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

Percentage Accurate: 68.1% → 90.6%

Time: 5.3s

Alternatives: 19

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: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ t_3 := x + \frac{\mathsf{fma}\left(-x, y - z, \left(y - z\right) \cdot t\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-254}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;-1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \frac{t}{x}, -1 \cdot \frac{\left(y + -1 \cdot \frac{t \cdot y - a \cdot t}{x}\right) - a}{z}\right)\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+298}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z))))
        (t_3 (+ x (/ (fma (- x) (- y z) (* (- y z) t)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-254)
       t_3
       (if (<= t_2 0.0)
         (*
          -1.0
          (*
           x
           (fma
            -1.0
            (/ t x)
            (* -1.0 (/ (- (+ y (* -1.0 (/ (- (* t y) (* a t)) x))) a) z)))))
         (if (<= t_2 1e+298) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double t_3 = x + (fma(-x, (y - z), ((y - z) * t)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-254) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 * (x * fma(-1.0, (t / x), (-1.0 * (((y + (-1.0 * (((t * y) - (a * t)) / x))) - a) / z))));
	} else if (t_2 <= 1e+298) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	t_3 = Float64(x + Float64(fma(Float64(-x), Float64(y - z), Float64(Float64(y - z) * t)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-254)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(-1.0 * Float64(x * fma(-1.0, Float64(t / x), Float64(-1.0 * Float64(Float64(Float64(y + Float64(-1.0 * Float64(Float64(Float64(t * y) - Float64(a * t)) / x))) - a) / z)))));
	elseif (t_2 <= 1e+298)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[((-x) * N[(y - z), $MachinePrecision] + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-254], t$95$3, If[LessEqual[t$95$2, 0.0], N[(-1.0 * N[(x * N[(-1.0 * N[(t / x), $MachinePrecision] + N[(-1.0 * N[(N[(N[(y + N[(-1.0 * N[(N[(N[(t * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+298], t$95$3, 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 9.9999999999999996e297 < (+.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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 81.6

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

   3. Applied rewrites 81.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000003e-254 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999996e297

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 96.7

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

   4. Applied rewrites 96.7%

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

   if -5.0000000000000003e-254 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 10.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 11.2

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

   3. Applied rewrites 11.2%

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

   4. Taylor expanded in a around inf

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

   6. Applied rewrites 9.3%

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

   7. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   9. Applied rewrites 74.5%

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

   10. Taylor expanded in z around -inf

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

       1. lower-fma.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-/.f64 N/A

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

   12. Applied rewrites 92.8%

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

Alternative 2: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ t_3 := x + \frac{\mathsf{fma}\left(-x, y - z, \left(y - z\right) \cdot t\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-254}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+298}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z))))
        (t_3 (+ x (/ (fma (- x) (- y z) (* (- y z) t)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-254)
       t_3
       (if (<= t_2 0.0)
         (+ t (- (/ (* (- t x) (- y a)) z)))
         (if (<= t_2 1e+298) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double t_3 = x + (fma(-x, (y - z), ((y - z) * t)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-254) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = t + -(((t - x) * (y - a)) / z);
	} else if (t_2 <= 1e+298) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	t_3 = Float64(x + Float64(fma(Float64(-x), Float64(y - z), Float64(Float64(y - z) * t)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-254)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)));
	elseif (t_2 <= 1e+298)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[((-x) * N[(y - z), $MachinePrecision] + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-254], t$95$3, If[LessEqual[t$95$2, 0.0], N[(t + (-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[t$95$2, 1e+298], t$95$3, 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 9.9999999999999996e297 < (+.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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 81.6

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

   3. Applied rewrites 81.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000003e-254 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999996e297

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 96.7

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

   4. Applied rewrites 96.7%

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

   if -5.0000000000000003e-254 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 10.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 11.2

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

   3. Applied rewrites 11.2%

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

   4. Taylor expanded in z around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower-neg.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 93.0

