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

Percentage Accurate: 67.5% → 90.0%

Time: 7.4s

Alternatives: 16

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - z}{t - a}, y - x, x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-301}:\\ \;\;\;\;y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t z) (- t a)) (- y x) x))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -1e-218)
     t_1
     (if (<= t_2 1e-301)
       (+ y (* -1.0 (/ (- (* z (- y x)) (* a (- y x))) t)))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - z) / (t - a)), (y - x), x);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -1e-218) {
		tmp = t_1;
	} else if (t_2 <= 1e-301) {
		tmp = y + (-1.0 * (((z * (y - x)) - (a * (y - x))) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - z) / Float64(t - a)), Float64(y - x), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e-218)
		tmp = t_1;
	elseif (t_2 <= 1e-301)
		tmp = Float64(y + Float64(-1.0 * Float64(Float64(Float64(z * Float64(y - x)) - Float64(a * Float64(y - x))) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-218], t$95$1, If[LessEqual[t$95$2, 1e-301], N[(y + N[(-1.0 * N[(N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-218 or 1.00000000000000007e-301 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   if -1e-218 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.00000000000000007e-301

   1. Initial program 67.5%

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

   2. Taylor expanded in t around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.3

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

   4. Applied rewrites 46.3%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - z}{t - a}, y - x, x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(-1, a \cdot x, -1 \cdot \left(z \cdot \left(y - x\right)\right)\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t z) (- t a)) (- y x) x))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -1e-218)
     t_1
     (if (<= t_2 0.0)
       (/ (fma -1.0 (* a x) (* -1.0 (* z (- y x)))) (- t a))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - z) / (t - a)), (y - x), x);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -1e-218) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = fma(-1.0, (a * x), (-1.0 * (z * (y - x)))) / (t - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - z) / Float64(t - a)), Float64(y - x), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e-218)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(fma(-1.0, Float64(a * x), Float64(-1.0 * Float64(z * Float64(y - x)))) / Float64(t - a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-218], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(-1.0 * N[(a * x), $MachinePrecision] + N[(-1.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-218 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   if -1e-218 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 79.5

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

   3. Applied rewrites 79.5%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg-rev N/A

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

      11. lower-/.f64 79.2

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

   5. Applied rewrites 79.2%

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

   7. Applied rewrites 62.6%

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

   8. Taylor expanded in t around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 55.7

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

   10. Applied rewrites 55.7%

       \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-1, a \cdot x, -1 \cdot \left(z \cdot \left(y - x\right)\right)\right)}}{t - a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 83.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+158}:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{t - a}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e+158)
   (* (/ (- z t) (- a t)) y)
   (fma (/ (- t z) (- t a)) (- y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+158) {
		tmp = ((z - t) / (a - t)) * y;
	} else {
		tmp = fma(((t - z) / (t - a)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e+158)
		tmp = Float64(Float64(Float64(z - t) / Float64(a - t)) * y);
	else
		tmp = fma(Float64(Float64(t - z) / Float64(t - a)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e+158], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e158

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 51.2

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

      14. lift-/.f64 N/A

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

      15. frac-2neg N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lift--.f64 N/A

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

      22. lower-/.f64 51.2

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

   6. Applied rewrites 51.2%

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

   if -3e158 < t

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

Alternative 4: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{x - y}{t - a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.1e+152)
   (* (/ (- z t) (- a t)) y)
   (fma (- z t) (/ (- x y) (- t a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.1e+152) {
		tmp = ((z - t) / (a - t)) * y;
	} else {
		tmp = fma((z - t), ((x - y) / (t - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.1e+152)
		tmp = Float64(Float64(Float64(z - t) / Float64(a - t)) * y);
	else
		tmp = fma(Float64(z - t), Float64(Float64(x - y) / Float64(t - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.1e+152], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0999999999999998e152

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 51.2

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

      14. lift-/.f64 N/A

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

      15. frac-2neg N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lift--.f64 N/A

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

      22. lower-/.f64 51.2

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

   6. Applied rewrites 51.2%

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

   if -4.0999999999999998e152 < t

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 79.5

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

   3. Applied rewrites 79.5%

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

Alternative 5: 69.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -120000000000:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -120000000000.0)
   (* (/ (- z t) (- a t)) y)
   (if (<= t 3.5e-136)
     (+ x (/ (* z (- y x)) (- a t)))
     (if (<= t 2.9e+114)
       (+ x (/ (* y (- z t)) (- a t)))
       (/ y (/ (- a t) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -120000000000.0) {
		tmp = ((z - t) / (a - t)) * y;
	} else if (t <= 3.5e-136) {
		tmp = x + ((z * (y - x)) / (a - t));
	} else if (t <= 2.9e+114) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-120000000000.0d0)) then
        tmp = ((z - t) / (a - t)) * y
    else if (t <= 3.5d-136) then
        tmp = x + ((z * (y - x)) / (a - t))
    else if (t <= 2.9d+114) then
        tmp = x + ((y * (z - t)) / (a - t))
    else
        tmp = y / ((a - t) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -120000000000.0) {
		tmp = ((z - t) / (a - t)) * y;
	} else if (t <= 3.5e-136) {
		tmp = x + ((z * (y - x)) / (a - t));
	} else if (t <= 2.9e+114) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -120000000000.0:
		tmp = ((z - t) / (a - t)) * y
	elif t <= 3.5e-136:
		tmp = x + ((z * (y - x)) / (a - t))
	elif t <= 2.9e+114:
		tmp = x + ((y * (z - t)) / (a - t))
	else:
		tmp = y / ((a - t) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -120000000000.0)
		tmp = Float64(Float64(Float64(z - t) / Float64(a - t)) * y);
	elseif (t <= 3.5e-136)
		tmp = Float64(x + Float64(Float64(z * Float64(y - x)) / Float64(a - t)));
	elseif (t <= 2.9e+114)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	else
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -120000000000.0)
		tmp = ((z - t) / (a - t)) * y;
	elseif (t <= 3.5e-136)
		tmp = x + ((z * (y - x)) / (a - t));
	elseif (t <= 2.9e+114)
		tmp = x + ((y * (z - t)) / (a - t));
	else
		tmp = y / ((a - t) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -120000000000.0], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 3.5e-136], N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+114], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2e11

