64(x * Float64(Float64(t_1 / x) * t_2)) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z + z));
	t_2 = (x * 0.5) - y;
	tmp = 0.0;
	if (((t * t) / 2.0) <= 3.6e+48)
		tmp = t_2 * (t_1 * 1.0);
	else
		tmp = (x * ((t_1 / x) * t_2)) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision], 3.6e+48], N[(t$95$2 * N[(t$95$1 * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(t$95$1 / x), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 t t) #s(literal 2 binary64)) < 3.5999999999999998e48

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 3.5999999999999998e48 < (/.f64 (*.f64 t t) #s(literal 2 binary64))

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \color{blue}{-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + -1 \cdot \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      4. mul-1-neg N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} + \left(\mathsf{neg}\left(\frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right)\right)\right) \cdot 1 \]

      5. sub-flip-reverse N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \color{blue}{\frac{y \cdot \sqrt{2 \cdot z}}{x}}\right)\right) \cdot 1 \]

      6. lift-/.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{y \cdot \sqrt{2 \cdot z}}{\color{blue}{x}}\right)\right) \cdot 1 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \left(\frac{1}{2} \cdot \sqrt{2 \cdot z} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      8. *-commutative N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y \cdot \sqrt{2 \cdot z}}}{x}\right)\right) \cdot 1 \]

      9. lift-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(\sqrt{2 \cdot z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      10. pow1/2 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      13. *-commutative N/A

          \[\leadsto \left(x \cdot \left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      14. count-2-rev N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      15. lift-+.f64 N/A

          \[\leadsto \left(x \cdot \left({\left(z + z\right)}^{\frac{1}{2}} \cdot \frac{1}{2} - \frac{y \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      16. pow1/2 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

      17. lift-sqrt.f64 N/A

          \[\leadsto \left(x \cdot \left(\sqrt{z + z} \cdot \frac{1}{2} - \frac{\color{blue}{y} \cdot \sqrt{2 \cdot z}}{x}\right)\right) \cdot 1 \]

   9. Applied rewrites 55.1%

      \[\leadsto \left(x \cdot \left(\frac{\sqrt{z + z}}{x} \cdot \color{blue}{\left(x \cdot 0.5 - y\right)}\right)\right) \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 63.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{t \cdot t}{2} \leq 6.5:\\ \;\;\;\;\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\sqrt{\frac{2}{z}} \cdot \left(0.5 \cdot x - y\right)\right)\right) \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= (/ (* t t) 2.0) 6.5)
  (* (- (* x 0.5) y) (* (sqrt (+ z z)) 1.0))
  (* (* z (* (sqrt (/ 2.0 z)) (- (* 0.5 x) y))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((t * t) / 2.0) <= 6.5) {
		tmp = ((x * 0.5) - y) * (sqrt((z + z)) * 1.0);
	} else {
		tmp = (z * (sqrt((2.0 / z)) * ((0.5 * x) - y))) * 1.0;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((t * t) / 2.0d0) <= 6.5d0) then
        tmp = ((x * 0.5d0) - y) * (sqrt((z + z)) * 1.0d0)
    else
        tmp = (z * (sqrt((2.0d0 / z)) * ((0.5d0 * x) - y))) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((t * t) / 2.0) <= 6.5) {
		tmp = ((x * 0.5) - y) * (Math.sqrt((z + z)) * 1.0);
	} else {
		tmp = (z * (Math.sqrt((2.0 / z)) * ((0.5 * x) - y))) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((t * t) / 2.0) <= 6.5:
		tmp = ((x * 0.5) - y) * (math.sqrt((z + z)) * 1.0)
	else:
		tmp = (z * (math.sqrt((2.0 / z)) * ((0.5 * x) - y))) * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(t * t) / 2.0) <= 6.5)
		tmp = Float64(Float64(Float64(x * 0.5) - y) * Float64(sqrt(Float64(z + z)) * 1.0));
	else
		tmp = Float64(Float64(z * Float64(sqrt(Float64(2.0 / z)) * Float64(Float64(0.5 * x) - y))) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((t * t) / 2.0) <= 6.5)
		tmp = ((x * 0.5) - y) * (sqrt((z + z)) * 1.0);
	else
		tmp = (z * (sqrt((2.0 / z)) * ((0.5 * x) - y))) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision], 6.5], N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[(N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[Sqrt[N[(2.0 / z), $MachinePrecision]], $MachinePrecision] * N[(N[(0.5 * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 t t) #s(literal 2 binary64)) < 6.5

