Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.3% → 96.5%

Time: 8.7s

Alternatives: 15

Speedup: 0.8×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - 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 = (x * (y - z)) / (t - z)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

Python

def code(x, y, z, t):
	return (x * (y - z)) / (t - z)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(y - z)) / Float64(t - z))
end

MATLAB

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

Wolfram

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

Initial Program: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - 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 = (x * (y - z)) / (t - z)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

Python

def code(x, y, z, t):
	return (x * (y - z)) / (t - z)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(y - z)) / Float64(t - z))
end

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 6 \cdot 10^{+20}:\\ \;\;\;\;\frac{x\_m \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 6e+20) (/ (* x_m (- y z)) (- t z)) (* (/ x_m (- t z)) (- y z)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 6e+20) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (x_m / (t - z)) * (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x_m <= 6d+20) then
        tmp = (x_m * (y - z)) / (t - z)
    else
        tmp = (x_m / (t - z)) * (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 6e+20) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (x_m / (t - z)) * (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if x_m <= 6e+20:
		tmp = (x_m * (y - z)) / (t - z)
	else:
		tmp = (x_m / (t - z)) * (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 6e+20)
		tmp = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(x_m / Float64(t - z)) * Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 6e+20)
		tmp = (x_m * (y - z)) / (t - z);
	else
		tmp = (x_m / (t - z)) * (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 6e+20], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 6e20

   1. Initial program 90.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   if 6e20 < x

   1. Initial program 58.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 98.3

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

   4. Applied rewrites 98.3%

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

Alternative 2: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{t - z} \cdot \left(y - z\right)\\ t_2 := \frac{x\_m \cdot \left(y - z\right)}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-301}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x\_m}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{-106}:\\ \;\;\;\;\frac{z}{t - z} \cdot \left(-x\_m\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (/ x_m (- t z)) (- y z))) (t_2 (/ (* x_m (- y z)) (- t z))))
   (*
    x_s
    (if (<= t_2 -1e-59)
      t_1
      (if (<= t_2 -5e-301)
        (/ (* (- y z) x_m) t)
        (if (<= t_2 1e-106) (* (/ z (- t z)) (- x_m)) t_1))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / (t - z)) * (y - z);
	double t_2 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -1e-59) {
		tmp = t_1;
	} else if (t_2 <= -5e-301) {
		tmp = ((y - z) * x_m) / t;
	} else if (t_2 <= 1e-106) {
		tmp = (z / (t - z)) * -x_m;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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 = (x_m / (t - z)) * (y - z)
    t_2 = (x_m * (y - z)) / (t - z)
    if (t_2 <= (-1d-59)) then
        tmp = t_1
    else if (t_2 <= (-5d-301)) then
        tmp = ((y - z) * x_m) / t
    else if (t_2 <= 1d-106) then
        tmp = (z / (t - z)) * -x_m
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / (t - z)) * (y - z);
	double t_2 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -1e-59) {
		tmp = t_1;
	} else if (t_2 <= -5e-301) {
		tmp = ((y - z) * x_m) / t;
	} else if (t_2 <= 1e-106) {
		tmp = (z / (t - z)) * -x_m;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / (t - z)) * (y - z)
	t_2 = (x_m * (y - z)) / (t - z)
	tmp = 0
	if t_2 <= -1e-59:
		tmp = t_1
	elif t_2 <= -5e-301:
		tmp = ((y - z) * x_m) / t
	elif t_2 <= 1e-106:
		tmp = (z / (t - z)) * -x_m
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / Float64(t - z)) * Float64(y - z))
	t_2 = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_2 <= -1e-59)
		tmp = t_1;
	elseif (t_2 <= -5e-301)
		tmp = Float64(Float64(Float64(y - z) * x_m) / t);
	elseif (t_2 <= 1e-106)
		tmp = Float64(Float64(z / Float64(t - z)) * Float64(-x_m));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / (t - z)) * (y - z);
	t_2 = (x_m * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_2 <= -1e-59)
		tmp = t_1;
	elseif (t_2 <= -5e-301)
		tmp = ((y - z) * x_m) / t;
	elseif (t_2 <= 1e-106)
		tmp = (z / (t - z)) * -x_m;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$2, -1e-59], t$95$1, If[LessEqual[t$95$2, -5e-301], N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$2, 1e-106], N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * (-x$95$m)), $MachinePrecision], t$95$1]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -1e-59 or 9.99999999999999941e-107 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 71.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 97.9

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

   4. Applied rewrites 97.9%

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

   if -1e-59 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -5.00000000000000013e-301

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{t}} \cdot x \]

      5. lower--.f64 32.9

         \[\leadsto \frac{\color{blue}{y - z}}{t} \cdot x \]

   5. Applied rewrites 32.9%

      \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 39.6%

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

   if -5.00000000000000013e-301 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 9.99999999999999941e-107

   1. Initial program 98.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x \cdot z}{t - z}\right)} \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \frac{z}{t - z}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{z}{t - z} \cdot x}\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\frac{z}{t - z} \cdot \left(\mathsf{neg}\left(x\right)\right)} \]

