(/ z1 (+ (* z1 (- z0 -1)) (* (* (sqrt (- (- 1 z1) z1)) 5641895665989011/10000000000000000) (exp (* (- z1) z1)))))

Percentage Accurate: 91.9% → 99.3%

Time: 2.4s

Alternatives: 10

Speedup: 0.4×

Specification

Math

\[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (/
 z1
 (+
  (* z1 (- z0 -1.0))
  (*
   (* (sqrt (- (- 1.0 z1) z1)) 0.5641895665989011)
   (exp (* (- z1) z1))))))

C

double code(double z1, double z0) {
	return z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
}

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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    code = z1 / ((z1 * (z0 - (-1.0d0))) + ((sqrt(((1.0d0 - z1) - z1)) * 0.5641895665989011d0) * exp((-z1 * z1))))
end function

Java

public static double code(double z1, double z0) {
	return z1 / ((z1 * (z0 - -1.0)) + ((Math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * Math.exp((-z1 * z1))));
}

Python

def code(z1, z0):
	return z1 / ((z1 * (z0 - -1.0)) + ((math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * math.exp((-z1 * z1))))

Julia

function code(z1, z0)
	return Float64(z1 / Float64(Float64(z1 * Float64(z0 - -1.0)) + Float64(Float64(sqrt(Float64(Float64(1.0 - z1) - z1)) * 0.5641895665989011) * exp(Float64(Float64(-z1) * z1)))))
end

MATLAB

function tmp = code(z1, z0)
	tmp = z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
end

Wolfram

code[z1_, z0_] := N[(z1 / N[(N[(z1 * N[(z0 - -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision] * 0.5641895665989011), $MachinePrecision] * N[Exp[N[((-z1) * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.9% accurate, 1.0× speedup

Math

\[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (/
 z1
 (+
  (* z1 (- z0 -1.0))
  (*
   (* (sqrt (- (- 1.0 z1) z1)) 0.5641895665989011)
   (exp (* (- z1) z1))))))

C

double code(double z1, double z0) {
	return z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
}

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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    code = z1 / ((z1 * (z0 - (-1.0d0))) + ((sqrt(((1.0d0 - z1) - z1)) * 0.5641895665989011d0) * exp((-z1 * z1))))
end function

Java

public static double code(double z1, double z0) {
	return z1 / ((z1 * (z0 - -1.0)) + ((Math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * Math.exp((-z1 * z1))));
}

Python

def code(z1, z0):
	return z1 / ((z1 * (z0 - -1.0)) + ((math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * math.exp((-z1 * z1))))

Julia

function code(z1, z0)
	return Float64(z1 / Float64(Float64(z1 * Float64(z0 - -1.0)) + Float64(Float64(sqrt(Float64(Float64(1.0 - z1) - z1)) * 0.5641895665989011) * exp(Float64(Float64(-z1) * z1)))))
end

MATLAB

function tmp = code(z1, z0)
	tmp = z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
end

Wolfram

code[z1_, z0_] := N[(z1 / N[(N[(z1 * N[(z0 - -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision] * 0.5641895665989011), $MachinePrecision] * N[Exp[N[((-z1) * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := e^{\left(-z1\right) \cdot z1}\\ t_1 := \sqrt{\left(1 - z1\right) - z1}\\ t_2 := \frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(t\_1 \cdot 0.5641895665989011\right) \cdot t\_0}\\ t_3 := \frac{1}{\frac{t\_0 \cdot \left(0.5641895665989011 \cdot t\_1\right) - \left(-1 - z0\right) \cdot z1}{z1}}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-304}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (let* ((t_0 (exp (* (- z1) z1)))
       (t_1 (sqrt (- (- 1.0 z1) z1)))
       (t_2
        (/
         z1
         (+ (* z1 (- z0 -1.0)) (* (* t_1 0.5641895665989011) t_0))))
       (t_3
        (/
         1.0
         (/
          (- (* t_0 (* 0.5641895665989011 t_1)) (* (- -1.0 z0) z1))
          z1))))
  (if (<= t_2 -1e-304) t_3 (if (<= t_2 0.0) (/ 1.0 z0) t_3))))

C

double code(double z1, double z0) {
	double t_0 = exp((-z1 * z1));
	double t_1 = sqrt(((1.0 - z1) - z1));
	double t_2 = z1 / ((z1 * (z0 - -1.0)) + ((t_1 * 0.5641895665989011) * t_0));
	double t_3 = 1.0 / (((t_0 * (0.5641895665989011 * t_1)) - ((-1.0 - z0) * z1)) / z1);
	double tmp;
	if (t_2 <= -1e-304) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = 1.0 / z0;
	} else {
		tmp = t_3;
	}
	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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = exp((-z1 * z1))
    t_1 = sqrt(((1.0d0 - z1) - z1))
    t_2 = z1 / ((z1 * (z0 - (-1.0d0))) + ((t_1 * 0.5641895665989011d0) * t_0))
    t_3 = 1.0d0 / (((t_0 * (0.5641895665989011d0 * t_1)) - (((-1.0d0) - z0) * z1)) / z1)
    if (t_2 <= (-1d-304)) then
        tmp = t_3
    else if (t_2 <= 0.0d0) then
        tmp = 1.0d0 / z0
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double t_0 = Math.exp((-z1 * z1));
	double t_1 = Math.sqrt(((1.0 - z1) - z1));
	double t_2 = z1 / ((z1 * (z0 - -1.0)) + ((t_1 * 0.5641895665989011) * t_0));
	double t_3 = 1.0 / (((t_0 * (0.5641895665989011 * t_1)) - ((-1.0 - z0) * z1)) / z1);
	double tmp;
	if (t_2 <= -1e-304) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = 1.0 / z0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(z1, z0):
	t_0 = math.exp((-z1 * z1))
	t_1 = math.sqrt(((1.0 - z1) - z1))
	t_2 = z1 / ((z1 * (z0 - -1.0)) + ((t_1 * 0.5641895665989011) * t_0))
	t_3 = 1.0 / (((t_0 * (0.5641895665989011 * t_1)) - ((-1.0 - z0) * z1)) / z1)
	tmp = 0
	if t_2 <= -1e-304:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = 1.0 / z0
	else:
		tmp = t_3
	return tmp

