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

Percentage Accurate: 68.1% → 89.5%

Time: 10.8s

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: 68.1% 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: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(1 - \frac{x}{t}\right) \cdot \frac{y - z}{a - z}\right) \cdot t\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-305}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \frac{a - y}{z} \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (* (- 1.0 (/ x t)) (/ (- y z) (- a z))) t)))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-305)
       t_2
       (if (<= t_2 0.0)
         (- t (* (/ (- a y) z) x))
         (if (<= t_2 5e+296) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((1.0 - (x / t)) * ((y - z) / (a - z))) * t);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-305) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t - (((a - y) / z) * x);
	} else if (t_2 <= 5e+296) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((1.0 - (x / t)) * ((y - z) / (a - z))) * t);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-305) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t - (((a - y) / z) * x);
	} else if (t_2 <= 5e+296) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((1.0 - (x / t)) * ((y - z) / (a - z))) * t)
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-305:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t - (((a - y) / z) * x)
	elif t_2 <= 5e+296:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(1.0 - Float64(x / t)) * Float64(Float64(y - z) / Float64(a - z))) * t))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-305)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(a - y) / z) * x));
	elseif (t_2 <= 5e+296)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((1.0 - (x / t)) * ((y - z) / (a - z))) * t);
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-305)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t - (((a - y) / z) * x);
	elseif (t_2 <= 5e+296)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(1.0 - N[(x / t), $MachinePrecision]), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $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, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-305], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+296], 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))) < -inf.0 or 5.0000000000000001e296 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 39.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 76.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -3.99999999999999999e-305 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000001e296

   1. Initial program 97.0%

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

   if -3.99999999999999999e-305 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.7%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 90.9

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 99.0%

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

Alternative 2: 81.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{+167}:\\ \;\;\;\;t - \frac{a - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+121}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.75e+167)
   (- t (* (/ (- a y) z) x))
   (if (<= z 6.8e+121)
     (+ x (/ (* (- y z) (- t x)) (- a z)))
     (- t (* (/ (- t x) z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.75e+167) {
		tmp = t - (((a - y) / z) * x);
	} else if (z <= 6.8e+121) {
		tmp = x + (((y - z) * (t - x)) / (a - z));
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	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 (z <= (-3.75d+167)) then
        tmp = t - (((a - y) / z) * x)
    else if (z <= 6.8d+121) then
        tmp = x + (((y - z) * (t - x)) / (a - z))
    else
        tmp = t - (((t - x) / z) * (y - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.75e+167) {
		tmp = t - (((a - y) / z) * x);
	} else if (z <= 6.8e+121) {
		tmp = x + (((y - z) * (t - x)) / (a - z));
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.75e+167:
		tmp = t - (((a - y) / z) * x)
	elif z <= 6.8e+121:
		tmp = x + (((y - z) * (t - x)) / (a - z))
	else:
		tmp = t - (((t - x) / z) * (y - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.75e+167)
		tmp = Float64(t - Float64(Float64(Float64(a - y) / z) * x));
	elseif (z <= 6.8e+121)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.75e+167)
		tmp = t - (((a - y) / z) * x);
	elseif (z <= 6.8e+121)
		tmp = x + (((y - z) * (t - x)) / (a - z));
	else
		tmp = t - (((t - x) / z) * (y - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.75e+167], N[(t - N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+121], N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7499999999999998e167