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \frac{z}{t - z} \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \]

      10. lower-neg.f64 74.6

          \[\leadsto \frac{z}{t - z} \cdot \color{blue}{\left(-x\right)} \]

   5. Applied rewrites 74.6%

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

Alternative 3: 70.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m \cdot \left(y - z\right)}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2000:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot y\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{y - z}{t} \cdot x\_m\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-85}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x\_m}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (* x_m (- y z)) (- t z))))
   (*
    x_s
    (if (<= t_1 -2000.0)
      (* (/ x_m (- t z)) y)
      (if (<= t_1 0.0)
        (* (/ (- y z) t) x_m)
        (if (<= t_1 5e-85) (* 1.0 x_m) (* (- z y) (/ x_m z))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -2000.0) {
		tmp = (x_m / (t - z)) * y;
	} else if (t_1 <= 0.0) {
		tmp = ((y - z) / t) * x_m;
	} else if (t_1 <= 5e-85) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (z - y) * (x_m / z);
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m * (y - z)) / (t - z)
    if (t_1 <= (-2000.0d0)) then
        tmp = (x_m / (t - z)) * y
    else if (t_1 <= 0.0d0) then
        tmp = ((y - z) / t) * x_m
    else if (t_1 <= 5d-85) then
        tmp = 1.0d0 * x_m
    else
        tmp = (z - y) * (x_m / z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -2000.0) {
		tmp = (x_m / (t - z)) * y;
	} else if (t_1 <= 0.0) {
		tmp = ((y - z) / t) * x_m;
	} else if (t_1 <= 5e-85) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (z - y) * (x_m / z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= -2000.0:
		tmp = (x_m / (t - z)) * y
	elif t_1 <= 0.0:
		tmp = ((y - z) / t) * x_m
	elif t_1 <= 5e-85:
		tmp = 1.0 * x_m
	else:
		tmp = (z - y) * (x_m / z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -2000.0)
		tmp = Float64(Float64(x_m / Float64(t - z)) * y);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(y - z) / t) * x_m);
	elseif (t_1 <= 5e-85)
		tmp = Float64(1.0 * x_m);
	else
		tmp = Float64(Float64(z - y) * Float64(x_m / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= -2000.0)
		tmp = (x_m / (t - z)) * y;
	elseif (t_1 <= 0.0)
		tmp = ((y - z) / t) * x_m;
	elseif (t_1 <= 5e-85)
		tmp = 1.0 * x_m;
	else
		tmp = (z - y) * (x_m / z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, -2000.0], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x$95$m), $MachinePrecision], If[LessEqual[t$95$1, 5e-85], N[(1.0 * x$95$m), $MachinePrecision], N[(N[(z - y), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -2e3

   1. Initial program 72.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot y} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{t - z}} \cdot y \]

      4. lower--.f64 58.8

         \[\leadsto \frac{x}{\color{blue}{t - z}} \cdot y \]

   5. Applied rewrites 58.8%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot y} \]

   if -2e3 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 0.0

   1. Initial program 98.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{t}} \cdot x \]

      5. lower--.f64 53.6

         \[\leadsto \frac{\color{blue}{y - z}}{t} \cdot x \]

   5. Applied rewrites 53.6%

      \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

   if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.0000000000000002e-85

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{t - z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}{t - z} \]

      2. lower-neg.f64 56.5

         \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]

   5. Applied rewrites 56.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{t - z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{t - z} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{-z}{t - z}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      6. lower-/.f64 56.5

         \[\leadsto \color{blue}{\frac{-z}{t - z}} \cdot x \]

   7. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 38.0%

       \[\leadsto \color{blue}{1} \cdot x \]

   if 5.0000000000000002e-85 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 66.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x \cdot \left(y - z\right)}{z}\right)} \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \frac{y - z}{z}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{y - z}{z} \cdot x}\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      6. distribute-neg-frac N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      14. remove-double-neg N/A

          \[\leadsto \frac{\color{blue}{z} + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      15. mul-1-neg N/A

          \[\leadsto \frac{z + \color{blue}{-1 \cdot y}}{z} \cdot x \]

      16. metadata-eval N/A

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

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

          \[\leadsto \frac{\color{blue}{z - 1 \cdot y}}{z} \cdot x \]

      18. *-lft-identity N/A

          \[\leadsto \frac{z - \color{blue}{y}}{z} \cdot x \]

      19. lower--.f64 66.7

          \[\leadsto \frac{\color{blue}{z - y}}{z} \cdot x \]

   5. Applied rewrites 66.7%

      \[\leadsto \color{blue}{\frac{z - y}{z} \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 69.8%

