Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.3% → 89.3%

Time: 4.6s

Alternatives: 17

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * (t - x)) / (a - 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, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * (t - x)) / (a - 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, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t - x}{a - z} + x\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{elif}\;t\_2 \leq 10^{+302}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* (- y z) (/ (- t x) (- a z))) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-248)
     t_1
     (if (<= t_2 0.0)
       (+ (- (/ (* (- t x) (- y a)) z)) t)
       (if (<= t_2 1e+302) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * ((t - x) / (a - z))) + x;
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-248) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else if (t_2 <= 1e+302) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((y - z) * ((t - x) / (a - z))) + x
    t_2 = x + (((y - z) * (t - x)) / (a - z))
    if (t_2 <= (-5d-248)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = -(((t - x) * (y - a)) / z) + t
    else if (t_2 <= 1d+302) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * ((t - x) / (a - z))) + x;
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-248) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else if (t_2 <= 1e+302) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * ((t - x) / (a - z))) + x
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -5e-248:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = -(((t - x) * (y - a)) / z) + t
	elif t_2 <= 1e+302:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))) + x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-248)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	elseif (t_2 <= 1e+302)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * ((t - x) / (a - z))) + x;
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -5e-248)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = -(((t - x) * (y - a)) / z) + t;
	elseif (t_2 <= 1e+302)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-248], t$95$1, If[LessEqual[t$95$2, 0.0], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], If[LessEqual[t$95$2, 1e+302], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000001e-248 or 1.0000000000000001e302 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 62.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. associate-/l* N/A

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

      10. sub-div N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-div N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. lift--.f64 85.7

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

   3. Applied rewrites 85.7%

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

   if -5.0000000000000001e-248 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 13.2%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 91.1%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.0000000000000001e302

   1. Initial program 96.9%

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

Alternative 2: 89.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{elif}\;t\_2 \leq 10^{+302}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-248)
     t_1
     (if (<= t_2 0.0)
       (+ (- (/ (* (- t x) (- y a)) z)) t)
       (if (<= t_2 1e+302) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-248) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else if (t_2 <= 1e+302) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-248)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	elseif (t_2 <= 1e+302)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-248], t$95$1, If[LessEqual[t$95$2, 0.0], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], If[LessEqual[t$95$2, 1e+302], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000001e-248 or 1.0000000000000001e302 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 62.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z} - \frac{x}{a - z}, x\right)} \]

      11. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y - z}, \frac{t}{a - z} - \frac{x}{a - z}, x\right) \]

      12. sub-div N/A

          \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{t - x}{a - z}}, x\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{t - x}{a - z}}, x\right) \]

      14. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - z, \frac{\color{blue}{t - x}}{a - z}, x\right) \]

      15. lift--.f64 85.7

          \[\leadsto \mathsf{fma}\left(y - z, \frac{t - x}{\color{blue}{a - z}}, x\right) \]

   3. Applied rewrites 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   if -5.0000000000000001e-248 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 13.2%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 91.1%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.0000000000000001e302

   1. Initial program 96.9%

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

Alternative 3: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-248)
     t_1
     (if (<= t_2 0.0) (+ (- (/ (* (- t x) (- y a)) z)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-248) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-248)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-248], t$95$1, If[LessEqual[t$95$2, 0.0], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000001e-248 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z} - \frac{x}{a - z}, x\right)} \]

      11. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y - z}, \frac{t}{a - z} - \frac{x}{a - z}, x\right) \]

      12. sub-div N/A

          \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{t - x}{a - z}}, x\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{t - x}{a - z}}, x\right) \]

      14. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - z, \frac{\color{blue}{t - x}}{a - z}, x\right) \]

      15. lift--.f64 86.5

          \[\leadsto \mathsf{fma}\left(y - z, \frac{t - x}{\color{blue}{a - z}}, x\right) \]

   3. Applied rewrites 86.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   if -5.0000000000000001e-248 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 13.2%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 91.1%

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

Alternative 4: 84.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \frac{-x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-248) t_1 (if (<= t_2 0.0) (- t (/ (- (* x y)) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-248) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - (-(x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-248)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(-Float64(x * y)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-248], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t - N[((-N[(x * y), $MachinePrecision]) / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000001e-248 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z} - \frac{x}{a - z}, x\right)} \]