Julia

function code(z1, z0)
	t_0 = exp(Float64(Float64(-z1) * z1))
	t_1 = sqrt(Float64(Float64(1.0 - z1) - z1))
	t_2 = Float64(z1 / Float64(Float64(z1 * Float64(z0 - -1.0)) + Float64(Float64(t_1 * 0.5641895665989011) * t_0)))
	t_3 = Float64(1.0 / Float64(Float64(Float64(t_0 * Float64(0.5641895665989011 * t_1)) - Float64(Float64(-1.0 - z0) * z1)) / z1))
	tmp = 0.0
	if (t_2 <= -1e-304)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(1.0 / z0);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	t_0 = exp((-z1 * z1));
	t_1 = sqrt(((1.0 - z1) - z1));
	t_2 = z1 / ((z1 * (z0 - -1.0)) + ((t_1 * 0.5641895665989011) * t_0));
	t_3 = 1.0 / (((t_0 * (0.5641895665989011 * t_1)) - ((-1.0 - z0) * z1)) / z1);
	tmp = 0.0;
	if (t_2 <= -1e-304)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = 1.0 / z0;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := Block[{t$95$0 = N[Exp[N[((-z1) * z1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(z1 / N[(N[(z1 * N[(z0 - -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * 0.5641895665989011), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 / N[(N[(N[(t$95$0 * N[(0.5641895665989011 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(-1.0 - z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-304], t$95$3, If[LessEqual[t$95$2, 0.0], N[(1.0 / z0), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < -9.9999999999999997e-305 or 0.0 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1)))))

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot \frac{5641895665989011}{10000000000000000}\right) \cdot e^{\left(-z1\right) \cdot z1}}} \]

      2. div-flip N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot \frac{5641895665989011}{10000000000000000}\right) \cdot e^{\left(-z1\right) \cdot z1}}{z1}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot \frac{5641895665989011}{10000000000000000}\right) \cdot e^{\left(-z1\right) \cdot z1}}{z1}}} \]

      4. lower-unsound-/.f64 91.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}}{z1}}} \]

   3. Applied rewrites 91.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{e^{\left(-z1\right) \cdot z1} \cdot \left(0.5641895665989011 \cdot \sqrt{\left(1 - z1\right) - z1}\right) - \left(-1 - z0\right) \cdot z1}{z1}}} \]

   if -9.9999999999999997e-305 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < 0.0

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 33.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-304}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (let* ((t_0
        (/
         z1
         (+
          (* z1 (- z0 -1.0))
          (*
           (* (sqrt (- (- 1.0 z1) z1)) 0.5641895665989011)
           (exp (* (- z1) z1)))))))
  (if (<= t_0 -1e-304) t_0 (if (<= t_0 0.0) (/ 1.0 z0) t_0))))

C

double code(double z1, double z0) {
	double t_0 = z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
	double tmp;
	if (t_0 <= -1e-304) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = 1.0 / z0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z1 / ((z1 * (z0 - (-1.0d0))) + ((sqrt(((1.0d0 - z1) - z1)) * 0.5641895665989011d0) * exp((-z1 * z1))))
    if (t_0 <= (-1d-304)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = 1.0d0 / z0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double t_0 = z1 / ((z1 * (z0 - -1.0)) + ((Math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * Math.exp((-z1 * z1))));
	double tmp;
	if (t_0 <= -1e-304) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = 1.0 / z0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z1, z0):
	t_0 = z1 / ((z1 * (z0 - -1.0)) + ((math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * math.exp((-z1 * z1))))
	tmp = 0
	if t_0 <= -1e-304:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = 1.0 / z0
	else:
		tmp = t_0
	return tmp

Julia

function code(z1, z0)
	t_0 = Float64(z1 / Float64(Float64(z1 * Float64(z0 - -1.0)) + Float64(Float64(sqrt(Float64(Float64(1.0 - z1) - z1)) * 0.5641895665989011) * exp(Float64(Float64(-z1) * z1)))))
	tmp = 0.0
	if (t_0 <= -1e-304)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(1.0 / z0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	t_0 = z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
	tmp = 0.0;
	if (t_0 <= -1e-304)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = 1.0 / z0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := Block[{t$95$0 = N[(z1 / N[(N[(z1 * N[(z0 - -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision] * 0.5641895665989011), $MachinePrecision] * N[Exp[N[((-z1) * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-304], t$95$0, If[LessEqual[t$95$0, 0.0], N[(1.0 / z0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < -9.9999999999999997e-305 or 0.0 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1)))))

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   if -9.9999999999999997e-305 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < 0.0

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 33.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-304}:\\ \;\;\;\;\frac{z1}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + z0\right)}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1 \cdot 0.5641895665989011 - \left(-1 - z0\right) \cdot z1}{z1}}\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (let* ((t_0
        (/
         z1
         (+
          (* z1 (- z0 -1.0))
          (*
           (* (sqrt (- (- 1.0 z1) z1)) 0.5641895665989011)
           (exp (* (- z1) z1)))))))
  (if (<= t_0 -1e-304)
    (/ z1 (+ 0.5641895665989011 (* z1 (+ 0.4358104334010989 z0))))
    (if (<= t_0 0.0)
      (/ 1.0 z0)
      (/
       1.0
       (/ (- (* 1.0 0.5641895665989011) (* (- -1.0 z0) z1)) z1))))))