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

Alternative 4: 67.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m \cdot \left(y - z\right)}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-59}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot y\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{y \cdot x\_m}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-85}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x\_m}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (* x_m (- y z)) (- t z))))
   (*
    x_s
    (if (<= t_1 -1e-59)
      (* (/ x_m (- t z)) y)
      (if (<= t_1 0.0)
        (/ (* y x_m) t)
        (if (<= t_1 5e-85) (* 1.0 x_m) (* (- z y) (/ x_m z))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -1e-59) {
		tmp = (x_m / (t - z)) * y;
	} else if (t_1 <= 0.0) {
		tmp = (y * x_m) / t;
	} else if (t_1 <= 5e-85) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (z - y) * (x_m / z);
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m * (y - z)) / (t - z)
    if (t_1 <= (-1d-59)) then
        tmp = (x_m / (t - z)) * y
    else if (t_1 <= 0.0d0) then
        tmp = (y * x_m) / t
    else if (t_1 <= 5d-85) then
        tmp = 1.0d0 * x_m
    else
        tmp = (z - y) * (x_m / z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -1e-59) {
		tmp = (x_m / (t - z)) * y;
	} else if (t_1 <= 0.0) {
		tmp = (y * x_m) / t;
	} else if (t_1 <= 5e-85) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (z - y) * (x_m / z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= -1e-59:
		tmp = (x_m / (t - z)) * y
	elif t_1 <= 0.0:
		tmp = (y * x_m) / t
	elif t_1 <= 5e-85:
		tmp = 1.0 * x_m
	else:
		tmp = (z - y) * (x_m / z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e-59)
		tmp = Float64(Float64(x_m / Float64(t - z)) * y);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(y * x_m) / t);
	elseif (t_1 <= 5e-85)
		tmp = Float64(1.0 * x_m);
	else
		tmp = Float64(Float64(z - y) * Float64(x_m / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= -1e-59)
		tmp = (x_m / (t - z)) * y;
	elseif (t_1 <= 0.0)
		tmp = (y * x_m) / t;
	elseif (t_1 <= 5e-85)
		tmp = 1.0 * x_m;
	else
		tmp = (z - y) * (x_m / z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, -1e-59], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(y * x$95$m), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 5e-85], N[(1.0 * x$95$m), $MachinePrecision], N[(N[(z - y), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -1e-59

   1. Initial program 77.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot y} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{t - z}} \cdot y \]

      4. lower--.f64 57.1

         \[\leadsto \frac{x}{\color{blue}{t - z}} \cdot y \]

   5. Applied rewrites 57.1%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot y} \]

   if -1e-59 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 0.0

   1. Initial program 98.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

      3. lower-*.f64 49.3

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

   5. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\frac{y \cdot x}{t}} \]

   if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.0000000000000002e-85

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{t - z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}{t - z} \]

      2. lower-neg.f64 56.5

         \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]

   5. Applied rewrites 56.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{t - z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{t - z} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{-z}{t - z}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      6. lower-/.f64 56.5

         \[\leadsto \color{blue}{\frac{-z}{t - z}} \cdot x \]

   7. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 38.0%

       \[\leadsto \color{blue}{1} \cdot x \]

   if 5.0000000000000002e-85 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 66.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x \cdot \left(y - z\right)}{z}\right)} \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \frac{y - z}{z}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{y - z}{z} \cdot x}\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      6. distribute-neg-frac N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      14. remove-double-neg N/A

          \[\leadsto \frac{\color{blue}{z} + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      15. mul-1-neg N/A

          \[\leadsto \frac{z + \color{blue}{-1 \cdot y}}{z} \cdot x \]

      16. metadata-eval N/A

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

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

          \[\leadsto \frac{\color{blue}{z - 1 \cdot y}}{z} \cdot x \]

      18. *-lft-identity N/A

          \[\leadsto \frac{z - \color{blue}{y}}{z} \cdot x \]

      19. lower--.f64 66.7

          \[\leadsto \frac{\color{blue}{z - y}}{z} \cdot x \]

   5. Applied rewrites 66.7%

      \[\leadsto \color{blue}{\frac{z - y}{z} \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 69.8%