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

   6. Applied rewrites 93.0%

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

Alternative 3: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-254}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+298}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-254)
       t_2
       (if (<= t_2 0.0)
         (+ t (- (/ (* (- t x) (- y a)) z)))
         (if (<= t_2 1e+298) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-254) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + -(((t - x) * (y - a)) / z);
	} else if (t_2 <= 1e+298) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-254)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)));
	elseif (t_2 <= 1e+298)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-254], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + (-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[t$95$2, 1e+298], 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 9.9999999999999996e297 < (+.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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 81.6

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

   3. Applied rewrites 81.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000003e-254 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999996e297

   1. Initial program 96.7%

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

   if -5.0000000000000003e-254 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 10.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 11.2

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

   3. Applied rewrites 11.2%

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

   4. Taylor expanded in z around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower-neg.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 93.0

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

   6. Applied rewrites 93.0%

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

Alternative 4: 86.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-60}:\\ \;\;\;\;-x \cdot \left(\mathsf{fma}\left(-1, \frac{t \cdot \left(y - z\right)}{x \cdot \left(a - z\right)}, \frac{y}{a - z}\right) - \left(1 + \frac{z}{a - z}\right)\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+298}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(-x, y - z, \left(y - z\right) \cdot t\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -1e+139)
     t_1
     (if (<= t_2 1e-60)
       (-
        (*
         x
         (-
          (fma -1.0 (/ (* t (- y z)) (* x (- a z))) (/ y (- a z)))
          (+ 1.0 (/ z (- a z))))))
       (if (<= t_2 1e+298)
         (+ x (/ (fma (- x) (- y z) (* (- y z) t)) (- a z)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -1e+139) {
		tmp = t_1;
	} else if (t_2 <= 1e-60) {
		tmp = -(x * (fma(-1.0, ((t * (y - z)) / (x * (a - z))), (y / (a - z))) - (1.0 + (z / (a - z)))));
	} else if (t_2 <= 1e+298) {
		tmp = x + (fma(-x, (y - z), ((y - z) * t)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -1e+139)
		tmp = t_1;
	elseif (t_2 <= 1e-60)
		tmp = Float64(-Float64(x * Float64(fma(-1.0, Float64(Float64(t * Float64(y - z)) / Float64(x * Float64(a - z))), Float64(y / Float64(a - z))) - Float64(1.0 + Float64(z / Float64(a - z))))));
	elseif (t_2 <= 1e+298)
		tmp = Float64(x + Float64(fma(Float64(-x), Float64(y - z), Float64(Float64(y - z) * t)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+139], t$95$1, If[LessEqual[t$95$2, 1e-60], (-N[(x * N[(N[(-1.0 * N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(x * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[t$95$2, 1e+298], N[(x + N[(N[((-x) * N[(y - z), $MachinePrecision] + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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))) < -1.00000000000000003e139 or 9.9999999999999996e297 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 50.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 82.5

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

   3. Applied rewrites 82.5%

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

   if -1.00000000000000003e139 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999997e-61

   1. Initial program 75.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 68.4

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

   3. Applied rewrites 68.4%

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

   4. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   6. Applied rewrites 87.1%

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

   if 9.9999999999999997e-61 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999996e297

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 96.8

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

   4. Applied rewrites 96.8%

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

Alternative 5: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(x \cdot \left(\mathsf{fma}\left(-1, \frac{t}{x} \cdot \frac{y - z}{a - z}, \frac{y}{a - z}\right) - \left(1 + \frac{z}{a - z}\right)\right)\right)\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{-156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1
         (*
          -1.0
          (*
           x
           (-
            (fma -1.0 (* (/ t x) (/ (- y z) (- a z))) (/ y (- a z)))
            (+ 1.0 (/ z (- a z))))))))
   (if (<= x -2.45e-156)
     t_1
     (if (<= x 4.4e-94) (fma (- y z) (/ (- t x) (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 * (x * (fma(-1.0, ((t / x) * ((y - z) / (a - z))), (y / (a - z))) - (1.0 + (z / (a - z)))));
	double tmp;
	if (x <= -2.45e-156) {
		tmp = t_1;
	} else if (x <= 4.4e-94) {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-1.0 * Float64(x * Float64(fma(-1.0, Float64(Float64(t / x) * Float64(Float64(y - z) / Float64(a - z))), Float64(y / Float64(a - z))) - Float64(1.0 + Float64(z / Float64(a - z))))))
	tmp = 0.0
	if (x <= -2.45e-156)
		tmp = t_1;
	elseif (x <= 4.4e-94)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(t / x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.45e-156], t$95$1, If[LessEqual[x, 4.4e-94], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.44999999999999976e-156 or 4.40000000000000002e-94 < x