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 6.5 < (/.f64 (*.f64 t t) #s(literal 2 binary64))

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-sqrt.f64 N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-*.f64 29.7%

         \[\leadsto \left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 29.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\sqrt{2 \cdot z} \cdot y\right)\right) \cdot 1 \]

      5. lift-sqrt.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\sqrt{2 \cdot z} \cdot y\right)\right) \cdot 1 \]

      6. pow1/2 N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      8. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      9. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      10. count-2-rev N/A

          \[\leadsto \left(\mathsf{neg}\left({\left(z + z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      11. lift-+.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left({\left(z + z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      12. pow1/2 N/A

          \[\leadsto \left(\mathsf{neg}\left(\sqrt{z + z} \cdot y\right)\right) \cdot 1 \]

      13. lift-sqrt.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(\sqrt{z + z} \cdot y\right)\right) \cdot 1 \]

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

          \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \cdot 1 \]

      15. lower-*.f64 N/A

          \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \cdot 1 \]

      16. lower-neg.f64 29.7%

          \[\leadsto \left(\sqrt{z + z} \cdot \left(-y\right)\right) \cdot 1 \]

   9. Applied rewrites 29.7%

      \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(-y\right)}\right) \cdot 1 \]

   10. Taylor expanded in z around inf

       \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt{\frac{2}{z}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right)\right)} \cdot 1 \]
   11. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \left(z \cdot \color{blue}{\left(\sqrt{\frac{2}{z}} \cdot \left(\frac{1}{2} \cdot x - y\right)\right)}\right) \cdot 1 \]

       2. lower-*.f64 N/A

          \[\leadsto \left(z \cdot \left(\sqrt{\frac{2}{z}} \cdot \color{blue}{\left(\frac{1}{2} \cdot x - y\right)}\right)\right) \cdot 1 \]

       3. lower-sqrt.f64 N/A

          \[\leadsto \left(z \cdot \left(\sqrt{\frac{2}{z}} \cdot \left(\color{blue}{\frac{1}{2} \cdot x} - y\right)\right)\right) \cdot 1 \]

       4. lower-/.f64 N/A

          \[\leadsto \left(z \cdot \left(\sqrt{\frac{2}{z}} \cdot \left(\color{blue}{\frac{1}{2}} \cdot x - y\right)\right)\right) \cdot 1 \]

       5. lower--.f64 N/A

          \[\leadsto \left(z \cdot \left(\sqrt{\frac{2}{z}} \cdot \left(\frac{1}{2} \cdot x - \color{blue}{y}\right)\right)\right) \cdot 1 \]

       6. lower-*.f64 56.6%

          \[\leadsto \left(z \cdot \left(\sqrt{\frac{2}{z}} \cdot \left(0.5 \cdot x - y\right)\right)\right) \cdot 1 \]

   12. Applied rewrites 56.6%

       \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt{\frac{2}{z}} \cdot \left(0.5 \cdot x - y\right)\right)\right)} \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 62.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} t_1 := \sqrt{z + z}\\ \mathbf{if}\;\frac{t \cdot t}{2} \leq 2.5 \cdot 10^{-9}:\\ \;\;\;\;\left(x \cdot 0.5 - y\right) \cdot \left(t\_1 \cdot 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(0.5 - \frac{y}{x}\right) \cdot t\_1\right) \cdot x\right) \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (sqrt (+ z z))))
  (if (<= (/ (* t t) 2.0) 2.5e-9)
    (* (- (* x 0.5) y) (* t_1 1.0))
    (* (* (* (- 0.5 (/ y x)) t_1) x) 1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z + z));
	double tmp;
	if (((t * t) / 2.0) <= 2.5e-9) {
		tmp = ((x * 0.5) - y) * (t_1 * 1.0);
	} else {
		tmp = (((0.5 - (y / x)) * t_1) * x) * 1.0;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt((z + z))
    if (((t * t) / 2.0d0) <= 2.5d-9) then
        tmp = ((x * 0.5d0) - y) * (t_1 * 1.0d0)
    else
        tmp = (((0.5d0 - (y / x)) * t_1) * x) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z + z));
	double tmp;
	if (((t * t) / 2.0) <= 2.5e-9) {
		tmp = ((x * 0.5) - y) * (t_1 * 1.0);
	} else {
		tmp = (((0.5 - (y / x)) * t_1) * x) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z + z))
	tmp = 0
	if ((t * t) / 2.0) <= 2.5e-9:
		tmp = ((x * 0.5) - y) * (t_1 * 1.0)
	else:
		tmp = (((0.5 - (y / x)) * t_1) * x) * 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z + z))
	tmp = 0.0
	if (Float64(Float64(t * t) / 2.0) <= 2.5e-9)
		tmp = Float64(Float64(Float64(x * 0.5) - y) * Float64(t_1 * 1.0));
	else
		tmp = Float64(Float64(Float64(Float64(0.5 - Float64(y / x)) * t_1) * x) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z + z));
	tmp = 0.0;
	if (((t * t) / 2.0) <= 2.5e-9)
		tmp = ((x * 0.5) - y) * (t_1 * 1.0);
	else
		tmp = (((0.5 - (y / x)) * t_1) * x) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision], 2.5e-9], N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[(t$95$1 * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.5 - N[(y / x), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] * x), $MachinePrecision] * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 t t) #s(literal 2 binary64)) < 2.5000000000000001e-9