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

Alternative 5: 60.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \left(z - y\right) \cdot \frac{x\_m}{z}\\ t_2 := \frac{x\_m \cdot \left(y - z\right)}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -2000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{y \cdot x\_m}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-85}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (- z y) (/ x_m z))) (t_2 (/ (* x_m (- y z)) (- t z))))
   (*
    x_s
    (if (<= t_2 -2000.0)
      t_1
      (if (<= t_2 0.0) (/ (* y x_m) t) (if (<= t_2 5e-85) (* 1.0 x_m) t_1))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (z - y) * (x_m / z);
	double t_2 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -2000.0) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = (y * x_m) / t;
	} else if (t_2 <= 5e-85) {
		tmp = 1.0 * x_m;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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 = (z - y) * (x_m / z)
    t_2 = (x_m * (y - z)) / (t - z)
    if (t_2 <= (-2000.0d0)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = (y * x_m) / t
    else if (t_2 <= 5d-85) then
        tmp = 1.0d0 * x_m
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (z - y) * (x_m / z);
	double t_2 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -2000.0) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = (y * x_m) / t;
	} else if (t_2 <= 5e-85) {
		tmp = 1.0 * x_m;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (z - y) * (x_m / z)
	t_2 = (x_m * (y - z)) / (t - z)
	tmp = 0
	if t_2 <= -2000.0:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = (y * x_m) / t
	elif t_2 <= 5e-85:
		tmp = 1.0 * x_m
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(z - y) * Float64(x_m / z))
	t_2 = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_2 <= -2000.0)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(y * x_m) / t);
	elseif (t_2 <= 5e-85)
		tmp = Float64(1.0 * x_m);
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (z - y) * (x_m / z);
	t_2 = (x_m * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_2 <= -2000.0)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = (y * x_m) / t;
	elseif (t_2 <= 5e-85)
		tmp = 1.0 * x_m;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z - y), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$2, -2000.0], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(y * x$95$m), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$2, 5e-85], N[(1.0 * x$95$m), $MachinePrecision], t$95$1]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -2e3 or 5.0000000000000002e-85 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 69.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x \cdot \left(y - z\right)}{z}\right)} \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \frac{y - z}{z}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{y - z}{z} \cdot x}\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      6. distribute-neg-frac N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      14. remove-double-neg N/A

          \[\leadsto \frac{\color{blue}{z} + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      15. mul-1-neg N/A

          \[\leadsto \frac{z + \color{blue}{-1 \cdot y}}{z} \cdot x \]

      16. metadata-eval N/A

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

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

          \[\leadsto \frac{\color{blue}{z - 1 \cdot y}}{z} \cdot x \]

      18. *-lft-identity N/A

          \[\leadsto \frac{z - \color{blue}{y}}{z} \cdot x \]

      19. lower--.f64 63.2

          \[\leadsto \frac{\color{blue}{z - y}}{z} \cdot x \]

   5. Applied rewrites 63.2%

      \[\leadsto \color{blue}{\frac{z - y}{z} \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 66.4%

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

   if -2e3 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 0.0

   1. Initial program 98.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

      3. lower-*.f64 46.5

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

   5. Applied rewrites 46.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{t}} \]

   if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.0000000000000002e-85

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{t - z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}{t - z} \]

      2. lower-neg.f64 56.5

         \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]

   5. Applied rewrites 56.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{t - z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{t - z} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{-z}{t - z}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      6. lower-/.f64 56.5

         \[\leadsto \color{blue}{\frac{-z}{t - z}} \cdot x \]

   7. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 38.0%

       \[\leadsto \color{blue}{1} \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 35.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{t - z} \leq 0:\\ \;\;\;\;\frac{x\_m}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= (/ (* x_m (- y z)) (- t z)) 0.0) (* (/ x_m z) t) (* 1.0 x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (((x_m * (y - z)) / (t - z)) <= 0.0) {
		tmp = (x_m / z) * t;
	} else {
		tmp = 1.0 * x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x_m * (y - z)) / (t - z)) <= 0.0d0) then
        tmp = (x_m / z) * t
    else
        tmp = 1.0d0 * x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (((x_m * (y - z)) / (t - z)) <= 0.0) {
		tmp = (x_m / z) * t;
	} else {
		tmp = 1.0 * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if ((x_m * (y - z)) / (t - z)) <= 0.0:
		tmp = (x_m / z) * t
	else:
		tmp = 1.0 * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x_m * Float64(y - z)) / Float64(t - z)) <= 0.0)
		tmp = Float64(Float64(x_m / z) * t);
	else
		tmp = Float64(1.0 * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (((x_m * (y - z)) / (t - z)) <= 0.0)
		tmp = (x_m / z) * t;
	else
		tmp = 1.0 * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], 0.0], N[(N[(x$95$m / z), $MachinePrecision] * t), $MachinePrecision], N[(1.0 * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 0.0

   1. Initial program 87.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

         \[\leadsto x - \color{blue}{\frac{x \cdot y - t \cdot x}{z}} \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \frac{x \cdot y - t \cdot x}{z}} \]

      10. div-sub N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. associate-/l* N/A

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

      14. distribute-rgt-out-- N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 49.2

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

   5. Applied rewrites 49.2%

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

   6. Taylor expanded in t around inf

      \[\leadsto \frac{t \cdot x}{\color{blue}{z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 7.5%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{t} \]

   if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 76.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{t - z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}{t - z} \]

      2. lower-neg.f64 32.3

         \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]

   5. Applied rewrites 32.3%

      \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{t - z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{t - z} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{-z}{t - z}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      6. lower-/.f64 51.6

         \[\leadsto \color{blue}{\frac{-z}{t - z}} \cdot x \]