   1. Initial program 62.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 77.1

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

   3. Applied rewrites 77.1%

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

   4. Taylor expanded in a around inf

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

   6. Applied rewrites 28.3%

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

   7. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   9. Applied rewrites 87.3%

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

   if -2.44999999999999976e-156 < x < 4.40000000000000002e-94

   1. Initial program 81.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 86.3

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

   3. Applied rewrites 86.3%

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

Alternative 6: 86.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -2e-266)
     t_1
     (if (<= t_2 0.0) (+ t (- (/ (* (- t x) (- y a)) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -2e-266) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + -(((t - x) * (y - a)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -2e-266)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-266], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + (-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2e-266 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 85.6

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

   3. Applied rewrites 85.6%

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

   if -2e-266 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 9.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 9.8

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

   3. Applied rewrites 9.8%

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

   4. Taylor expanded in z around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower-neg.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 94.6

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

   6. Applied rewrites 94.6%

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

Alternative 7: 84.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -2e-266) t_1 (if (<= t_2 0.0) (+ t (/ (* x y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -2e-266) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -2e-266)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-266], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2e-266 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 85.6

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

   3. Applied rewrites 85.6%

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

   if -2e-266 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 9.0%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 94.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 69.4

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

   7. Applied rewrites 69.4%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 69.2

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

   10. Applied rewrites 69.2%

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

Alternative 8: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-212}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -2.25e+43)
     t_1
     (if (<= a 3.5e-212)
       (+ t (* y (/ (- x t) z)))
       (if (<= a 1.6e+132) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / a), x);
	double tmp;
	if (a <= -2.25e+43) {
		tmp = t_1;
	} else if (a <= 3.5e-212) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 1.6e+132) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -2.25e+43)
		tmp = t_1;
	elseif (a <= 3.5e-212)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (a <= 1.6e+132)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.25e+43], t$95$1, If[LessEqual[a, 3.5e-212], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+132], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.25e43 or 1.5999999999999999e132 < a

   1. Initial program 67.9%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 79.0

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

   4. Applied rewrites 79.0%

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

   if -2.25e43 < a < 3.4999999999999998e-212

   1. Initial program 66.7%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 61.2%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 68.5

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

   7. Applied rewrites 68.5%

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

   8. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 71.9

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

   10. Applied rewrites 71.9%

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

   if 3.4999999999999998e-212 < a < 1.5999999999999999e132

   1. Initial program 70.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 78.1

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

   3. Applied rewrites 78.1%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 56.8

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

   6. Applied rewrites 56.8%

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

Alternative 9: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-212}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= a -9.5e+101)
     t_1
     (if (<= a 3.5e-212)
       (+ t (* y (/ (- x t) z)))
       (if (<= a 1.65e+157) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (a <= -9.5e+101) {
		tmp = t_1;
	} else if (a <= 3.5e-212) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 1.65e+157) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -9.5e+101)
		tmp = t_1;
	elseif (a <= 3.5e-212)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (a <= 1.65e+157)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -9.5e+101], t$95$1, If[LessEqual[a, 3.5e-212], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+157], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.49999999999999947e101 or 1.6500000000000001e157 < a

   1. Initial program 67.7%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 71.2

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

   4. Applied rewrites 71.2%

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

   if -9.49999999999999947e101 < a < 3.4999999999999998e-212

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 57.2%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 64.2