      11. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y - z}, \frac{t}{a - z} - \frac{x}{a - z}, x\right) \]

      12. sub-div N/A

          \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{t - x}{a - z}}, x\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{t - x}{a - z}}, x\right) \]

      14. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - z, \frac{\color{blue}{t - x}}{a - z}, x\right) \]

      15. lift--.f64 86.5

          \[\leadsto \mathsf{fma}\left(y - z, \frac{t - x}{\color{blue}{a - z}}, x\right) \]

   3. Applied rewrites 86.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   if -5.0000000000000001e-248 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 13.2%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 63.8

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

   7. Applied rewrites 63.8%

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

   8. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-*.f64 63.8

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

   10. Applied rewrites 63.8%

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

Alternative 5: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.48 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-174}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.48e-8)
   (fma (- t x) (/ (- y z) a) x)
   (if (<= a 3.7e-174)
     (- t (/ (* y (- t x)) z))
     (fma (- y z) (/ t (- a z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.48e-8) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else if (a <= 3.7e-174) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = fma((y - z), (t / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.48e-8)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	elseif (a <= 3.7e-174)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	else
		tmp = fma(Float64(y - z), Float64(t / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.48e-8], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 3.7e-174], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.48e-8

   1. Initial program 68.7%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - x, \color{blue}{\frac{y - z}{a}}, x\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - x, \frac{\color{blue}{y - z}}{a}, x\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{\color{blue}{a}}, x\right) \]

      6. lift--.f64 74.7

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right) \]

   4. Applied rewrites 74.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)} \]

   if -1.48e-8 < a < 3.7000000000000001e-174

   1. Initial program 67.4%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 64.4%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 73.2

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

   7. Applied rewrites 73.2%

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

   if 3.7000000000000001e-174 < a

   1. Initial program 68.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z} - \frac{x}{a - z}, x\right)} \]

      11. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y - z}, \frac{t}{a - z} - \frac{x}{a - z}, x\right) \]

      12. sub-div N/A

          \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{t - x}{a - z}}, x\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{t - x}{a - z}}, x\right) \]

      14. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - z, \frac{\color{blue}{t - x}}{a - z}, x\right) \]

      15. lift--.f64 83.5

          \[\leadsto \mathsf{fma}\left(y - z, \frac{t - x}{\color{blue}{a - z}}, x\right) \]

   3. Applied rewrites 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(y - z, \frac{\color{blue}{t}}{a - z}, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 69.6%

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

Alternative 6: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -1.48 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-83}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -1.48e-8) t_1 (if (<= a 1.7e-83) (- t (/ (* y (- t x)) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / a), x);
	double tmp;
	if (a <= -1.48e-8) {
		tmp = t_1;
	} else if (a <= 1.7e-83) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -1.48e-8)
		tmp = t_1;
	elseif (a <= 1.7e-83)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.48e-8], t$95$1, If[LessEqual[a, 1.7e-83], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.48e-8 or 1.6999999999999999e-83 < a

   1. Initial program 68.8%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - x, \color{blue}{\frac{y - z}{a}}, x\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - x, \frac{\color{blue}{y - z}}{a}, x\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{\color{blue}{a}}, x\right) \]

      6. lift--.f64 71.3

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right) \]

   4. Applied rewrites 71.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)} \]

   if -1.48e-8 < a < 1.6999999999999999e-83

   1. Initial program 67.5%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 63.4%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 71.6

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

   7. Applied rewrites 71.6%

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

Alternative 7: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -1.48 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-74}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= a -1.48e-8) t_1 (if (<= a 2.1e-74) (- t (/ (* y (- t x)) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (a <= -1.48e-8) {
		tmp = t_1;
	} else if (a <= 2.1e-74) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -1.48e-8)
		tmp = t_1;
	elseif (a <= 2.1e-74)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.48e-8], t$95$1, If[LessEqual[a, 2.1e-74], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.48e-8 or 2.1e-74 < a