   7. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 39.2%

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

Alternative 7: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1760000000 \lor \neg \left(z \leq 1.2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{z}{t - z} \cdot \left(-x\_m\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x\_m}{t - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1760000000.0) (not (<= z 1.2e-31)))
    (* (/ z (- t z)) (- x_m))
    (/ (* y x_m) (- t z)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1760000000.0) || !(z <= 1.2e-31)) {
		tmp = (z / (t - z)) * -x_m;
	} else {
		tmp = (y * x_m) / (t - z);
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1760000000.0d0)) .or. (.not. (z <= 1.2d-31))) then
        tmp = (z / (t - z)) * -x_m
    else
        tmp = (y * x_m) / (t - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1760000000.0) || !(z <= 1.2e-31)) {
		tmp = (z / (t - z)) * -x_m;
	} else {
		tmp = (y * x_m) / (t - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -1760000000.0) or not (z <= 1.2e-31):
		tmp = (z / (t - z)) * -x_m
	else:
		tmp = (y * x_m) / (t - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -1760000000.0) || !(z <= 1.2e-31))
		tmp = Float64(Float64(z / Float64(t - z)) * Float64(-x_m));
	else
		tmp = Float64(Float64(y * x_m) / Float64(t - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -1760000000.0) || ~((z <= 1.2e-31)))
		tmp = (z / (t - z)) * -x_m;
	else
		tmp = (y * x_m) / (t - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -1760000000.0], N[Not[LessEqual[z, 1.2e-31]], $MachinePrecision]], N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * (-x$95$m)), $MachinePrecision], N[(N[(y * x$95$m), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.76e9 or 1.2e-31 < z

   1. Initial program 70.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t - z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x \cdot z}{t - z}\right)} \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \frac{z}{t - z}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{z}{t - z} \cdot x}\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\frac{z}{t - z} \cdot \left(\mathsf{neg}\left(x\right)\right)} \]

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \frac{z}{t - z} \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \]

      10. lower-neg.f64 80.1

          \[\leadsto \frac{z}{t - z} \cdot \color{blue}{\left(-x\right)} \]

   5. Applied rewrites 80.1%

      \[\leadsto \color{blue}{\frac{z}{t - z} \cdot \left(-x\right)} \]

   if -1.76e9 < z < 1.2e-31

   1. Initial program 95.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{x \cdot y}}{t - z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t - z} \]

      2. lower-*.f64 84.4

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t - z} \]

   5. Applied rewrites 84.4%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{t - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1760000000 \lor \neg \left(z \leq 1.2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{z}{t - z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3450000000 \lor \neg \left(z \leq 0.0285\right):\\ \;\;\;\;\frac{z - y}{z} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x\_m}{t - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -3450000000.0) (not (<= z 0.0285)))
    (* (/ (- z y) z) x_m)
    (/ (* y x_m) (- t z)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -3450000000.0) || !(z <= 0.0285)) {
		tmp = ((z - y) / z) * x_m;
	} else {
		tmp = (y * x_m) / (t - z);
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3450000000.0d0)) .or. (.not. (z <= 0.0285d0))) then
        tmp = ((z - y) / z) * x_m
    else
        tmp = (y * x_m) / (t - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -3450000000.0) || !(z <= 0.0285)) {
		tmp = ((z - y) / z) * x_m;
	} else {
		tmp = (y * x_m) / (t - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -3450000000.0) or not (z <= 0.0285):
		tmp = ((z - y) / z) * x_m
	else:
		tmp = (y * x_m) / (t - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -3450000000.0) || !(z <= 0.0285))
		tmp = Float64(Float64(Float64(z - y) / z) * x_m);
	else
		tmp = Float64(Float64(y * x_m) / Float64(t - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -3450000000.0) || ~((z <= 0.0285)))
		tmp = ((z - y) / z) * x_m;
	else
		tmp = (y * x_m) / (t - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -3450000000.0], N[Not[LessEqual[z, 0.0285]], $MachinePrecision]], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x$95$m), $MachinePrecision], N[(N[(y * x$95$m), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.45e9 or 0.028500000000000001 < z

   1. Initial program 69.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x \cdot \left(y - z\right)}{z}\right)} \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \frac{y - z}{z}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{y - z}{z} \cdot x}\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      6. distribute-neg-frac N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      14. remove-double-neg N/A

          \[\leadsto \frac{\color{blue}{z} + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      15. mul-1-neg N/A

          \[\leadsto \frac{z + \color{blue}{-1 \cdot y}}{z} \cdot x \]

      16. metadata-eval N/A

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

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

          \[\leadsto \frac{\color{blue}{z - 1 \cdot y}}{z} \cdot x \]

      18. *-lft-identity N/A

          \[\leadsto \frac{z - \color{blue}{y}}{z} \cdot x \]

      19. lower--.f64 76.5

          \[\leadsto \frac{\color{blue}{z - y}}{z} \cdot x \]

   5. Applied rewrites 76.5%

      \[\leadsto \color{blue}{\frac{z - y}{z} \cdot x} \]

   if -3.45e9 < z < 0.028500000000000001

   1. Initial program 95.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{x \cdot y}}{t - z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t - z} \]

      2. lower-*.f64 83.4

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t - z} \]