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

   7. Applied rewrites 64.2%

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

   8. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 67.9

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

   10. Applied rewrites 67.9%

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

   if 3.4999999999999998e-212 < a < 1.6500000000000001e157

   1. Initial program 69.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 78.3

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

   3. Applied rewrites 78.3%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 56.1

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

   6. Applied rewrites 56.1%

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

Alternative 10: 51.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+48}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.3e+48)
   (+ t (/ (* x y) z))
   (if (<= z 9.5e-135)
     (+ x (/ (* t y) a))
     (if (<= z 7e+155) (* y (/ (- x t) z)) (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.3e+48) {
		tmp = t + ((x * y) / z);
	} else if (z <= 9.5e-135) {
		tmp = x + ((t * y) / a);
	} else if (z <= 7e+155) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	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 <= (-5.3d+48)) then
        tmp = t + ((x * y) / z)
    else if (z <= 9.5d-135) then
        tmp = x + ((t * y) / a)
    else if (z <= 7d+155) then
        tmp = y * ((x - t) / z)
    else
        tmp = t * (1.0d0 - (y / z))
    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 <= -5.3e+48) {
		tmp = t + ((x * y) / z);
	} else if (z <= 9.5e-135) {
		tmp = x + ((t * y) / a);
	} else if (z <= 7e+155) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.3e+48:
		tmp = t + ((x * y) / z)
	elif z <= 9.5e-135:
		tmp = x + ((t * y) / a)
	elif z <= 7e+155:
		tmp = y * ((x - t) / z)
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.3e+48)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (z <= 9.5e-135)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (z <= 7e+155)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.3e+48)
		tmp = t + ((x * y) / z);
	elseif (z <= 9.5e-135)
		tmp = x + ((t * y) / a);
	elseif (z <= 7e+155)
		tmp = y * ((x - t) / z);
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.3e+48], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-135], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+155], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.3e48

   1. Initial program 42.5%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 60.1%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 59.8

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

   7. Applied rewrites 59.8%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.1

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

   10. Applied rewrites 59.1%

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

   if -5.3e48 < z < 9.50000000000000007e-135

   1. Initial program 89.2%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 57.1%

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

   if 9.50000000000000007e-135 < z < 6.99999999999999969e155

   1. Initial program 73.0%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 45.5%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 49.0

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

   7. Applied rewrites 49.0%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 31.8

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

   10. Applied rewrites 31.8%

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

   if 6.99999999999999969e155 < z

   1. Initial program 29.0%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 60.9%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 60.9

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

   7. Applied rewrites 60.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 59.9

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

   10. Applied rewrites 59.9%

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

Alternative 11: 48.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-163}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+124)
   x
   (if (<= a -2.1e-163)
     (+ t (/ (* x y) z))
     (if (<= a 1.25e+118) (* t (- 1.0 (/ y z))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+124) {
		tmp = x;
	} else if (a <= -2.1e-163) {
		tmp = t + ((x * y) / z);
	} else if (a <= 1.25e+118) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+124)) then
        tmp = x
    else if (a <= (-2.1d-163)) then
        tmp = t + ((x * y) / z)
    else if (a <= 1.25d+118) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+124) {
		tmp = x;
	} else if (a <= -2.1e-163) {
		tmp = t + ((x * y) / z);
	} else if (a <= 1.25e+118) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+124:
		tmp = x
	elif a <= -2.1e-163:
		tmp = t + ((x * y) / z)
	elif a <= 1.25e+118:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+124)
		tmp = x;
	elseif (a <= -2.1e-163)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (a <= 1.25e+118)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+124)
		tmp = x;
	elseif (a <= -2.1e-163)
		tmp = t + ((x * y) / z);
	elseif (a <= 1.25e+118)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+124], x, If[LessEqual[a, -2.1e-163], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+118], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000004e124 or 1.24999999999999993e118 < a

   1. Initial program 67.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 51.2%

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

   if -9.50000000000000004e124 < a < -2.09999999999999998e-163

   1. Initial program 70.1%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 42.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 45.8

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

   7. Applied rewrites 45.8%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 40.5

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

   10. Applied rewrites 40.5%

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

   if -2.09999999999999998e-163 < a < 1.24999999999999993e118

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 57.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 65.6