   1. Initial program 30.3%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 81.9%

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

   if -3.7499999999999998e167 < z < 6.80000000000000021e121

   1. Initial program 81.6%

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

   if 6.80000000000000021e121 < z

   1. Initial program 30.8%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 81.5

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

   4. Applied rewrites 81.5%

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

Alternative 3: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+191}:\\ \;\;\;\;t - \frac{a - y}{z} \cdot x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+69}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e+191)
   (- t (* (/ (- a y) z) x))
   (if (<= z -1.1e+69)
     (- x (* (- t x) (/ z (- a z))))
     (if (<= z 3.2e-11)
       (+ x (/ (* y (- t x)) (- a z)))
       (- t (* (/ (- t x) z) (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+191) {
		tmp = t - (((a - y) / z) * x);
	} else if (z <= -1.1e+69) {
		tmp = x - ((t - x) * (z / (a - z)));
	} else if (z <= 3.2e-11) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	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 (z <= (-1.55d+191)) then
        tmp = t - (((a - y) / z) * x)
    else if (z <= (-1.1d+69)) then
        tmp = x - ((t - x) * (z / (a - z)))
    else if (z <= 3.2d-11) then
        tmp = x + ((y * (t - x)) / (a - z))
    else
        tmp = t - (((t - x) / z) * (y - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+191) {
		tmp = t - (((a - y) / z) * x);
	} else if (z <= -1.1e+69) {
		tmp = x - ((t - x) * (z / (a - z)));
	} else if (z <= 3.2e-11) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.55e+191:
		tmp = t - (((a - y) / z) * x)
	elif z <= -1.1e+69:
		tmp = x - ((t - x) * (z / (a - z)))
	elif z <= 3.2e-11:
		tmp = x + ((y * (t - x)) / (a - z))
	else:
		tmp = t - (((t - x) / z) * (y - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e+191)
		tmp = Float64(t - Float64(Float64(Float64(a - y) / z) * x));
	elseif (z <= -1.1e+69)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(z / Float64(a - z))));
	elseif (z <= 3.2e-11)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.55e+191)
		tmp = t - (((a - y) / z) * x);
	elseif (z <= -1.1e+69)
		tmp = x - ((t - x) * (z / (a - z)));
	elseif (z <= 3.2e-11)
		tmp = x + ((y * (t - x)) / (a - z));
	else
		tmp = t - (((t - x) / z) * (y - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e+191], N[(t - N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e+69], N[(x - N[(N[(t - x), $MachinePrecision] * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-11], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.54999999999999999e191

   1. Initial program 27.8%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 85.8

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

   4. Applied rewrites 85.8%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 83.9%

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

   if -1.54999999999999999e191 < z < -1.1000000000000001e69

   1. Initial program 51.9%

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

   2. Taylor expanded in y around 0

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

      1. metadata-eval N/A

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

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

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 49.3

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

   4. Applied rewrites 49.3%

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

   if -1.1000000000000001e69 < z < 3.19999999999999994e-11

   1. Initial program 88.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 78.4%

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

   if 3.19999999999999994e-11 < z

   1. Initial program 45.7%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 72.8

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

   4. Applied rewrites 72.8%

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

Alternative 4: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -6 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -6e-95)
     t_1
     (if (<= a 1.6e-97) (- t (* (/ (- t x) z) (- y a))) 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 <= -6e-95) {
		tmp = t_1;
	} else if (a <= 1.6e-97) {
		tmp = t - (((t - x) / z) * (y - a));
	} 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 <= -6e-95)
		tmp = t_1;
	elseif (a <= 1.6e-97)
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	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, -6e-95], t$95$1, If[LessEqual[a, 1.6e-97], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6e-95 or 1.5999999999999999e-97 < a

   1. Initial program 69.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 79.4%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 67.7

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

   7. Applied rewrites 67.7%

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

   if -6e-95 < a < 1.5999999999999999e-97

   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

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 83.3

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

   4. Applied rewrites 83.3%

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

Alternative 5: 72.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -2.3e-95) t_1 (if (<= a 1.6e-97) (fma (/ (- x t) z) y t) 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 <= -2.3e-95) {
		tmp = t_1;
	} else if (a <= 1.6e-97) {
		tmp = fma(((x - t) / z), y, t);
	} 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 <= -2.3e-95)
		tmp = t_1;
	elseif (a <= 1.6e-97)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	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, -2.3e-95], t$95$1, If[LessEqual[a, 1.6e-97], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.29999999999999999e-95 or 1.5999999999999999e-97 < a

   1. Initial program 69.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 79.4%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 67.7

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

   7. Applied rewrites 67.7%

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

   if -2.29999999999999999e-95 < a < 1.5999999999999999e-97

   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

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 83.3

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

   4. Applied rewrites 83.3%

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

   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. associate-/l* N/A

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

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

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

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

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

      4. associate-/l* N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot \frac{t - x}{z}, y, t\right) \]

   7. Applied rewrites 81.1%

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

Alternative 6: 68.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+163}:\\ \;\;\;\;t - \frac{a - y}{z} \cdot x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-150}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e+163)
   (- t (* (/ (- a y) z) x))
   (if (<= z -3.1e-150)
     (fma t (/ (- y z) a) x)
     (if (<= z 1.15e-48) (fma (/ (- t x) a) y x) (fma (/ (- x t) z) y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+163) {
		tmp = t - (((a - y) / z) * x);
	} else if (z <= -3.1e-150) {
		tmp = fma(t, ((y - z) / a), x);
	} else if (z <= 1.15e-48) {
		tmp = fma(((t - x) / a), y, x);
	} else {
		tmp = fma(((x - t) / z), y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e+163)
		tmp = Float64(t - Float64(Float64(Float64(a - y) / z) * x));
	elseif (z <= -3.1e-150)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	elseif (z <= 1.15e-48)
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	else
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e+163], N[(t - N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-150], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.15e-48], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.9e163