   5. Applied rewrites 83.4%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{t - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3450000000 \lor \neg \left(z \leq 0.0285\right):\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+30} \lor \neg \left(t \leq 1700000000\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;x\_m - \frac{x\_m}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= t -2.35e+30) (not (<= t 1700000000.0)))
    (* (/ (- y z) t) x_m)
    (- x_m (* (/ x_m z) y)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((t <= -2.35e+30) || !(t <= 1700000000.0)) {
		tmp = ((y - z) / t) * x_m;
	} else {
		tmp = x_m - ((x_m / z) * y);
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.35d+30)) .or. (.not. (t <= 1700000000.0d0))) then
        tmp = ((y - z) / t) * x_m
    else
        tmp = x_m - ((x_m / z) * y)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((t <= -2.35e+30) || !(t <= 1700000000.0)) {
		tmp = ((y - z) / t) * x_m;
	} else {
		tmp = x_m - ((x_m / z) * y);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (t <= -2.35e+30) or not (t <= 1700000000.0):
		tmp = ((y - z) / t) * x_m
	else:
		tmp = x_m - ((x_m / z) * y)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((t <= -2.35e+30) || !(t <= 1700000000.0))
		tmp = Float64(Float64(Float64(y - z) / t) * x_m);
	else
		tmp = Float64(x_m - Float64(Float64(x_m / z) * y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((t <= -2.35e+30) || ~((t <= 1700000000.0)))
		tmp = ((y - z) / t) * x_m;
	else
		tmp = x_m - ((x_m / z) * y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[t, -2.35e+30], N[Not[LessEqual[t, 1700000000.0]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x$95$m), $MachinePrecision], N[(x$95$m - N[(N[(x$95$m / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -2.34999999999999995e30 or 1.7e9 < t

   1. Initial program 79.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{t}} \cdot x \]

      5. lower--.f64 75.7

         \[\leadsto \frac{\color{blue}{y - z}}{t} \cdot x \]

   5. Applied rewrites 75.7%

      \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

   if -2.34999999999999995e30 < t < 1.7e9

   1. Initial program 84.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

         \[\leadsto x - \color{blue}{\frac{x \cdot y - t \cdot x}{z}} \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \frac{x \cdot y - t \cdot x}{z}} \]

      10. div-sub N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. associate-/l* N/A

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

      14. distribute-rgt-out-- N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 82.9

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

   5. Applied rewrites 82.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto x - \frac{x \cdot y}{\color{blue}{z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 83.1%

      \[\leadsto x - \frac{x}{z} \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+30} \lor \neg \left(t \leq 1700000000\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+30} \lor \neg \left(t \leq 1700000000\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= t -2.35e+30) (not (<= t 1700000000.0)))
    (* (/ (- y z) t) x_m)
    (* (/ (- z y) z) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((t <= -2.35e+30) || !(t <= 1700000000.0)) {
		tmp = ((y - z) / t) * x_m;
	} else {
		tmp = ((z - y) / z) * x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.35d+30)) .or. (.not. (t <= 1700000000.0d0))) then
        tmp = ((y - z) / t) * x_m
    else
        tmp = ((z - y) / z) * x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((t <= -2.35e+30) || !(t <= 1700000000.0)) {
		tmp = ((y - z) / t) * x_m;
	} else {
		tmp = ((z - y) / z) * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (t <= -2.35e+30) or not (t <= 1700000000.0):
		tmp = ((y - z) / t) * x_m
	else:
		tmp = ((z - y) / z) * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((t <= -2.35e+30) || !(t <= 1700000000.0))
		tmp = Float64(Float64(Float64(y - z) / t) * x_m);
	else
		tmp = Float64(Float64(Float64(z - y) / z) * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((t <= -2.35e+30) || ~((t <= 1700000000.0)))
		tmp = ((y - z) / t) * x_m;
	else
		tmp = ((z - y) / z) * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[t, -2.35e+30], N[Not[LessEqual[t, 1700000000.0]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x$95$m), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -2.34999999999999995e30 or 1.7e9 < t

   1. Initial program 79.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y - z}{t}} \cdot x \]

      5. lower--.f64 75.7

         \[\leadsto \frac{\color{blue}{y - z}}{t} \cdot x \]

   5. Applied rewrites 75.7%

      \[\leadsto \color{blue}{\frac{y - z}{t} \cdot x} \]

   if -2.34999999999999995e30 < t < 1.7e9

   1. Initial program 84.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x \cdot \left(y - z\right)}{z}\right)} \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \frac{y - z}{z}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{y - z}{z} \cdot x}\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right) \cdot x} \]

      6. distribute-neg-frac N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right)\right)}{z}} \cdot x \]

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      14. remove-double-neg N/A

          \[\leadsto \frac{\color{blue}{z} + \left(\mathsf{neg}\left(y\right)\right)}{z} \cdot x \]

      15. mul-1-neg N/A

          \[\leadsto \frac{z + \color{blue}{-1 \cdot y}}{z} \cdot x \]