C

double code(double z1, double z0) {
	double t_0 = z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
	double tmp;
	if (t_0 <= -1e-304) {
		tmp = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)));
	} else if (t_0 <= 0.0) {
		tmp = 1.0 / z0;
	} else {
		tmp = 1.0 / (((1.0 * 0.5641895665989011) - ((-1.0 - z0) * z1)) / z1);
	}
	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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z1 / ((z1 * (z0 - (-1.0d0))) + ((sqrt(((1.0d0 - z1) - z1)) * 0.5641895665989011d0) * exp((-z1 * z1))))
    if (t_0 <= (-1d-304)) then
        tmp = z1 / (0.5641895665989011d0 + (z1 * (0.4358104334010989d0 + z0)))
    else if (t_0 <= 0.0d0) then
        tmp = 1.0d0 / z0
    else
        tmp = 1.0d0 / (((1.0d0 * 0.5641895665989011d0) - (((-1.0d0) - z0) * z1)) / z1)
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double t_0 = z1 / ((z1 * (z0 - -1.0)) + ((Math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * Math.exp((-z1 * z1))));
	double tmp;
	if (t_0 <= -1e-304) {
		tmp = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)));
	} else if (t_0 <= 0.0) {
		tmp = 1.0 / z0;
	} else {
		tmp = 1.0 / (((1.0 * 0.5641895665989011) - ((-1.0 - z0) * z1)) / z1);
	}
	return tmp;
}

Python

def code(z1, z0):
	t_0 = z1 / ((z1 * (z0 - -1.0)) + ((math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * math.exp((-z1 * z1))))
	tmp = 0
	if t_0 <= -1e-304:
		tmp = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)))
	elif t_0 <= 0.0:
		tmp = 1.0 / z0
	else:
		tmp = 1.0 / (((1.0 * 0.5641895665989011) - ((-1.0 - z0) * z1)) / z1)
	return tmp

Julia

function code(z1, z0)
	t_0 = Float64(z1 / Float64(Float64(z1 * Float64(z0 - -1.0)) + Float64(Float64(sqrt(Float64(Float64(1.0 - z1) - z1)) * 0.5641895665989011) * exp(Float64(Float64(-z1) * z1)))))
	tmp = 0.0
	if (t_0 <= -1e-304)
		tmp = Float64(z1 / Float64(0.5641895665989011 + Float64(z1 * Float64(0.4358104334010989 + z0))));
	elseif (t_0 <= 0.0)
		tmp = Float64(1.0 / z0);
	else
		tmp = Float64(1.0 / Float64(Float64(Float64(1.0 * 0.5641895665989011) - Float64(Float64(-1.0 - z0) * z1)) / z1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	t_0 = z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
	tmp = 0.0;
	if (t_0 <= -1e-304)
		tmp = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)));
	elseif (t_0 <= 0.0)
		tmp = 1.0 / z0;
	else
		tmp = 1.0 / (((1.0 * 0.5641895665989011) - ((-1.0 - z0) * z1)) / z1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := Block[{t$95$0 = N[(z1 / N[(N[(z1 * N[(z0 - -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision] * 0.5641895665989011), $MachinePrecision] * N[Exp[N[((-z1) * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-304], N[(z1 / N[(0.5641895665989011 + N[(z1 * N[(0.4358104334010989 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(1.0 / z0), $MachinePrecision], N[(1.0 / N[(N[(N[(1.0 * 0.5641895665989011), $MachinePrecision] - N[(N[(-1.0 - z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < -9.9999999999999997e-305

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1}{\color{blue}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + \color{blue}{z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \color{blue}{\left(\frac{4358104334010989}{10000000000000000} + z0\right)}} \]

      3. lower-+.f64 77.2%

         \[\leadsto \frac{z1}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)} \]

   4. Applied rewrites 77.2%

      \[\leadsto \frac{z1}{\color{blue}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + z0\right)}} \]

   if -9.9999999999999997e-305 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < 0.0

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 33.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if 0.0 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1)))))

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1}{z1 \cdot \left(z0 - -1\right) + \color{blue}{\frac{5641895665989011}{10000000000000000}} \cdot e^{\left(-z1\right) \cdot z1}} \]
   3. Step-by-step derivation

   4. Applied rewrites 91.2%

      \[\leadsto \frac{z1}{z1 \cdot \left(z0 - -1\right) + \color{blue}{0.5641895665989011} \cdot e^{\left(-z1\right) \cdot z1}} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1}{z1 \cdot \left(z0 - -1\right) + 0.5641895665989011 \cdot \color{blue}{1}} \]
   6. Step-by-step derivation

   7. Applied rewrites 90.8%

      \[\leadsto \frac{z1}{z1 \cdot \left(z0 - -1\right) + 0.5641895665989011 \cdot \color{blue}{1}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z1}{z1 \cdot \left(z0 - -1\right) + \frac{5641895665989011}{10000000000000000} \cdot 1}} \]

      2. div-flip N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z1 \cdot \left(z0 - -1\right) + \frac{5641895665989011}{10000000000000000} \cdot 1}{z1}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z1 \cdot \left(z0 - -1\right) + \frac{5641895665989011}{10000000000000000} \cdot 1}{z1}}} \]

      4. lower-unsound-/.f64 90.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{z1 \cdot \left(z0 - -1\right) + 0.5641895665989011 \cdot 1}{z1}}} \]

   9. Applied rewrites 90.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{1 \cdot 0.5641895665989011 - \left(-1 - z0\right) \cdot z1}{z1}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := z1 \cdot \left(z0 - -1\right)\\ t_1 := \frac{z1}{t\_0 + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-304}:\\ \;\;\;\;\frac{z1}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + z0\right)}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{else}:\\ \;\;\;\;\frac{z1}{t\_0 + 0.5641895665989011 \cdot 1}\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (let* ((t_0 (* z1 (- z0 -1.0)))
       (t_1
        (/
         z1
         (+
          t_0
          (*
           (* (sqrt (- (- 1.0 z1) z1)) 0.5641895665989011)
           (exp (* (- z1) z1)))))))
  (if (<= t_1 -1e-304)
    (/ z1 (+ 0.5641895665989011 (* z1 (+ 0.4358104334010989 z0))))
    (if (<= t_1 0.0)
      (/ 1.0 z0)
      (/ z1 (+ t_0 (* 0.5641895665989011 1.0)))))))