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

   7. Applied rewrites 65.6%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 51.1

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

   10. Applied rewrites 51.1%

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

Alternative 12: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-102}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ t (- a z)) x)))
   (if (<= a -2.25e+43)
     t_1
     (if (<= a 3.8e-102) (+ t (* y (/ (- x t) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), (t / (a - z)), x);
	double tmp;
	if (a <= -2.25e+43) {
		tmp = t_1;
	} else if (a <= 3.8e-102) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(t / Float64(a - z)), x)
	tmp = 0.0
	if (a <= -2.25e+43)
		tmp = t_1;
	elseif (a <= 3.8e-102)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.25e+43], t$95$1, If[LessEqual[a, 3.8e-102], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.25e43 or 3.80000000000000026e-102 < a

   1. Initial program 69.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 86.4

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

   3. Applied rewrites 86.4%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 74.5%

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

   if -2.25e43 < a < 3.80000000000000026e-102

   1. Initial program 66.5%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 68.9

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

   7. Applied rewrites 68.9%

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

   8. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 72.7

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

   10. Applied rewrites 72.7%

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

Alternative 13: 37.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-118}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+117}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+124)
   x
   (if (<= a -3.15e-118)
     t
     (if (<= a -5.8e-292) (* x (/ y z)) (if (<= a 8.2e+117) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+124) {
		tmp = x;
	} else if (a <= -3.15e-118) {
		tmp = t;
	} else if (a <= -5.8e-292) {
		tmp = x * (y / z);
	} else if (a <= 8.2e+117) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+124)) then
        tmp = x
    else if (a <= (-3.15d-118)) then
        tmp = t
    else if (a <= (-5.8d-292)) then
        tmp = x * (y / z)
    else if (a <= 8.2d+117) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+124) {
		tmp = x;
	} else if (a <= -3.15e-118) {
		tmp = t;
	} else if (a <= -5.8e-292) {
		tmp = x * (y / z);
	} else if (a <= 8.2e+117) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+124:
		tmp = x
	elif a <= -3.15e-118:
		tmp = t
	elif a <= -5.8e-292:
		tmp = x * (y / z)
	elif a <= 8.2e+117:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+124)
		tmp = x;
	elseif (a <= -3.15e-118)
		tmp = t;
	elseif (a <= -5.8e-292)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 8.2e+117)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+124)
		tmp = x;
	elseif (a <= -3.15e-118)
		tmp = t;
	elseif (a <= -5.8e-292)
		tmp = x * (y / z);
	elseif (a <= 8.2e+117)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+124], x, If[LessEqual[a, -3.15e-118], t, If[LessEqual[a, -5.8e-292], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+117], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000004e124 or 8.1999999999999999e117 < a

   1. Initial program 67.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 51.2%

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

   if -9.50000000000000004e124 < a < -3.1499999999999999e-118 or -5.79999999999999985e-292 < a < 8.1999999999999999e117

   1. Initial program 68.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 30.5%

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

   if -3.1499999999999999e-118 < a < -5.79999999999999985e-292

   1. Initial program 65.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 69.8

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

   3. Applied rewrites 69.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. sub-div N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 31.5

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

   6. Applied rewrites 31.5%

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

   7. Taylor expanded in a around 0

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

      1. lower-/.f64 32.6

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

   9. Applied rewrites 32.6%

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

Alternative 14: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-67}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= a -9.5e+101)
     t_1
     (if (<= a 3.3e-67) (+ t (* y (/ (- x t) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (a <= -9.5e+101) {
		tmp = t_1;
	} else if (a <= 3.3e-67) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -9.5e+101)
		tmp = t_1;
	elseif (a <= 3.3e-67)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -9.5e+101], t$95$1, If[LessEqual[a, 3.3e-67], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.49999999999999947e101 or 3.3000000000000002e-67 < a

   1. Initial program 69.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 64.6

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

   4. Applied rewrites 64.6%

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

   if -9.49999999999999947e101 < a < 3.3000000000000002e-67

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 57.9%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 64.9

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

   7. Applied rewrites 64.9%

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

   8. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 69.0

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

   10. Applied rewrites 69.0%

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

Alternative 15: 61.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+61}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+61)
   (+ t (/ (* x y) z))
   (if (<= z 7e+155) (fma y (/ (- t x) a) x) (* t (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+61) {
		tmp = t + ((x * y) / z);
	} else if (z <= 7e+155) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+61)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (z <= 7e+155)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+61], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+155], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.49999999999999959e61