      16. metadata-eval N/A

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

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

          \[\leadsto \frac{\color{blue}{z - 1 \cdot y}}{z} \cdot x \]

      18. *-lft-identity N/A

          \[\leadsto \frac{z - \color{blue}{y}}{z} \cdot x \]

      19. lower--.f64 82.3

          \[\leadsto \frac{\color{blue}{z - y}}{z} \cdot x \]

   5. Applied rewrites 82.3%

      \[\leadsto \color{blue}{\frac{z - y}{z} \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+30} \lor \neg \left(t \leq 1700000000\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-12}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+63}:\\ \;\;\;\;\frac{y \cdot x\_m}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x\_m}{z}, t, x\_m\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -1.55e-12)
    (* 1.0 x_m)
    (if (<= z 4.4e+63) (/ (* y x_m) t) (fma (/ x_m z) t x_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e-12) {
		tmp = 1.0 * x_m;
	} else if (z <= 4.4e+63) {
		tmp = (y * x_m) / t;
	} else {
		tmp = fma((x_m / z), t, x_m);
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -1.55e-12)
		tmp = Float64(1.0 * x_m);
	elseif (z <= 4.4e+63)
		tmp = Float64(Float64(y * x_m) / t);
	else
		tmp = fma(Float64(x_m / z), t, x_m);
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -1.55e-12], N[(1.0 * x$95$m), $MachinePrecision], If[LessEqual[z, 4.4e+63], N[(N[(y * x$95$m), $MachinePrecision] / t), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * t + x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.5500000000000001e-12

   1. Initial program 72.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{t - z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}{t - z} \]

      2. lower-neg.f64 50.5

         \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]

   5. Applied rewrites 50.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{t - z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{t - z} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{-z}{t - z}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      6. lower-/.f64 75.5

         \[\leadsto \color{blue}{\frac{-z}{t - z}} \cdot x \]

   7. Applied rewrites 75.5%

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 56.3%

       \[\leadsto \color{blue}{1} \cdot x \]

   if -1.5500000000000001e-12 < z < 4.3999999999999997e63

   1. Initial program 94.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

      3. lower-*.f64 59.7

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

   5. Applied rewrites 59.7%

      \[\leadsto \color{blue}{\frac{y \cdot x}{t}} \]

   if 4.3999999999999997e63 < z

   1. Initial program 63.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

         \[\leadsto x - \color{blue}{\frac{x \cdot y - t \cdot x}{z}} \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \frac{x \cdot y - t \cdot x}{z}} \]

      10. div-sub N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. associate-/l* N/A

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

      14. distribute-rgt-out-- N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 85.4

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

   5. Applied rewrites 85.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot x}{z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 77.3%

      \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \color{blue}{t}, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-12} \lor \neg \left(z \leq 0.0305\right):\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x\_m}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.55e-12) (not (<= z 0.0305))) (* 1.0 x_m) (/ (* y x_m) t))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e-12) || !(z <= 0.0305)) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (y * x_m) / t;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.55d-12)) .or. (.not. (z <= 0.0305d0))) then
        tmp = 1.0d0 * x_m
    else
        tmp = (y * x_m) / t
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e-12) || !(z <= 0.0305)) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (y * x_m) / t;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -1.55e-12) or not (z <= 0.0305):
		tmp = 1.0 * x_m
	else:
		tmp = (y * x_m) / t
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -1.55e-12) || !(z <= 0.0305))
		tmp = Float64(1.0 * x_m);
	else
		tmp = Float64(Float64(y * x_m) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -1.55e-12) || ~((z <= 0.0305)))
		tmp = 1.0 * x_m;
	else
		tmp = (y * x_m) / t;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -1.55e-12], N[Not[LessEqual[z, 0.0305]], $MachinePrecision]], N[(1.0 * x$95$m), $MachinePrecision], N[(N[(y * x$95$m), $MachinePrecision] / t), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.5500000000000001e-12 or 0.030499999999999999 < z

   1. Initial program 70.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{t - z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}{t - z} \]

      2. lower-neg.f64 53.2

         \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]

   5. Applied rewrites 53.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{t - z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{t - z} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{-z}{t - z}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      6. lower-/.f64 78.7

         \[\leadsto \color{blue}{\frac{-z}{t - z}} \cdot x \]

   7. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 60.5%

       \[\leadsto \color{blue}{1} \cdot x \]

   if -1.5500000000000001e-12 < z < 0.030499999999999999

   1. Initial program 95.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

      3. lower-*.f64 63.5

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

   5. Applied rewrites 63.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-12} \lor \neg \left(z \leq 0.0305\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-12} \lor \neg \left(z \leq 0.0305\right):\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.6e-12) (not (<= z 0.0305))) (* 1.0 x_m) (* (/ y t) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-12) || !(z <= 0.0305)) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (y / t) * x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d-12)) .or. (.not. (z <= 0.0305d0))) then
        tmp = 1.0d0 * x_m
    else
        tmp = (y / t) * x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-12) || !(z <= 0.0305)) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (y / t) * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -1.6e-12) or not (z <= 0.0305):
		tmp = 1.0 * x_m
	else:
		tmp = (y / t) * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-12) || !(z <= 0.0305))
		tmp = Float64(1.0 * x_m);
	else
		tmp = Float64(Float64(y / t) * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-12) || ~((z <= 0.0305)))
		tmp = 1.0 * x_m;
	else
		tmp = (y / t) * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -1.6e-12], N[Not[LessEqual[z, 0.0305]], $MachinePrecision]], N[(1.0 * x$95$m), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e-12 or 0.030499999999999999 < z