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 2.5000000000000001e-9 < (/.f64 (*.f64 t t) #s(literal 2 binary64))

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2} \cdot \sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \color{blue}{\frac{1}{2}} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      6. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      10. lower-*.f64 57.6%

          \[\leadsto \left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 57.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + 0.5 \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. *-commutative N/A

         \[\leadsto \left(\left(-1 \cdot \frac{y \cdot \sqrt{2 \cdot z}}{x} + \frac{1}{2} \cdot \sqrt{2 \cdot z}\right) \cdot \color{blue}{x}\right) \cdot 1 \]

   9. Applied rewrites 57.9%

      \[\leadsto \left(\left(\left(0.5 - \frac{y}{x}\right) \cdot \sqrt{z + z}\right) \cdot \color{blue}{x}\right) \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 59.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} t_1 := \sqrt{z + z}\\ \mathbf{if}\;\frac{t \cdot t}{2} \leq 3.1 \cdot 10^{+49}:\\ \;\;\;\;\left(x \cdot 0.5 - y\right) \cdot \left(t\_1 \cdot 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\frac{t\_1}{x} \cdot \left(-y\right)\right)\right) \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (sqrt (+ z z))))
  (if (<= (/ (* t t) 2.0) 3.1e+49)
    (* (- (* x 0.5) y) (* t_1 1.0))
    (* (* x (* (/ t_1 x) (- y))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z + z));
	double tmp;
	if (((t * t) / 2.0) <= 3.1e+49) {
		tmp = ((x * 0.5) - y) * (t_1 * 1.0);
	} else {
		tmp = (x * ((t_1 / x) * -y)) * 1.0;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt((z + z))
    if (((t * t) / 2.0d0) <= 3.1d+49) then
        tmp = ((x * 0.5d0) - y) * (t_1 * 1.0d0)
    else
        tmp = (x * ((t_1 / x) * -y)) * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z + z));
	double tmp;
	if (((t * t) / 2.0) <= 3.1e+49) {
		tmp = ((x * 0.5) - y) * (t_1 * 1.0);
	} else {
		tmp = (x * ((t_1 / x) * -y)) * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z + z))
	tmp = 0
	if ((t * t) / 2.0) <= 3.1e+49:
		tmp = ((x * 0.5) - y) * (t_1 * 1.0)
	else:
		tmp = (x * ((t_1 / x) * -y)) * 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z + z))
	tmp = 0.0
	if (Float64(Float64(t * t) / 2.0) <= 3.1e+49)
		tmp = Float64(Float64(Float64(x * 0.5) - y) * Float64(t_1 * 1.0));
	else
		tmp = Float64(Float64(x * Float64(Float64(t_1 / x) * Float64(-y))) * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z + z));
	tmp = 0.0;
	if (((t * t) / 2.0) <= 3.1e+49)
		tmp = ((x * 0.5) - y) * (t_1 * 1.0);
	else
		tmp = (x * ((t_1 / x) * -y)) * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision], 3.1e+49], N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[(t$95$1 * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(t$95$1 / x), $MachinePrecision] * (-y)), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 t t) #s(literal 2 binary64)) < 3.0999999999999999e49