C

double code(double z1, double z0) {
	double t_0 = z1 * (z0 - -1.0);
	double t_1 = z1 / (t_0 + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
	double tmp;
	if (t_1 <= -1e-304) {
		tmp = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)));
	} else if (t_1 <= 0.0) {
		tmp = 1.0 / z0;
	} else {
		tmp = z1 / (t_0 + (0.5641895665989011 * 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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z1 * (z0 - (-1.0d0))
    t_1 = z1 / (t_0 + ((sqrt(((1.0d0 - z1) - z1)) * 0.5641895665989011d0) * exp((-z1 * z1))))
    if (t_1 <= (-1d-304)) then
        tmp = z1 / (0.5641895665989011d0 + (z1 * (0.4358104334010989d0 + z0)))
    else if (t_1 <= 0.0d0) then
        tmp = 1.0d0 / z0
    else
        tmp = z1 / (t_0 + (0.5641895665989011d0 * 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double t_0 = z1 * (z0 - -1.0);
	double t_1 = z1 / (t_0 + ((Math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * Math.exp((-z1 * z1))));
	double tmp;
	if (t_1 <= -1e-304) {
		tmp = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)));
	} else if (t_1 <= 0.0) {
		tmp = 1.0 / z0;
	} else {
		tmp = z1 / (t_0 + (0.5641895665989011 * 1.0));
	}
	return tmp;
}

Python

def code(z1, z0):
	t_0 = z1 * (z0 - -1.0)
	t_1 = z1 / (t_0 + ((math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * math.exp((-z1 * z1))))
	tmp = 0
	if t_1 <= -1e-304:
		tmp = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)))
	elif t_1 <= 0.0:
		tmp = 1.0 / z0
	else:
		tmp = z1 / (t_0 + (0.5641895665989011 * 1.0))
	return tmp

Julia

function code(z1, z0)
	t_0 = Float64(z1 * Float64(z0 - -1.0))
	t_1 = Float64(z1 / Float64(t_0 + Float64(Float64(sqrt(Float64(Float64(1.0 - z1) - z1)) * 0.5641895665989011) * exp(Float64(Float64(-z1) * z1)))))
	tmp = 0.0
	if (t_1 <= -1e-304)
		tmp = Float64(z1 / Float64(0.5641895665989011 + Float64(z1 * Float64(0.4358104334010989 + z0))));
	elseif (t_1 <= 0.0)
		tmp = Float64(1.0 / z0);
	else
		tmp = Float64(z1 / Float64(t_0 + Float64(0.5641895665989011 * 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	t_0 = z1 * (z0 - -1.0);
	t_1 = z1 / (t_0 + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
	tmp = 0.0;
	if (t_1 <= -1e-304)
		tmp = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)));
	elseif (t_1 <= 0.0)
		tmp = 1.0 / z0;
	else
		tmp = z1 / (t_0 + (0.5641895665989011 * 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := Block[{t$95$0 = N[(z1 * N[(z0 - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z1 / N[(t$95$0 + N[(N[(N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision] * 0.5641895665989011), $MachinePrecision] * N[Exp[N[((-z1) * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-304], N[(z1 / N[(0.5641895665989011 + N[(z1 * N[(0.4358104334010989 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(1.0 / z0), $MachinePrecision], N[(z1 / N[(t$95$0 + N[(0.5641895665989011 * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < -9.9999999999999997e-305

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1}{\color{blue}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + \color{blue}{z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \color{blue}{\left(\frac{4358104334010989}{10000000000000000} + z0\right)}} \]

      3. lower-+.f64 77.2%

         \[\leadsto \frac{z1}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)} \]

   4. Applied rewrites 77.2%

      \[\leadsto \frac{z1}{\color{blue}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + z0\right)}} \]

   if -9.9999999999999997e-305 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < 0.0

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 33.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if 0.0 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1)))))

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1}{z1 \cdot \left(z0 - -1\right) + \color{blue}{\frac{5641895665989011}{10000000000000000}} \cdot e^{\left(-z1\right) \cdot z1}} \]
   3. Step-by-step derivation

   4. Applied rewrites 91.2%

      \[\leadsto \frac{z1}{z1 \cdot \left(z0 - -1\right) + \color{blue}{0.5641895665989011} \cdot e^{\left(-z1\right) \cdot z1}} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1}{z1 \cdot \left(z0 - -1\right) + 0.5641895665989011 \cdot \color{blue}{1}} \]
   6. Step-by-step derivation

   7. Applied rewrites 90.8%

      \[\leadsto \frac{z1}{z1 \cdot \left(z0 - -1\right) + 0.5641895665989011 \cdot \color{blue}{1}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}}\\ t_1 := \frac{z1}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + z0\right)}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (let* ((t_0
        (/
         z1
         (+
          (* z1 (- z0 -1.0))
          (*
           (* (sqrt (- (- 1.0 z1) z1)) 0.5641895665989011)
           (exp (* (- z1) z1))))))
       (t_1
        (/
         z1
         (+ 0.5641895665989011 (* z1 (+ 0.4358104334010989 z0))))))
  (if (<= t_0 -1e-304) t_1 (if (<= t_0 0.0) (/ 1.0 z0) t_1))))

C

double code(double z1, double z0) {
	double t_0 = z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
	double t_1 = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)));
	double tmp;
	if (t_0 <= -1e-304) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 1.0 / z0;
	} 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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z1 / ((z1 * (z0 - (-1.0d0))) + ((sqrt(((1.0d0 - z1) - z1)) * 0.5641895665989011d0) * exp((-z1 * z1))))
    t_1 = z1 / (0.5641895665989011d0 + (z1 * (0.4358104334010989d0 + z0)))
    if (t_0 <= (-1d-304)) then
        tmp = t_1
    else if (t_0 <= 0.0d0) then
        tmp = 1.0d0 / z0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double t_0 = z1 / ((z1 * (z0 - -1.0)) + ((Math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * Math.exp((-z1 * z1))));
	double t_1 = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)));
	double tmp;
	if (t_0 <= -1e-304) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 1.0 / z0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z1, z0):
	t_0 = z1 / ((z1 * (z0 - -1.0)) + ((math.sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * math.exp((-z1 * z1))))
	t_1 = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)))
	tmp = 0
	if t_0 <= -1e-304:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = 1.0 / z0
	else:
		tmp = t_1
	return tmp