   1. Initial program 41.0%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 61.1%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 60.4

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

   7. Applied rewrites 60.4%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.9

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

   10. Applied rewrites 59.9%

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

   if -9.49999999999999959e61 < z < 6.99999999999999969e155

   1. Initial program 83.2%

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

   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. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 62.5

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

   4. Applied rewrites 62.5%

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

   if 6.99999999999999969e155 < z

   1. Initial program 29.0%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 60.9%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 60.9

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

   7. Applied rewrites 60.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 59.9

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

   10. Applied rewrites 59.9%

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

Alternative 16: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+64}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e+64)
   (+ t (/ (* x y) z))
   (if (<= z 2.5e-66) (* x (- 1.0 (/ y a))) (* t (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+64) {
		tmp = t + ((x * y) / z);
	} else if (z <= 2.5e-66) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	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 <= (-1.85d+64)) then
        tmp = t + ((x * y) / z)
    else if (z <= 2.5d-66) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * (1.0d0 - (y / z))
    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 <= -1.85e+64) {
		tmp = t + ((x * y) / z);
	} else if (z <= 2.5e-66) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e+64:
		tmp = t + ((x * y) / z)
	elif z <= 2.5e-66:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e+64)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (z <= 2.5e-66)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e+64)
		tmp = t + ((x * y) / z);
	elseif (z <= 2.5e-66)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e+64], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-66], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.84999999999999992e64

   1. Initial program 40.8%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 61.1%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 60.3

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

   7. Applied rewrites 60.3%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.8

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

   10. Applied rewrites 59.8%

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

   if -1.84999999999999992e64 < z < 2.49999999999999981e-66

   1. Initial program 88.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 91.1

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

   3. Applied rewrites 91.1%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. sub-div N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 57.9

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

   6. Applied rewrites 57.9%

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

   7. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 53.1

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

   9. Applied rewrites 53.1%

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

   if 2.49999999999999981e-66 < z

   1. Initial program 52.4%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 55.7

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

   7. Applied rewrites 55.7%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 47.2

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

   10. Applied rewrites 47.2%

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

Alternative 17: 48.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+125) x (if (<= a 1.25e+118) (* t (- 1.0 (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+125) {
		tmp = x;
	} else if (a <= 1.25e+118) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d+125)) then
        tmp = x
    else if (a <= 1.25d+118) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+125) {
		tmp = x;
	} else if (a <= 1.25e+118) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+125:
		tmp = x
	elif a <= 1.25e+118:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+125)
		tmp = x;
	elseif (a <= 1.25e+118)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+125)
		tmp = x;
	elseif (a <= 1.25e+118)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+125], x, If[LessEqual[a, 1.25e+118], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999983e125 or 1.24999999999999993e118 < a

   1. Initial program 67.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 51.1%

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

   if -3.19999999999999983e125 < a < 1.24999999999999993e118

   1. Initial program 68.2%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 52.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 58.8

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

   7. Applied rewrites 58.8%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 47.5

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

   10. Applied rewrites 47.5%

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

Alternative 18: 37.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+117}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+124) x (if (<= a 8.2e+117) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+124) {
		tmp = x;
	} else if (a <= 8.2e+117) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+124)) then
        tmp = x
    else if (a <= 8.2d+117) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+124) {
		tmp = x;
	} else if (a <= 8.2e+117) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+124:
		tmp = x
	elif a <= 8.2e+117:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+124)
		tmp = x;
	elseif (a <= 8.2e+117)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+124)
		tmp = x;
	elseif (a <= 8.2e+117)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+124], x, If[LessEqual[a, 8.2e+117], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.50000000000000004e124 or 8.1999999999999999e117 < a

   1. Initial program 67.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 51.2%

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

   if -9.50000000000000004e124 < a < 8.1999999999999999e117

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 31.6%

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

Alternative 19: 25.7% accurate, 29.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.1%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 25.7%

   \[\leadsto \color{blue}{t} \]
5. Add Preprocessing

Developer Target 1: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025095 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))