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

      12. *-commutative N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      14. lower-*.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

      16. count-2-rev N/A

          \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

      17. lift-+.f64 57.2%

          \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   6. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]

   if 3.0999999999999999e49 < (/.f64 (*.f64 t t) #s(literal 2 binary64))

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-sqrt.f64 N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-*.f64 29.7%

         \[\leadsto \left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 29.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\sqrt{2 \cdot z} \cdot y\right)\right) \cdot 1 \]

      5. lift-sqrt.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\sqrt{2 \cdot z} \cdot y\right)\right) \cdot 1 \]

      6. pow1/2 N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      8. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      9. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      10. count-2-rev N/A

          \[\leadsto \left(\mathsf{neg}\left({\left(z + z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      11. lift-+.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left({\left(z + z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      12. pow1/2 N/A

          \[\leadsto \left(\mathsf{neg}\left(\sqrt{z + z} \cdot y\right)\right) \cdot 1 \]

      13. lift-sqrt.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(\sqrt{z + z} \cdot y\right)\right) \cdot 1 \]

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

          \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \cdot 1 \]

      15. lower-*.f64 N/A

          \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \cdot 1 \]

      16. lower-neg.f64 29.7%

          \[\leadsto \left(\sqrt{z + z} \cdot \left(-y\right)\right) \cdot 1 \]

   9. Applied rewrites 29.7%

      \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(-y\right)}\right) \cdot 1 \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(-y\right)}\right) \cdot 1 \]

       2. *-rgt-identity N/A

          \[\leadsto \left(\left(\sqrt{z + z} \cdot 1\right) \cdot \left(-\color{blue}{y}\right)\right) \cdot 1 \]

       3. *-inverses N/A

          \[\leadsto \left(\left(\sqrt{z + z} \cdot \frac{x}{x}\right) \cdot \left(-y\right)\right) \cdot 1 \]

       4. associate-/l* N/A

          \[\leadsto \left(\frac{\sqrt{z + z} \cdot x}{x} \cdot \left(-\color{blue}{y}\right)\right) \cdot 1 \]

       5. *-commutative N/A

          \[\leadsto \left(\frac{x \cdot \sqrt{z + z}}{x} \cdot \left(-y\right)\right) \cdot 1 \]

       6. associate-*r/ N/A

          \[\leadsto \left(\left(x \cdot \frac{\sqrt{z + z}}{x}\right) \cdot \left(-\color{blue}{y}\right)\right) \cdot 1 \]

       7. lift-/.f64 N/A

          \[\leadsto \left(\left(x \cdot \frac{\sqrt{z + z}}{x}\right) \cdot \left(-y\right)\right) \cdot 1 \]

       8. associate-*l* N/A

          \[\leadsto \left(x \cdot \color{blue}{\left(\frac{\sqrt{z + z}}{x} \cdot \left(-y\right)\right)}\right) \cdot 1 \]

       9. lower-*.f64 N/A

          \[\leadsto \left(x \cdot \color{blue}{\left(\frac{\sqrt{z + z}}{x} \cdot \left(-y\right)\right)}\right) \cdot 1 \]

       10. lower-*.f64 30.5%

           \[\leadsto \left(x \cdot \left(\frac{\sqrt{z + z}}{x} \cdot \color{blue}{\left(-y\right)}\right)\right) \cdot 1 \]

   11. Applied rewrites 30.5%

       \[\leadsto \left(x \cdot \color{blue}{\left(\frac{\sqrt{z + z}}{x} \cdot \left(-y\right)\right)}\right) \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 57.2% accurate, 4.7× speedup

Math

\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (* (- (* x 0.5) y) (* (sqrt (+ z z)) 1.0)))

C

double code(double x, double y, double z, double t) {
	return ((x * 0.5) - y) * (sqrt((z + z)) * 1.0);
}

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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x * 0.5d0) - y) * (sqrt((z + z)) * 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x * 0.5) - y) * (Math.sqrt((z + z)) * 1.0);
}

Python

def code(x, y, z, t):
	return ((x * 0.5) - y) * (math.sqrt((z + z)) * 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x * 0.5) - y) * Float64(sqrt(Float64(z + z)) * 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x * 0.5) - y) * (sqrt((z + z)) * 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[(N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

2. Taylor expanded in t around 0

   \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
3. Step-by-step derivation