   1. Initial program 30.9%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 81.5%

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

   if -4.9e163 < z < -3.09999999999999998e-150

   1. Initial program 74.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 78.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 52.7

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

   7. Applied rewrites 52.7%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 47.0%

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

   if -3.09999999999999998e-150 < z < 1.15e-48

   1. Initial program 91.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 85.2%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 85.1

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

   7. Applied rewrites 85.1%

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

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   9. 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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 79.9

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

   10. Applied rewrites 79.9%

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

   if 1.15e-48 < z

   1. Initial program 49.3%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 70.6

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

   4. Applied rewrites 70.6%

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

   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. associate-/l* N/A

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

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

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

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

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

      4. associate-/l* N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot \frac{t - x}{z}, y, t\right) \]

   7. Applied rewrites 63.6%

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

Alternative 7: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-150}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e+163)
   (fma (/ (- t x) z) a t)
   (if (<= z -3.1e-150)
     (fma t (/ (- y z) a) x)
     (if (<= z 1.15e-48) (fma (/ (- t x) a) y x) (fma (/ (- x t) z) y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+163) {
		tmp = fma(((t - x) / z), a, t);
	} else if (z <= -3.1e-150) {
		tmp = fma(t, ((y - z) / a), x);
	} else if (z <= 1.15e-48) {
		tmp = fma(((t - x) / a), y, x);
	} else {
		tmp = fma(((x - t) / z), y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e+163)
		tmp = fma(Float64(Float64(t - x) / z), a, t);
	elseif (z <= -3.1e-150)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	elseif (z <= 1.15e-48)
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	else
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e+163], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision], If[LessEqual[z, -3.1e-150], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.15e-48], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.9e163

   1. Initial program 30.9%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 64.5%

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

   if -4.9e163 < z < -3.09999999999999998e-150

   1. Initial program 74.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 78.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 52.7

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

   7. Applied rewrites 52.7%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 47.0%

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

   if -3.09999999999999998e-150 < z < 1.15e-48

   1. Initial program 91.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 85.2%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 85.1

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

   7. Applied rewrites 85.1%

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

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   9. 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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 79.9

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

   10. Applied rewrites 79.9%

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

   if 1.15e-48 < z

   1. Initial program 49.3%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 70.6

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

   4. Applied rewrites 70.6%

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

   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. associate-/l* N/A

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

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

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

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

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

      4. associate-/l* N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot \frac{t - x}{z}, y, t\right) \]

   7. Applied rewrites 63.6%

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

Alternative 8: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.6e+92)
   (fma t (/ (- y z) a) x)
   (if (<= a 1.6e-97) (fma (/ (- x t) z) y t) (fma (- t x) (/ y a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.6e+92) {
		tmp = fma(t, ((y - z) / a), x);
	} else if (a <= 1.6e-97) {
		tmp = fma(((x - t) / z), y, t);
	} else {
		tmp = fma((t - x), (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.6e+92)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	elseif (a <= 1.6e-97)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	else
		tmp = fma(Float64(t - x), Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.6e+92], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 1.6e-97], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.6000000000000001e92

   1. Initial program 68.3%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 82.2%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 81.7

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

   7. Applied rewrites 81.7%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 74.0%

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

   if -7.6000000000000001e92 < a < 1.5999999999999999e-97

   1. Initial program 67.9%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 74.3

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

   4. Applied rewrites 74.3%

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

   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. associate-/l* N/A

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

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

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

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

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

      4. associate-/l* N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot \frac{t - x}{z}, y, t\right) \]

   7. Applied rewrites 71.1%

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

   if 1.5999999999999999e-97 < a

   1. Initial program 68.5%

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

   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 59.9

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

   4. Applied rewrites 59.9%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 60.6

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

   6. Applied rewrites 60.6%

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

Alternative 9: 64.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (/ (- y z) a) x)))
   (if (<= a -7.6e+92) t_1 (if (<= a 5.6e-46) (fma (/ (- x t) z) y t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -7.6e+92) {
		tmp = t_1;
	} else if (a <= 5.6e-46) {
		tmp = fma(((x - t) / z), y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -7.6e+92)
		tmp = t_1;
	elseif (a <= 5.6e-46)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -7.6e+92], t$95$1, If[LessEqual[a, 5.6e-46], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.6000000000000001e92 or 5.5999999999999997e-46 < a