   1. Initial program 70.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{t - z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}{t - z} \]

      2. lower-neg.f64 53.2

         \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]

   5. Applied rewrites 53.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{t - z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{t - z} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{-z}{t - z}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      6. lower-/.f64 78.7

         \[\leadsto \color{blue}{\frac{-z}{t - z}} \cdot x \]

   7. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 60.5%

       \[\leadsto \color{blue}{1} \cdot x \]

   if -1.6e-12 < z < 0.030499999999999999

   1. Initial program 95.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

      3. lower-*.f64 63.5

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

   5. Applied rewrites 63.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{t}} \]
   6. Step-by-step derivation

   7. Applied rewrites 62.3%

      \[\leadsto \frac{y}{t} \cdot \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-12} \lor \neg \left(z \leq 0.0305\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-12} \lor \neg \left(z \leq 0.0305\right):\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.6e-12) (not (<= z 0.0305))) (* 1.0 x_m) (* (/ x_m t) y))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-12) || !(z <= 0.0305)) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (x_m / t) * y;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d-12)) .or. (.not. (z <= 0.0305d0))) then
        tmp = 1.0d0 * x_m
    else
        tmp = (x_m / t) * y
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-12) || !(z <= 0.0305)) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (x_m / t) * y;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -1.6e-12) or not (z <= 0.0305):
		tmp = 1.0 * x_m
	else:
		tmp = (x_m / t) * y
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-12) || !(z <= 0.0305))
		tmp = Float64(1.0 * x_m);
	else
		tmp = Float64(Float64(x_m / t) * y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-12) || ~((z <= 0.0305)))
		tmp = 1.0 * x_m;
	else
		tmp = (x_m / t) * y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -1.6e-12], N[Not[LessEqual[z, 0.0305]], $MachinePrecision]], N[(1.0 * x$95$m), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] * y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e-12 or 0.030499999999999999 < z

   1. Initial program 70.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{t - z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}{t - z} \]

      2. lower-neg.f64 53.2

         \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]

   5. Applied rewrites 53.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{t - z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{t - z} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{-z}{t - z}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

      6. lower-/.f64 78.7

         \[\leadsto \color{blue}{\frac{-z}{t - z}} \cdot x \]

   7. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 60.5%

       \[\leadsto \color{blue}{1} \cdot x \]

   if -1.6e-12 < z < 0.030499999999999999

   1. Initial program 95.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

      3. lower-*.f64 63.5

         \[\leadsto \frac{\color{blue}{y \cdot x}}{t} \]

   5. Applied rewrites 63.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{t}} \]
   6. Step-by-step derivation

   7. Applied rewrites 58.7%

      \[\leadsto \frac{x}{t} \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-12} \lor \neg \left(z \leq 0.0305\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(1 \cdot x\_m\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t) :precision binary64 (* x_s (* 1.0 x_m)))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (1.0 * x_m);
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * (1.0d0 * x_m)
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (1.0 * x_m);
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * (1.0 * x_m)

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(1.0 * x_m))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * (1.0 * x_m);
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(1.0 * x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.2%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{t - z} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \frac{x \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}{t - z} \]

   2. lower-neg.f64 41.8

      \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]

5. Applied rewrites 41.8%

   \[\leadsto \frac{x \cdot \color{blue}{\left(-z\right)}}{t - z} \]
6. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{t - z}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{t - z} \]

   3. associate-/l* N/A

      \[\leadsto \color{blue}{x \cdot \frac{-z}{t - z}} \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   5. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

   6. lower-/.f64 55.4

      \[\leadsto \color{blue}{\frac{-z}{t - z}} \cdot x \]

7. Applied rewrites 55.4%

   \[\leadsto \color{blue}{\frac{-z}{t - z} \cdot x} \]

8. Taylor expanded in z around inf

   \[\leadsto \color{blue}{1} \cdot x \]
9. Step-by-step derivation

10. Applied rewrites 35.7%

    \[\leadsto \color{blue}{1} \cdot x \]
11. Add Preprocessing

Developer Target 1: 97.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (/ (- t z) (- y z))))

C

double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - 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 = x / ((t - z) / (y - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - z));
}

Python

def code(x, y, z, t):
	return x / ((t - z) / (y - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(t - z) / Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((t - z) / (y - z));
end

Wolfram

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

Reproduce

herbie shell --seed 2024364 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ (- t z) (- y z))))

  (/ (* x (- y z)) (- t z)))