   1. Initial program 68.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{t - x}{a} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{t - x}{a}}, x\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{t - x}{\color{blue}{a}}, x\right) \]

      5. lift--.f64 63.3

         \[\leadsto \mathsf{fma}\left(y, \frac{t - x}{a}, x\right) \]

   4. Applied rewrites 63.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)} \]

   if -1.48e-8 < a < 2.1e-74

   1. Initial program 67.5%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 63.2%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 71.4

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

   7. Applied rewrites 71.4%

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

Alternative 8: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-267}:\\ \;\;\;\;t - \frac{-x \cdot y}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= a -5.2e-12)
     t_1
     (if (<= a -3.6e-267)
       (- t (/ (- (* x y)) z))
       (if (<= a 1.8e-74) (- t (/ (* t y) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (a <= -5.2e-12) {
		tmp = t_1;
	} else if (a <= -3.6e-267) {
		tmp = t - (-(x * y) / z);
	} else if (a <= 1.8e-74) {
		tmp = t - ((t * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -5.2e-12)
		tmp = t_1;
	elseif (a <= -3.6e-267)
		tmp = Float64(t - Float64(Float64(-Float64(x * y)) / z));
	elseif (a <= 1.8e-74)
		tmp = Float64(t - Float64(Float64(t * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -5.2e-12], t$95$1, If[LessEqual[a, -3.6e-267], N[(t - N[((-N[(x * y), $MachinePrecision]) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-74], N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.19999999999999965e-12 or 1.8000000000000001e-74 < a

   1. Initial program 68.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{t - x}{a} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{t - x}{a}}, x\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{t - x}{\color{blue}{a}}, x\right) \]

      5. lift--.f64 63.2

         \[\leadsto \mathsf{fma}\left(y, \frac{t - x}{a}, x\right) \]

   4. Applied rewrites 63.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)} \]

   if -5.19999999999999965e-12 < a < -3.6000000000000001e-267

   1. Initial program 69.7%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 59.7%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 66.6

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

   7. Applied rewrites 66.6%

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

   8. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-*.f64 53.8

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

   10. Applied rewrites 53.8%

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

   if -3.6000000000000001e-267 < a < 1.8000000000000001e-74

   1. Initial program 65.2%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 66.9%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 76.0

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

   7. Applied rewrites 76.0%

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

   8. Taylor expanded in x around 0

      \[\leadsto t - \frac{t \cdot y}{z} \]
   9. Step-by-step derivation

      1. lower-*.f64 53.3

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

   10. Applied rewrites 53.3%

       \[\leadsto t - \frac{t \cdot y}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= a -2.55e-15) t_1 (if (<= a 1.8e-74) (- t (/ (* t y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (a <= -2.55e-15) {
		tmp = t_1;
	} else if (a <= 1.8e-74) {
		tmp = t - ((t * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -2.55e-15)
		tmp = t_1;
	elseif (a <= 1.8e-74)
		tmp = Float64(t - Float64(Float64(t * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.55e-15], t$95$1, If[LessEqual[a, 1.8e-74], N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.55e-15 or 1.8000000000000001e-74 < a

   1. Initial program 68.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{t - x}{a} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{t - x}{a}}, x\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{t - x}{\color{blue}{a}}, x\right) \]

      5. lift--.f64 63.1

         \[\leadsto \mathsf{fma}\left(y, \frac{t - x}{a}, x\right) \]

   4. Applied rewrites 63.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)} \]

   if -2.55e-15 < a < 1.8000000000000001e-74

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 63.5%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 71.6

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

   7. Applied rewrites 71.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto t - \frac{t \cdot y}{z} \]
   9. Step-by-step derivation

      1. lower-*.f64 51.3

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

   10. Applied rewrites 51.3%

       \[\leadsto t - \frac{t \cdot y}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{z - y}{a}, x\right)\\ \mathbf{if}\;a \leq -1.56 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-83}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ (- z y) a) x)))
   (if (<= a -1.56e-12) t_1 (if (<= a 1.7e-83) (- t (/ (* t y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, ((z - y) / a), x);
	double tmp;
	if (a <= -1.56e-12) {
		tmp = t_1;
	} else if (a <= 1.7e-83) {
		tmp = t - ((t * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(Float64(z - y) / a), x)
	tmp = 0.0
	if (a <= -1.56e-12)
		tmp = t_1;
	elseif (a <= 1.7e-83)
		tmp = Float64(t - Float64(Float64(t * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.56e-12], t$95$1, If[LessEqual[a, 1.7e-83], N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.56000000000000002e-12 or 1.6999999999999999e-83 < a