Julia

function code(z1, z0)
	t_0 = Float64(z1 / Float64(Float64(z1 * Float64(z0 - -1.0)) + Float64(Float64(sqrt(Float64(Float64(1.0 - z1) - z1)) * 0.5641895665989011) * exp(Float64(Float64(-z1) * z1)))))
	t_1 = Float64(z1 / Float64(0.5641895665989011 + Float64(z1 * Float64(0.4358104334010989 + z0))))
	tmp = 0.0
	if (t_0 <= -1e-304)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(1.0 / z0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	t_0 = z1 / ((z1 * (z0 - -1.0)) + ((sqrt(((1.0 - z1) - z1)) * 0.5641895665989011) * exp((-z1 * z1))));
	t_1 = z1 / (0.5641895665989011 + (z1 * (0.4358104334010989 + z0)));
	tmp = 0.0;
	if (t_0 <= -1e-304)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = 1.0 / z0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := Block[{t$95$0 = N[(z1 / N[(N[(z1 * N[(z0 - -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sqrt[N[(N[(1.0 - z1), $MachinePrecision] - z1), $MachinePrecision]], $MachinePrecision] * 0.5641895665989011), $MachinePrecision] * N[Exp[N[((-z1) * z1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z1 / N[(0.5641895665989011 + N[(z1 * N[(0.4358104334010989 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-304], t$95$1, If[LessEqual[t$95$0, 0.0], N[(1.0 / z0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < -9.9999999999999997e-305 or 0.0 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1)))))

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1}{\color{blue}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + \color{blue}{z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \color{blue}{\left(\frac{4358104334010989}{10000000000000000} + z0\right)}} \]

      3. lower-+.f64 77.2%

         \[\leadsto \frac{z1}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)} \]

   4. Applied rewrites 77.2%

      \[\leadsto \frac{z1}{\color{blue}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + z0\right)}} \]

   if -9.9999999999999997e-305 < (/.f64 z1 (+.f64 (*.f64 z1 (-.f64 z0 #s(literal -1 binary64))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) z1) z1)) #s(literal 5641895665989011/10000000000000000 binary64)) (exp.f64 (*.f64 (neg.f64 z1) z1))))) < 0.0

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 33.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 69.9% accurate, 4.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z0 \leq -2.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{elif}\;z0 \leq 3.4 \cdot 10^{+120}:\\ \;\;\;\;\frac{z1}{0.5641895665989011 + z1 \cdot 0.4358104334010989}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z0}\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (if (<= z0 -2.8e+152)
  (/ 1.0 z0)
  (if (<= z0 3.4e+120)
    (/ z1 (+ 0.5641895665989011 (* z1 0.4358104334010989)))
    (/ 1.0 z0))))

C

double code(double z1, double z0) {
	double tmp;
	if (z0 <= -2.8e+152) {
		tmp = 1.0 / z0;
	} else if (z0 <= 3.4e+120) {
		tmp = z1 / (0.5641895665989011 + (z1 * 0.4358104334010989));
	} else {
		tmp = 1.0 / z0;
	}
	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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: tmp
    if (z0 <= (-2.8d+152)) then
        tmp = 1.0d0 / z0
    else if (z0 <= 3.4d+120) then
        tmp = z1 / (0.5641895665989011d0 + (z1 * 0.4358104334010989d0))
    else
        tmp = 1.0d0 / z0
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double tmp;
	if (z0 <= -2.8e+152) {
		tmp = 1.0 / z0;
	} else if (z0 <= 3.4e+120) {
		tmp = z1 / (0.5641895665989011 + (z1 * 0.4358104334010989));
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Python

def code(z1, z0):
	tmp = 0
	if z0 <= -2.8e+152:
		tmp = 1.0 / z0
	elif z0 <= 3.4e+120:
		tmp = z1 / (0.5641895665989011 + (z1 * 0.4358104334010989))
	else:
		tmp = 1.0 / z0
	return tmp

Julia

function code(z1, z0)
	tmp = 0.0
	if (z0 <= -2.8e+152)
		tmp = Float64(1.0 / z0);
	elseif (z0 <= 3.4e+120)
		tmp = Float64(z1 / Float64(0.5641895665989011 + Float64(z1 * 0.4358104334010989)));
	else
		tmp = Float64(1.0 / z0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	tmp = 0.0;
	if (z0 <= -2.8e+152)
		tmp = 1.0 / z0;
	elseif (z0 <= 3.4e+120)
		tmp = z1 / (0.5641895665989011 + (z1 * 0.4358104334010989));
	else
		tmp = 1.0 / z0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := If[LessEqual[z0, -2.8e+152], N[(1.0 / z0), $MachinePrecision], If[LessEqual[z0, 3.4e+120], N[(z1 / N[(0.5641895665989011 + N[(z1 * 0.4358104334010989), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / z0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z0 < -2.8000000000000002e152 or 3.4e120 < z0

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 33.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if -2.8000000000000002e152 < z0 < 3.4e120

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1}{\color{blue}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + \left(z0 + \frac{-16925686997967033}{20000000000000000} \cdot z1\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + \color{blue}{z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + \left(z0 + \frac{-16925686997967033}{20000000000000000} \cdot z1\right)\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \color{blue}{\left(\frac{4358104334010989}{10000000000000000} + \left(z0 + \frac{-16925686997967033}{20000000000000000} \cdot z1\right)\right)}} \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + \color{blue}{\left(z0 + \frac{-16925686997967033}{20000000000000000} \cdot z1\right)}\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + \left(z0 + \color{blue}{\frac{-16925686997967033}{20000000000000000} \cdot z1}\right)\right)} \]

      5. lower-*.f64 71.4%

         \[\leadsto \frac{z1}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + \left(z0 + -0.8462843498983517 \cdot \color{blue}{z1}\right)\right)} \]

   4. Applied rewrites 71.4%

      \[\leadsto \frac{z1}{\color{blue}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + \left(z0 + -0.8462843498983517 \cdot z1\right)\right)}} \]