   1. Initial program 68.6%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 74.9

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

   7. Applied rewrites 74.9%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 66.1%

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

   if -7.6000000000000001e92 < a < 5.5999999999999997e-46

   1. Initial program 67.7%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 73.6

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

   4. Applied rewrites 73.6%

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

   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. associate-/l* N/A

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

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

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

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

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

      4. associate-/l* N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot \frac{t - x}{z}, y, t\right) \]

   7. Applied rewrites 70.1%

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

Alternative 10: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t a) y x)))
   (if (<= a -8.2e+93) t_1 (if (<= a 1.15e-45) (fma (/ (- x t) z) y t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / a), y, x);
	double tmp;
	if (a <= -8.2e+93) {
		tmp = t_1;
	} else if (a <= 1.15e-45) {
		tmp = fma(((x - t) / z), y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / a), y, x)
	tmp = 0.0
	if (a <= -8.2e+93)
		tmp = t_1;
	elseif (a <= 1.15e-45)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[a, -8.2e+93], t$95$1, If[LessEqual[a, 1.15e-45], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.2000000000000002e93 or 1.14999999999999996e-45 < a

   1. Initial program 68.6%

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

   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 66.6

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

   4. Applied rewrites 66.6%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 58.3%

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

   if -8.2000000000000002e93 < a < 1.14999999999999996e-45

   1. Initial program 67.8%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 73.5

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

   4. Applied rewrites 73.5%

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

   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. associate-/l* N/A

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

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

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

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

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

      4. associate-/l* N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot \frac{t - x}{z}, y, t\right) \]

   7. Applied rewrites 70.0%

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

Alternative 11: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;t - \frac{-y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t a) y x)))
   (if (<= a -7.6e+92) t_1 (if (<= a 3.1e-60) (- t (* (/ (- y) z) x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / a), y, x);
	double tmp;
	if (a <= -7.6e+92) {
		tmp = t_1;
	} else if (a <= 3.1e-60) {
		tmp = t - ((-y / z) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / a), y, x)
	tmp = 0.0
	if (a <= -7.6e+92)
		tmp = t_1;
	elseif (a <= 3.1e-60)
		tmp = Float64(t - Float64(Float64(Float64(-y) / z) * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[a, -7.6e+92], t$95$1, If[LessEqual[a, 3.1e-60], N[(t - N[(N[((-y) / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.6000000000000001e92 or 3.09999999999999988e-60 < a

   1. Initial program 68.4%

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

   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 65.8

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

   4. Applied rewrites 65.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 57.5%

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

   if -7.6000000000000001e92 < a < 3.09999999999999988e-60

   1. Initial program 67.9%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 62.6%

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

   8. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 59.4

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

   10. Applied rewrites 59.4%

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

Alternative 12: 54.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{a}{z} \cdot x\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+105}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ a z) x))))
   (if (<= z -4.9e+163) t_1 (if (<= z 1.25e+105) (fma (/ t a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((a / z) * x);
	double tmp;
	if (z <= -4.9e+163) {
		tmp = t_1;
	} else if (z <= 1.25e+105) {
		tmp = fma((t / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(a / z) * x))
	tmp = 0.0
	if (z <= -4.9e+163)
		tmp = t_1;
	elseif (z <= 1.25e+105)
		tmp = fma(Float64(t / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(a / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+163], t$95$1, If[LessEqual[z, 1.25e+105], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9e163 or 1.25000000000000011e105 < z

   1. Initial program 31.9%

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

   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 82.3

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

   4. Applied rewrites 82.3%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 78.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 62.1%

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

   if -4.9e163 < z < 1.25000000000000011e105

   1. Initial program 82.2%

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

   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 61.3

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

   4. Applied rewrites 61.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 51.1%

      \[\leadsto \mathsf{fma}\left(\frac{t}{a}, y, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 51.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+163}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+105}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e+163) t (if (<= z 1.25e+105) (fma (/ t a) y x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+163) {
		tmp = t;
	} else if (z <= 1.25e+105) {
		tmp = fma((t / a), y, x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e+163)
		tmp = t;
	elseif (z <= 1.25e+105)
		tmp = fma(Float64(t / a), y, x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e+163], t, If[LessEqual[z, 1.25e+105], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9e163 or 1.25000000000000011e105 < z