   1. Initial program 68.9%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 50.8

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

   4. Applied rewrites 50.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \left(1 - \frac{y}{a}\right) \cdot x \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(1 - \frac{y}{a}\right) \cdot x \]

      2. lower-/.f64 47.6

         \[\leadsto \left(1 - \frac{y}{a}\right) \cdot x \]

   7. Applied rewrites 47.6%

      \[\leadsto \left(1 - \frac{y}{a}\right) \cdot x \]

   8. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto x \cdot \frac{z - y}{a} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \frac{z - y}{\color{blue}{a}}, x\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \frac{z - y}{a}, x\right) \]

      5. lift--.f64 47.6

         \[\leadsto \mathsf{fma}\left(x, \frac{z - y}{a}, x\right) \]

   10. Applied rewrites 47.6%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{z - y}{a}}, x\right) \]

   if -1.56000000000000002e-12 < a < 1.6999999999999999e-83

   1. Initial program 67.4%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 63.6%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 71.7

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

   7. Applied rewrites 71.7%

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

   8. Taylor expanded in x around 0

      \[\leadsto t - \frac{t \cdot y}{z} \]
   9. Step-by-step derivation

      1. lower-*.f64 51.4

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

   10. Applied rewrites 51.4%

       \[\leadsto t - \frac{t \cdot y}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{y}{a}\right) \cdot x\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-83}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ y a)) x)))
   (if (<= a -2.55e-15) t_1 (if (<= a 1.7e-83) (- t (/ (* t y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 - (y / a)) * x;
	double tmp;
	if (a <= -2.55e-15) {
		tmp = t_1;
	} else if (a <= 1.7e-83) {
		tmp = t - ((t * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - (y / a)) * x
    if (a <= (-2.55d-15)) then
        tmp = t_1
    else if (a <= 1.7d-83) then
        tmp = t - ((t * y) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 - (y / a)) * x;
	double tmp;
	if (a <= -2.55e-15) {
		tmp = t_1;
	} else if (a <= 1.7e-83) {
		tmp = t - ((t * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (1.0 - (y / a)) * x
	tmp = 0
	if a <= -2.55e-15:
		tmp = t_1
	elif a <= 1.7e-83:
		tmp = t - ((t * y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(1.0 - Float64(y / a)) * x)
	tmp = 0.0
	if (a <= -2.55e-15)
		tmp = t_1;
	elseif (a <= 1.7e-83)
		tmp = Float64(t - Float64(Float64(t * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (1.0 - (y / a)) * x;
	tmp = 0.0;
	if (a <= -2.55e-15)
		tmp = t_1;
	elseif (a <= 1.7e-83)
		tmp = t - ((t * y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[a, -2.55e-15], t$95$1, If[LessEqual[a, 1.7e-83], N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.55e-15 or 1.6999999999999999e-83 < a

   1. Initial program 68.9%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 50.8

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

   4. Applied rewrites 50.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \left(1 - \frac{y}{a}\right) \cdot x \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(1 - \frac{y}{a}\right) \cdot x \]

      2. lower-/.f64 47.5

         \[\leadsto \left(1 - \frac{y}{a}\right) \cdot x \]

   7. Applied rewrites 47.5%

      \[\leadsto \left(1 - \frac{y}{a}\right) \cdot x \]

   if -2.55e-15 < a < 1.6999999999999999e-83

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 63.6%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 71.8