4. Applied rewrites 57.2%

   \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot 1} \]

   2. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x \cdot \frac{1}{2} - y\right) \cdot \sqrt{z \cdot 2}\right)} \cdot 1 \]

   3. associate-*l* N/A

      \[\leadsto \color{blue}{\left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

   5. *-commutative N/A

      \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

   6. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

   7. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot x - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right)} \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{\frac{1}{2} \cdot x} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

   10. lift-*.f64 N/A

       \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot 1\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z \cdot 2}} \cdot 1\right) \]

   12. *-commutative N/A

       \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

   13. lift-*.f64 N/A

       \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

   14. lower-*.f64 57.2%

       \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\sqrt{2 \cdot z} \cdot 1\right)} \]

   15. lift-*.f64 N/A

       \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{2 \cdot z}} \cdot 1\right) \]

   16. count-2-rev N/A

       \[\leadsto \left(x \cdot \frac{1}{2} - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

   17. lift-+.f64 57.2%

       \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{\color{blue}{z + z}} \cdot 1\right) \]

6. Applied rewrites 57.2%

   \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z + z} \cdot 1\right)} \]
7. Add Preprocessing

Alternative 17: 44.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} t_1 := \left(0.5 \cdot \left(x \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\left(\sqrt{z + z} \cdot \left(-y\right)\right) \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (* 0.5 (* x (sqrt (* 2.0 z)))) 1.0)))
  (if (<= x -3.5e+47)
    t_1
    (if (<= x 4.2e-24) (* (* (sqrt (+ z z)) (- y)) 1.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (0.5 * (x * sqrt((2.0 * z)))) * 1.0;
	double tmp;
	if (x <= -3.5e+47) {
		tmp = t_1;
	} else if (x <= 4.2e-24) {
		tmp = (sqrt((z + z)) * -y) * 1.0;
	} else {
		tmp = t_1;
	}
	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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (0.5d0 * (x * sqrt((2.0d0 * z)))) * 1.0d0
    if (x <= (-3.5d+47)) then
        tmp = t_1
    else if (x <= 4.2d-24) then
        tmp = (sqrt((z + z)) * -y) * 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (0.5 * (x * Math.sqrt((2.0 * z)))) * 1.0;
	double tmp;
	if (x <= -3.5e+47) {
		tmp = t_1;
	} else if (x <= 4.2e-24) {
		tmp = (Math.sqrt((z + z)) * -y) * 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (0.5 * (x * math.sqrt((2.0 * z)))) * 1.0
	tmp = 0
	if x <= -3.5e+47:
		tmp = t_1
	elif x <= 4.2e-24:
		tmp = (math.sqrt((z + z)) * -y) * 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(0.5 * Float64(x * sqrt(Float64(2.0 * z)))) * 1.0)
	tmp = 0.0
	if (x <= -3.5e+47)
		tmp = t_1;
	elseif (x <= 4.2e-24)
		tmp = Float64(Float64(sqrt(Float64(z + z)) * Float64(-y)) * 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (0.5 * (x * sqrt((2.0 * z)))) * 1.0;
	tmp = 0.0;
	if (x <= -3.5e+47)
		tmp = t_1;
	elseif (x <= 4.2e-24)
		tmp = (sqrt((z + z)) * -y) * 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(0.5 * N[(x * N[Sqrt[N[(2.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -3.5e+47], t$95$1, If[LessEqual[x, 4.2e-24], N[(N[(N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision] * (-y)), $MachinePrecision] * 1.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000002e47 or 4.1999999999999999e-24 < x

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \left(x \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{2} \cdot \color{blue}{\left(x \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{2} \cdot \left(x \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-sqrt.f64 N/A

         \[\leadsto \left(\frac{1}{2} \cdot \left(x \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-*.f64 30.4%

         \[\leadsto \left(0.5 \cdot \left(x \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 30.4%

      \[\leadsto \color{blue}{\left(0.5 \cdot \left(x \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]

   if -3.5000000000000002e47 < x < 4.1999999999999999e-24

   1. Initial program 99.5%

      \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.2%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

      3. lower-sqrt.f64 N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. lower-*.f64 29.7%

         \[\leadsto \left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   7. Applied rewrites 29.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

      4. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\sqrt{2 \cdot z} \cdot y\right)\right) \cdot 1 \]