   1. Initial program 31.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 53.5%

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

   if -4.9e163 < z < 1.25000000000000011e105

   1. Initial program 82.2%

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

   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 61.3

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

   4. Applied rewrites 61.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 51.1%

      \[\leadsto \mathsf{fma}\left(\frac{t}{a}, y, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 39.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, x, x\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{z}, a, t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.25e+22)
   (fma (/ z a) x x)
   (if (<= a 7.2e-47) (fma (/ t z) a t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.25e+22) {
		tmp = fma((z / a), x, x);
	} else if (a <= 7.2e-47) {
		tmp = fma((t / z), a, t);
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.25e+22)
		tmp = fma(Float64(z / a), x, x);
	elseif (a <= 7.2e-47)
		tmp = fma(Float64(t / z), a, t);
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.25e+22], N[(N[(z / a), $MachinePrecision] * x + x), $MachinePrecision], If[LessEqual[a, 7.2e-47], N[(N[(t / z), $MachinePrecision] * a + t), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if a < -3.2499999999999999e22

   1. Initial program 69.3%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 81.7%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 76.9

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

   7. Applied rewrites 76.9%

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

   8. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. fp-cancel-sub-sign N/A

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

      5. associate-/l* N/A

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

      6. lower--.f64 N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 52.5

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

   10. Applied rewrites 52.5%

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

   11. Taylor expanded in x around inf

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

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

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

       2. metadata-eval N/A

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

       3. *-lft-identity N/A

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

       4. +-commutative N/A

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

       5. distribute-rgt-in N/A

          \[\leadsto \frac{z}{a} \cdot x + 1 \cdot x \]

       6. *-lft-identity N/A

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

       7. lower-fma.f64 N/A

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

       8. lower-/.f64 45.4

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

   13. Applied rewrites 45.4%

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

   if -3.2499999999999999e22 < a < 7.19999999999999982e-47

   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

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   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. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 77.2

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

   4. Applied rewrites 77.2%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 42.0%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{z}, a, t\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 37.3%

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

   if 7.19999999999999982e-47 < a

   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

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

   4. Applied rewrites 38.4%

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

Alternative 15: 38.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+163}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e+163) t (if (<= z 8.6e+74) (fma (/ z a) x x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+163) {
		tmp = t;
	} else if (z <= 8.6e+74) {
		tmp = fma((z / a), x, x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e+163)
		tmp = t;
	elseif (z <= 8.6e+74)
		tmp = fma(Float64(z / a), x, x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e+163], t, If[LessEqual[z, 8.6e+74], N[(N[(z / a), $MachinePrecision] * x + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9e163 or 8.60000000000000001e74 < z

   1. Initial program 34.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 52.0%

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

   if -4.9e163 < z < 8.60000000000000001e74

   1. Initial program 83.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 81.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. 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 68.4

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

   7. Applied rewrites 68.4%

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

   8. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. fp-cancel-sub-sign N/A

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

      5. associate-/l* N/A

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

      6. lower--.f64 N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 39.9

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

   10. Applied rewrites 39.9%

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

   11. Taylor expanded in x around inf

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

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

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

       2. metadata-eval N/A

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

       3. *-lft-identity N/A

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

       4. +-commutative N/A

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

       5. distribute-rgt-in N/A

          \[\leadsto \frac{z}{a} \cdot x + 1 \cdot x \]

       6. *-lft-identity N/A

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

       7. lower-fma.f64 N/A

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

       8. lower-/.f64 32.6

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

   13. Applied rewrites 32.6%

       \[\leadsto \mathsf{fma}\left(\frac{z}{a}, x, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 37.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+163}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e+163) t (if (<= z 8.6e+74) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+163) {
		tmp = t;
	} else if (z <= 8.6e+74) {
		tmp = x;
	} else {
		tmp = t;
	}
	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 (z <= (-4.9d+163)) then
        tmp = t
    else if (z <= 8.6d+74) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+163) {
		tmp = t;
	} else if (z <= 8.6e+74) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.9e+163:
		tmp = t
	elif z <= 8.6e+74:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e+163)
		tmp = t;
	elseif (z <= 8.6e+74)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.9e+163)
		tmp = t;
	elseif (z <= 8.6e+74)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e+163], t, If[LessEqual[z, 8.6e+74], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9e163 or 8.60000000000000001e74 < z

   1. Initial program 34.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 52.0%

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

   if -4.9e163 < z < 8.60000000000000001e74

   1. Initial program 83.0%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 31.4%

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

Alternative 17: 25.2% accurate, 17.9× 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 68.1%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 25.2%

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

Reproduce

herbie shell --seed 2025130 
(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))))