   5. Taylor expanded in z0 around 0

      \[\leadsto \frac{z1}{0.5641895665989011 + z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + \color{blue}{\frac{-16925686997967033}{20000000000000000} \cdot z1}\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{z1}{\frac{5641895665989011}{10000000000000000} + z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + \frac{-16925686997967033}{20000000000000000} \cdot \color{blue}{z1}\right)} \]

      2. lower-*.f64 51.5%

         \[\leadsto \frac{z1}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + -0.8462843498983517 \cdot z1\right)} \]

   7. Applied rewrites 51.5%

      \[\leadsto \frac{z1}{0.5641895665989011 + z1 \cdot \left(0.4358104334010989 + \color{blue}{-0.8462843498983517 \cdot z1}\right)} \]

   8. Taylor expanded in z1 around 0

      \[\leadsto \frac{z1}{0.5641895665989011 + z1 \cdot \frac{4358104334010989}{10000000000000000}} \]
   9. Step-by-step derivation

   10. Applied rewrites 53.5%

       \[\leadsto \frac{z1}{0.5641895665989011 + z1 \cdot 0.4358104334010989} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 66.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z0 \leq -2.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{elif}\;z0 \leq 3.4 \cdot 10^{+120}:\\ \;\;\;\;\left(-1.369138938191455 \cdot z1\right) \cdot z1 + 1.7724539041519165 \cdot z1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z0}\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (if (<= z0 -2.8e+152)
  (/ 1.0 z0)
  (if (<= z0 3.4e+120)
    (+ (* (* -1.369138938191455 z1) z1) (* 1.7724539041519165 z1))
    (/ 1.0 z0))))

C

double code(double z1, double z0) {
	double tmp;
	if (z0 <= -2.8e+152) {
		tmp = 1.0 / z0;
	} else if (z0 <= 3.4e+120) {
		tmp = ((-1.369138938191455 * z1) * z1) + (1.7724539041519165 * z1);
	} else {
		tmp = 1.0 / z0;
	}
	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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: tmp
    if (z0 <= (-2.8d+152)) then
        tmp = 1.0d0 / z0
    else if (z0 <= 3.4d+120) then
        tmp = (((-1.369138938191455d0) * z1) * z1) + (1.7724539041519165d0 * z1)
    else
        tmp = 1.0d0 / z0
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double tmp;
	if (z0 <= -2.8e+152) {
		tmp = 1.0 / z0;
	} else if (z0 <= 3.4e+120) {
		tmp = ((-1.369138938191455 * z1) * z1) + (1.7724539041519165 * z1);
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Python

def code(z1, z0):
	tmp = 0
	if z0 <= -2.8e+152:
		tmp = 1.0 / z0
	elif z0 <= 3.4e+120:
		tmp = ((-1.369138938191455 * z1) * z1) + (1.7724539041519165 * z1)
	else:
		tmp = 1.0 / z0
	return tmp

Julia

function code(z1, z0)
	tmp = 0.0
	if (z0 <= -2.8e+152)
		tmp = Float64(1.0 / z0);
	elseif (z0 <= 3.4e+120)
		tmp = Float64(Float64(Float64(-1.369138938191455 * z1) * z1) + Float64(1.7724539041519165 * z1));
	else
		tmp = Float64(1.0 / z0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	tmp = 0.0;
	if (z0 <= -2.8e+152)
		tmp = 1.0 / z0;
	elseif (z0 <= 3.4e+120)
		tmp = ((-1.369138938191455 * z1) * z1) + (1.7724539041519165 * z1);
	else
		tmp = 1.0 / z0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := If[LessEqual[z0, -2.8e+152], N[(1.0 / z0), $MachinePrecision], If[LessEqual[z0, 3.4e+120], N[(N[(N[(-1.369138938191455 * z1), $MachinePrecision] * z1), $MachinePrecision] + N[(1.7724539041519165 * z1), $MachinePrecision]), $MachinePrecision], N[(1.0 / z0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z0 < -2.8000000000000002e152 or 3.4e120 < z0

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 33.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if -2.8000000000000002e152 < z0 < 3.4e120

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z1 \cdot \color{blue}{\left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \color{blue}{\frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \color{blue}{\left(z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z1 \cdot \color{blue}{\left(\frac{4358104334010989}{10000000000000000} + z0\right)}\right)\right) \]

      5. lower-+.f64 50.1%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.1415928423433717 \cdot \left(z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)\right)\right) \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{z1 \cdot \left(1.7724539041519165 + -3.1415928423433717 \cdot \left(z1 \cdot \left(0.4358104334010989 + z0\right)\right)\right)} \]

   5. Taylor expanded in z0 around inf

      \[\leadsto z1 \cdot \left(1.7724539041519165 + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \color{blue}{\left(z0 \cdot z1\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z0 \cdot \color{blue}{z1}\right)\right) \]

      2. lower-*.f64 49.9%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.1415928423433717 \cdot \left(z0 \cdot z1\right)\right) \]

   7. Applied rewrites 49.9%

      \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.1415928423433717 \cdot \color{blue}{\left(z0 \cdot z1\right)}\right) \]

   8. Taylor expanded in z0 around 0

      \[\leadsto z1 \cdot \left(1.7724539041519165 + \frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot \color{blue}{z1}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 50.3%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -1.369138938191455 \cdot z1\right) \]

   10. Applied rewrites 50.3%

       \[\leadsto z1 \cdot \left(1.7724539041519165 + -1.369138938191455 \cdot \color{blue}{z1}\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto z1 \cdot \color{blue}{\left(\frac{10000000000000000}{5641895665989011} + \frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot z1\right)} \]

       2. lift-+.f64 N/A

          \[\leadsto z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \color{blue}{\frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot z1}\right) \]

       3. +-commutative N/A

          \[\leadsto z1 \cdot \left(\frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot z1 + \color{blue}{\frac{10000000000000000}{5641895665989011}}\right) \]