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

   7. Applied rewrites 71.8%

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

   8. Taylor expanded in x around 0

      \[\leadsto t - \frac{t \cdot y}{z} \]
   9. Step-by-step derivation

      1. lower-*.f64 51.5

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

   10. Applied rewrites 51.5%

       \[\leadsto t - \frac{t \cdot y}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 42.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-74}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+48)
   x
   (if (<= a -8e-213)
     (* y (/ (- x t) z))
     (if (<= a 2.4e-74) (- t (/ (* t y) z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+48) {
		tmp = x;
	} else if (a <= -8e-213) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.4e-74) {
		tmp = t - ((t * y) / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7d+48)) then
        tmp = x
    else if (a <= (-8d-213)) then
        tmp = y * ((x - t) / z)
    else if (a <= 2.4d-74) then
        tmp = t - ((t * y) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+48) {
		tmp = x;
	} else if (a <= -8e-213) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.4e-74) {
		tmp = t - ((t * y) / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+48:
		tmp = x
	elif a <= -8e-213:
		tmp = y * ((x - t) / z)
	elif a <= 2.4e-74:
		tmp = t - ((t * y) / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+48)
		tmp = x;
	elseif (a <= -8e-213)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 2.4e-74)
		tmp = Float64(t - Float64(Float64(t * y) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e+48)
		tmp = x;
	elseif (a <= -8e-213)
		tmp = y * ((x - t) / z);
	elseif (a <= 2.4e-74)
		tmp = t - ((t * y) / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+48], x, If[LessEqual[a, -8e-213], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-74], N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.9999999999999995e48 or 2.3999999999999999e-74 < a

   1. Initial program 68.4%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 40.4%

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

   if -6.9999999999999995e48 < a < -7.9999999999999996e-213

   1. Initial program 71.1%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 51.5%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 56.5

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

   7. Applied rewrites 56.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 32.4

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

   10. Applied rewrites 32.4%

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

   if -7.9999999999999996e-213 < a < 2.3999999999999999e-74

   1. Initial program 65.7%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 67.5%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 76.9

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

   7. Applied rewrites 76.9%

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

   8. Taylor expanded in x around 0

      \[\leadsto t - \frac{t \cdot y}{z} \]
   9. Step-by-step derivation

      1. lower-*.f64 53.8

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

   10. Applied rewrites 53.8%

       \[\leadsto t - \frac{t \cdot y}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 39.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-74}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+48)
   x
   (if (<= a 3.5e-231) (* y (/ (- x t) z)) (if (<= a 2.4e-74) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+48) {
		tmp = x;
	} else if (a <= 3.5e-231) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.4e-74) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7d+48)) then
        tmp = x
    else if (a <= 3.5d-231) then
        tmp = y * ((x - t) / z)
    else if (a <= 2.4d-74) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+48) {
		tmp = x;
	} else if (a <= 3.5e-231) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.4e-74) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+48:
		tmp = x
	elif a <= 3.5e-231:
		tmp = y * ((x - t) / z)
	elif a <= 2.4e-74:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+48)
		tmp = x;
	elseif (a <= 3.5e-231)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 2.4e-74)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e+48)
		tmp = x;
	elseif (a <= 3.5e-231)
		tmp = y * ((x - t) / z);
	elseif (a <= 2.4e-74)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+48], x, If[LessEqual[a, 3.5e-231], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-74], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.9999999999999995e48 or 2.3999999999999999e-74 < a

   1. Initial program 68.4%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 40.4%

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

   if -6.9999999999999995e48 < a < 3.5000000000000001e-231

   1. Initial program 68.6%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 59.9%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 67.6