      5. lift-sqrt.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\sqrt{2 \cdot z} \cdot y\right)\right) \cdot 1 \]

      6. pow1/2 N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      8. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      9. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      10. count-2-rev N/A

          \[\leadsto \left(\mathsf{neg}\left({\left(z + z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      11. lift-+.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left({\left(z + z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

      12. pow1/2 N/A

          \[\leadsto \left(\mathsf{neg}\left(\sqrt{z + z} \cdot y\right)\right) \cdot 1 \]

      13. lift-sqrt.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(\sqrt{z + z} \cdot y\right)\right) \cdot 1 \]

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

          \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \cdot 1 \]

      15. lower-*.f64 N/A

          \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \cdot 1 \]

      16. lower-neg.f64 29.7%

          \[\leadsto \left(\sqrt{z + z} \cdot \left(-y\right)\right) \cdot 1 \]

   9. Applied rewrites 29.7%

      \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(-y\right)}\right) \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 29.7% accurate, 5.8× speedup

Math

\[\left(\sqrt{z + z} \cdot \left(-y\right)\right) \cdot 1 \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (* (* (sqrt (+ z z)) (- y)) 1.0))

C

double code(double x, double y, double z, double t) {
	return (sqrt((z + z)) * -y) * 1.0;
}

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(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (sqrt((z + z)) * -y) * 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return (Math.sqrt((z + z)) * -y) * 1.0;
}

Python

def code(x, y, z, t):
	return (math.sqrt((z + z)) * -y) * 1.0

Julia

function code(x, y, z, t)
	return Float64(Float64(sqrt(Float64(z + z)) * Float64(-y)) * 1.0)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (sqrt((z + z)) * -y) * 1.0;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[Sqrt[N[(z + z), $MachinePrecision]], $MachinePrecision] * (-y)), $MachinePrecision] * 1.0), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

2. Taylor expanded in t around 0

   \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]
3. Step-by-step derivation

4. Applied rewrites 57.2%

   \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

   2. lower-*.f64 N/A

      \[\leadsto \left(-1 \cdot \left(y \cdot \color{blue}{\sqrt{2 \cdot z}}\right)\right) \cdot 1 \]

   3. lower-sqrt.f64 N/A

      \[\leadsto \left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   4. lower-*.f64 29.7%

      \[\leadsto \left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

7. Applied rewrites 29.7%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \sqrt{2 \cdot z}\right)\right)} \cdot 1 \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot \sqrt{2 \cdot z}\right)}\right) \cdot 1 \]

   2. mul-1-neg N/A

      \[\leadsto \left(\mathsf{neg}\left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   3. lift-*.f64 N/A

      \[\leadsto \left(\mathsf{neg}\left(y \cdot \sqrt{2 \cdot z}\right)\right) \cdot 1 \]

   4. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left(\sqrt{2 \cdot z} \cdot y\right)\right) \cdot 1 \]

   5. lift-sqrt.f64 N/A

      \[\leadsto \left(\mathsf{neg}\left(\sqrt{2 \cdot z} \cdot y\right)\right) \cdot 1 \]

   6. pow1/2 N/A

      \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

   8. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left({\left(z \cdot 2\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

   9. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left({\left(2 \cdot z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

   10. count-2-rev N/A

       \[\leadsto \left(\mathsf{neg}\left({\left(z + z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

   11. lift-+.f64 N/A

       \[\leadsto \left(\mathsf{neg}\left({\left(z + z\right)}^{\frac{1}{2}} \cdot y\right)\right) \cdot 1 \]

   12. pow1/2 N/A

       \[\leadsto \left(\mathsf{neg}\left(\sqrt{z + z} \cdot y\right)\right) \cdot 1 \]

   13. lift-sqrt.f64 N/A

       \[\leadsto \left(\mathsf{neg}\left(\sqrt{z + z} \cdot y\right)\right) \cdot 1 \]

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

       \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \cdot 1 \]

   15. lower-*.f64 N/A

       \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \cdot 1 \]

   16. lower-neg.f64 29.7%

       \[\leadsto \left(\sqrt{z + z} \cdot \left(-y\right)\right) \cdot 1 \]

9. Applied rewrites 29.7%

   \[\leadsto \left(\sqrt{z + z} \cdot \color{blue}{\left(-y\right)}\right) \cdot 1 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"
  :precision binary64
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))