       4. distribute-rgt-in N/A

          \[\leadsto \left(\frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot z1\right) \cdot z1 + \color{blue}{\frac{10000000000000000}{5641895665989011} \cdot z1} \]

       5. *-commutative N/A

          \[\leadsto \left(\frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot z1\right) \cdot z1 + z1 \cdot \color{blue}{\frac{10000000000000000}{5641895665989011}} \]

       6. lower-+.f64 N/A

          \[\leadsto \left(\frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot z1\right) \cdot z1 + \color{blue}{z1 \cdot \frac{10000000000000000}{5641895665989011}} \]

       7. lower-*.f64 N/A

          \[\leadsto \left(\frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot z1\right) \cdot z1 + \color{blue}{z1} \cdot \frac{10000000000000000}{5641895665989011} \]

       8. *-commutative N/A

          \[\leadsto \left(\frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot z1\right) \cdot z1 + \frac{10000000000000000}{5641895665989011} \cdot \color{blue}{z1} \]

       9. lower-*.f64 50.3%

          \[\leadsto \left(-1.369138938191455 \cdot z1\right) \cdot z1 + 1.7724539041519165 \cdot \color{blue}{z1} \]

   12. Applied rewrites 50.3%

       \[\leadsto \left(-1.369138938191455 \cdot z1\right) \cdot z1 + \color{blue}{1.7724539041519165 \cdot z1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 66.8% accurate, 4.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z0 - -1 \leq -2 \cdot 10^{+152}:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{elif}\;z0 - -1 \leq 2 \cdot 10^{+117}:\\ \;\;\;\;z1 \cdot \left(1.7724539041519165 + -1.369138938191455 \cdot z1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z0}\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (if (<= (- z0 -1.0) -2e+152)
  (/ 1.0 z0)
  (if (<= (- z0 -1.0) 2e+117)
    (* z1 (+ 1.7724539041519165 (* -1.369138938191455 z1)))
    (/ 1.0 z0))))

C

double code(double z1, double z0) {
	double tmp;
	if ((z0 - -1.0) <= -2e+152) {
		tmp = 1.0 / z0;
	} else if ((z0 - -1.0) <= 2e+117) {
		tmp = z1 * (1.7724539041519165 + (-1.369138938191455 * z1));
	} else {
		tmp = 1.0 / z0;
	}
	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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: tmp
    if ((z0 - (-1.0d0)) <= (-2d+152)) then
        tmp = 1.0d0 / z0
    else if ((z0 - (-1.0d0)) <= 2d+117) then
        tmp = z1 * (1.7724539041519165d0 + ((-1.369138938191455d0) * z1))
    else
        tmp = 1.0d0 / z0
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double tmp;
	if ((z0 - -1.0) <= -2e+152) {
		tmp = 1.0 / z0;
	} else if ((z0 - -1.0) <= 2e+117) {
		tmp = z1 * (1.7724539041519165 + (-1.369138938191455 * z1));
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Python

def code(z1, z0):
	tmp = 0
	if (z0 - -1.0) <= -2e+152:
		tmp = 1.0 / z0
	elif (z0 - -1.0) <= 2e+117:
		tmp = z1 * (1.7724539041519165 + (-1.369138938191455 * z1))
	else:
		tmp = 1.0 / z0
	return tmp

Julia

function code(z1, z0)
	tmp = 0.0
	if (Float64(z0 - -1.0) <= -2e+152)
		tmp = Float64(1.0 / z0);
	elseif (Float64(z0 - -1.0) <= 2e+117)
		tmp = Float64(z1 * Float64(1.7724539041519165 + Float64(-1.369138938191455 * z1)));
	else
		tmp = Float64(1.0 / z0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	tmp = 0.0;
	if ((z0 - -1.0) <= -2e+152)
		tmp = 1.0 / z0;
	elseif ((z0 - -1.0) <= 2e+117)
		tmp = z1 * (1.7724539041519165 + (-1.369138938191455 * z1));
	else
		tmp = 1.0 / z0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := If[LessEqual[N[(z0 - -1.0), $MachinePrecision], -2e+152], N[(1.0 / z0), $MachinePrecision], If[LessEqual[N[(z0 - -1.0), $MachinePrecision], 2e+117], N[(z1 * N[(1.7724539041519165 + N[(-1.369138938191455 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / z0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z0 #s(literal -1 binary64)) < -2.0000000000000001e152 or 2.0000000000000001e117 < (-.f64 z0 #s(literal -1 binary64))

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 33.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if -2.0000000000000001e152 < (-.f64 z0 #s(literal -1 binary64)) < 2.0000000000000001e117

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \color{blue}{z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z1 \cdot \color{blue}{\left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \color{blue}{\frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \color{blue}{\left(z1 \cdot \left(\frac{4358104334010989}{10000000000000000} + z0\right)\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z1 \cdot \color{blue}{\left(\frac{4358104334010989}{10000000000000000} + z0\right)}\right)\right) \]

      5. lower-+.f64 50.1%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.1415928423433717 \cdot \left(z1 \cdot \left(0.4358104334010989 + \color{blue}{z0}\right)\right)\right) \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{z1 \cdot \left(1.7724539041519165 + -3.1415928423433717 \cdot \left(z1 \cdot \left(0.4358104334010989 + z0\right)\right)\right)} \]

   5. Taylor expanded in z0 around inf

      \[\leadsto z1 \cdot \left(1.7724539041519165 + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \color{blue}{\left(z0 \cdot z1\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z1 \cdot \left(\frac{10000000000000000}{5641895665989011} + \frac{-100000000000000000000000000000000}{31830986705905585973052772758121} \cdot \left(z0 \cdot \color{blue}{z1}\right)\right) \]

      2. lower-*.f64 49.9%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.1415928423433717 \cdot \left(z0 \cdot z1\right)\right) \]

   7. Applied rewrites 49.9%

      \[\leadsto z1 \cdot \left(1.7724539041519165 + -3.1415928423433717 \cdot \color{blue}{\left(z0 \cdot z1\right)}\right) \]