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

   7. Applied rewrites 67.6%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 40.8

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

   10. Applied rewrites 40.8%

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

   if 3.5000000000000001e-231 < a < 2.3999999999999999e-74

   1. Initial program 66.7%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   3. Step-by-step derivation

   4. Applied rewrites 35.0%

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

Alternative 14: 37.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-213}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-74}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e+50)
   x
   (if (<= a -7.6e-213) (* (/ y z) x) (if (<= a 2.4e-74) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+50) {
		tmp = x;
	} else if (a <= -7.6e-213) {
		tmp = (y / z) * x;
	} else if (a <= 2.4e-74) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5d+50)) then
        tmp = x
    else if (a <= (-7.6d-213)) then
        tmp = (y / z) * x
    else if (a <= 2.4d-74) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+50) {
		tmp = x;
	} else if (a <= -7.6e-213) {
		tmp = (y / z) * x;
	} else if (a <= 2.4e-74) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e+50:
		tmp = x
	elif a <= -7.6e-213:
		tmp = (y / z) * x
	elif a <= 2.4e-74:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e+50)
		tmp = x;
	elseif (a <= -7.6e-213)
		tmp = Float64(Float64(y / z) * x);
	elseif (a <= 2.4e-74)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e+50)
		tmp = x;
	elseif (a <= -7.6e-213)
		tmp = (y / z) * x;
	elseif (a <= 2.4e-74)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e+50], x, If[LessEqual[a, -7.6e-213], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 2.4e-74], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -5e50 or 2.3999999999999999e-74 < a

   1. Initial program 68.4%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 40.4%

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

   if -5e50 < a < -7.5999999999999999e-213

   1. Initial program 71.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 34.8

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

   4. Applied rewrites 34.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-/.f64 22.1

         \[\leadsto \frac{y}{z} \cdot x \]

   7. Applied rewrites 22.1%

      \[\leadsto \frac{y}{z} \cdot x \]

   if -7.5999999999999999e-213 < a < 2.3999999999999999e-74

   1. Initial program 65.7%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   3. Step-by-step derivation

   4. Applied rewrites 36.5%

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

Alternative 15: 35.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-74}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e+50)
   x
   (if (<= a -4.3e-228) (/ (* x y) z) (if (<= a 2.4e-74) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+50) {
		tmp = x;
	} else if (a <= -4.3e-228) {
		tmp = (x * y) / z;
	} else if (a <= 2.4e-74) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5d+50)) then
        tmp = x
    else if (a <= (-4.3d-228)) then
        tmp = (x * y) / z
    else if (a <= 2.4d-74) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+50) {
		tmp = x;
	} else if (a <= -4.3e-228) {
		tmp = (x * y) / z;
	} else if (a <= 2.4e-74) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e+50:
		tmp = x
	elif a <= -4.3e-228:
		tmp = (x * y) / z
	elif a <= 2.4e-74:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e+50)
		tmp = x;
	elseif (a <= -4.3e-228)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 2.4e-74)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e+50)
		tmp = x;
	elseif (a <= -4.3e-228)
		tmp = (x * y) / z;
	elseif (a <= 2.4e-74)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e+50], x, If[LessEqual[a, -4.3e-228], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.4e-74], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -5e50 or 2.3999999999999999e-74 < a

   1. Initial program 68.4%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 40.4%

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

   if -5e50 < a < -4.3e-228

   1. Initial program 70.8%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 34.6

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

   4. Applied rewrites 34.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{z} \]

      2. lower-*.f64 20.1

         \[\leadsto \frac{x \cdot y}{z} \]

   7. Applied rewrites 20.1%

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

   if -4.3e-228 < a < 2.3999999999999999e-74

   1. Initial program 65.6%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   3. Step-by-step derivation

   4. Applied rewrites 36.8%

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

Alternative 16: 34.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-74}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e-15) x (if (<= a 2.4e-74) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e-15) {
		tmp = x;
	} else if (a <= 2.4e-74) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.6d-15)) then
        tmp = x
    else if (a <= 2.4d-74) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e-15) {
		tmp = x;
	} else if (a <= 2.4e-74) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e-15:
		tmp = x
	elif a <= 2.4e-74:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e-15)
		tmp = x;
	elseif (a <= 2.4e-74)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e-15)
		tmp = x;
	elseif (a <= 2.4e-74)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e-15], x, If[LessEqual[a, 2.4e-74], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6000000000000001e-15 or 2.3999999999999999e-74 < a

   1. Initial program 69.0%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 38.7%

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

   if -3.6000000000000001e-15 < a < 2.3999999999999999e-74

   1. Initial program 67.3%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   3. Step-by-step derivation

   4. Applied rewrites 35.0%

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

Alternative 17: 25.2% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

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, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 68.3%

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

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{t} \]
3. Step-by-step derivation

4. Applied rewrites 25.2%

   \[\leadsto \color{blue}{t} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025101 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y z) (- t x)) (- a z))))