   8. Taylor expanded in z0 around 0

      \[\leadsto z1 \cdot \left(1.7724539041519165 + \frac{-43581043340109890000000000000000}{31830986705905585973052772758121} \cdot \color{blue}{z1}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 50.3%

         \[\leadsto z1 \cdot \left(1.7724539041519165 + -1.369138938191455 \cdot z1\right) \]

   10. Applied rewrites 50.3%

       \[\leadsto z1 \cdot \left(1.7724539041519165 + -1.369138938191455 \cdot \color{blue}{z1}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 66.6% accurate, 5.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z0 - -1 \leq -2 \cdot 10^{+152}:\\ \;\;\;\;\frac{1}{z0}\\ \mathbf{elif}\;z0 - -1 \leq 2 \cdot 10^{+117}:\\ \;\;\;\;1.7724539041519165 \cdot z1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z0}\\ \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (if (<= (- z0 -1.0) -2e+152)
  (/ 1.0 z0)
  (if (<= (- z0 -1.0) 2e+117) (* 1.7724539041519165 z1) (/ 1.0 z0))))

C

double code(double z1, double z0) {
	double tmp;
	if ((z0 - -1.0) <= -2e+152) {
		tmp = 1.0 / z0;
	} else if ((z0 - -1.0) <= 2e+117) {
		tmp = 1.7724539041519165 * z1;
	} else {
		tmp = 1.0 / z0;
	}
	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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: tmp
    if ((z0 - (-1.0d0)) <= (-2d+152)) then
        tmp = 1.0d0 / z0
    else if ((z0 - (-1.0d0)) <= 2d+117) then
        tmp = 1.7724539041519165d0 * z1
    else
        tmp = 1.0d0 / z0
    end if
    code = tmp
end function

Java

public static double code(double z1, double z0) {
	double tmp;
	if ((z0 - -1.0) <= -2e+152) {
		tmp = 1.0 / z0;
	} else if ((z0 - -1.0) <= 2e+117) {
		tmp = 1.7724539041519165 * z1;
	} else {
		tmp = 1.0 / z0;
	}
	return tmp;
}

Python

def code(z1, z0):
	tmp = 0
	if (z0 - -1.0) <= -2e+152:
		tmp = 1.0 / z0
	elif (z0 - -1.0) <= 2e+117:
		tmp = 1.7724539041519165 * z1
	else:
		tmp = 1.0 / z0
	return tmp

Julia

function code(z1, z0)
	tmp = 0.0
	if (Float64(z0 - -1.0) <= -2e+152)
		tmp = Float64(1.0 / z0);
	elseif (Float64(z0 - -1.0) <= 2e+117)
		tmp = Float64(1.7724539041519165 * z1);
	else
		tmp = Float64(1.0 / z0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z1, z0)
	tmp = 0.0;
	if ((z0 - -1.0) <= -2e+152)
		tmp = 1.0 / z0;
	elseif ((z0 - -1.0) <= 2e+117)
		tmp = 1.7724539041519165 * z1;
	else
		tmp = 1.0 / z0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z1_, z0_] := If[LessEqual[N[(z0 - -1.0), $MachinePrecision], -2e+152], N[(1.0 / z0), $MachinePrecision], If[LessEqual[N[(z0 - -1.0), $MachinePrecision], 2e+117], N[(1.7724539041519165 * z1), $MachinePrecision], N[(1.0 / z0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z0 #s(literal -1 binary64)) < -2.0000000000000001e152 or 2.0000000000000001e117 < (-.f64 z0 #s(literal -1 binary64))

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \]
   3. Step-by-step derivation

      1. lower-/.f64 33.9%

         \[\leadsto \frac{1}{\color{blue}{z0}} \]

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{\frac{1}{z0}} \]

   if -2.0000000000000001e152 < (-.f64 z0 #s(literal -1 binary64)) < 2.0000000000000001e117

   1. Initial program 91.9%

      \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \color{blue}{\frac{10000000000000000}{5641895665989011} \cdot z1} \]
   3. Step-by-step derivation

      1. lower-*.f64 50.0%

         \[\leadsto 1.7724539041519165 \cdot \color{blue}{z1} \]

   4. Applied rewrites 50.0%

      \[\leadsto \color{blue}{1.7724539041519165 \cdot z1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 50.0% accurate, 26.0× speedup

Math

\[1.7724539041519165 \cdot z1 \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (* 1.7724539041519165 z1))

C

double code(double z1, double z0) {
	return 1.7724539041519165 * z1;
}

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(z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    code = 1.7724539041519165d0 * z1
end function

Java

public static double code(double z1, double z0) {
	return 1.7724539041519165 * z1;
}

Python

def code(z1, z0):
	return 1.7724539041519165 * z1

Julia

function code(z1, z0)
	return Float64(1.7724539041519165 * z1)
end

MATLAB

function tmp = code(z1, z0)
	tmp = 1.7724539041519165 * z1;
end

Wolfram

code[z1_, z0_] := N[(1.7724539041519165 * z1), $MachinePrecision]

Derivation

1. Initial program 91.9%

   \[\frac{z1}{z1 \cdot \left(z0 - -1\right) + \left(\sqrt{\left(1 - z1\right) - z1} \cdot 0.5641895665989011\right) \cdot e^{\left(-z1\right) \cdot z1}} \]

2. Taylor expanded in z1 around 0

   \[\leadsto \color{blue}{\frac{10000000000000000}{5641895665989011} \cdot z1} \]
3. Step-by-step derivation

   1. lower-*.f64 50.0%

      \[\leadsto 1.7724539041519165 \cdot \color{blue}{z1} \]

4. Applied rewrites 50.0%

   \[\leadsto \color{blue}{1.7724539041519165 \cdot z1} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z1 z0)
  :name "(/ z1 (+ (* z1 (- z0 -1)) (* (* (sqrt (- (- 1 z1) z1)) 5641895665989011/10000000000000000) (exp (* (- z1) z1)))))"
  :precision binary64
  (/ z1 (+ (* z1 (- z0 -1.0)) (* (* (sqrt (- (- 1.0 z1) z1)) 0.5641895665989011) (exp (* (- z1) z1))))))