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 51.2

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

      14. lift-/.f64 N/A

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

      15. frac-2neg N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lift--.f64 N/A

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

      22. lower-/.f64 51.2

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

   6. Applied rewrites 51.2%

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

   if -1.2e11 < t < 3.50000000000000029e-136

   1. Initial program 67.5%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 54.2

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

   4. Applied rewrites 54.2%

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

   if 3.50000000000000029e-136 < t < 2.9e114

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 54.4%

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

   if 2.9e114 < t

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg N/A

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

      11. div-flip N/A

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

      12. mult-flip-rev N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. lift--.f64 N/A

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

      18. sub-negate-rev N/A

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

      19. lift--.f64 N/A

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

      20. frac-2neg-rev N/A

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

      21. lower-/.f64 51.1

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

   6. Applied rewrites 51.1%

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

Alternative 6: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -120000000000:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-177}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -120000000000.0)
   (* (/ (- z t) (- a t)) y)
   (if (<= t -2.9e-177)
     (+ x (/ (* z (- y x)) (- a t)))
     (if (<= t 7.5e+86) (fma (/ z a) (- y x) x) (/ y (/ (- a t) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -120000000000.0) {
		tmp = ((z - t) / (a - t)) * y;
	} else if (t <= -2.9e-177) {
		tmp = x + ((z * (y - x)) / (a - t));
	} else if (t <= 7.5e+86) {
		tmp = fma((z / a), (y - x), x);
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -120000000000.0)
		tmp = Float64(Float64(Float64(z - t) / Float64(a - t)) * y);
	elseif (t <= -2.9e-177)
		tmp = Float64(x + Float64(Float64(z * Float64(y - x)) / Float64(a - t)));
	elseif (t <= 7.5e+86)
		tmp = fma(Float64(z / a), Float64(y - x), x);
	else
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -120000000000.0], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, -2.9e-177], N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+86], N[(N[(z / a), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2e11

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 51.2

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

      14. lift-/.f64 N/A

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

      15. frac-2neg N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lift--.f64 N/A

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

      22. lower-/.f64 51.2

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

   6. Applied rewrites 51.2%

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

   if -1.2e11 < t < -2.89999999999999997e-177

   1. Initial program 67.5%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 54.2

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

   4. Applied rewrites 54.2%

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

   if -2.89999999999999997e-177 < t < 7.4999999999999997e86

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 48.0

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

   6. Applied rewrites 48.0%

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

   if 7.4999999999999997e86 < t

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg N/A

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

      11. div-flip N/A

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

      12. mult-flip-rev N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. lift--.f64 N/A

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

      18. sub-negate-rev N/A

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

      19. lift--.f64 N/A

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

      20. frac-2neg-rev N/A

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

      21. lower-/.f64 51.1

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

   6. Applied rewrites 51.1%

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

Alternative 7: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.5e-34)
   (* (/ (- z t) (- a t)) y)
   (if (<= t 7.5e+86) (fma (/ z a) (- y x) x) (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e-34) {
		tmp = ((z - t) / (a - t)) * y;
	} else if (t <= 7.5e+86) {
		tmp = fma((z / a), (y - x), x);
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.5e-34)
		tmp = Float64(Float64(Float64(z - t) / Float64(a - t)) * y);
	elseif (t <= 7.5e+86)
		tmp = fma(Float64(z / a), Float64(y - x), x);
	else
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.5e-34], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 7.5e+86], N[(N[(z / a), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5000000000000004e-34

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 51.2

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

      14. lift-/.f64 N/A

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

      15. frac-2neg N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lift--.f64 N/A

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

      22. lower-/.f64 51.2

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

   6. Applied rewrites 51.2%

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

   if -7.5000000000000004e-34 < t < 7.4999999999999997e86

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 48.0

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

   6. Applied rewrites 48.0%

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

   if 7.4999999999999997e86 < t

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg N/A

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

      11. div-flip N/A

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

      12. mult-flip-rev N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. lift--.f64 N/A

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

      18. sub-negate-rev N/A

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

      19. lift--.f64 N/A

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

      20. frac-2neg-rev N/A

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

      21. lower-/.f64 51.1

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

   6. Applied rewrites 51.1%

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

Alternative 8: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t} \cdot y\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- z t) (- a t)) y)))
   (if (<= t -7.5e-34) t_1 (if (<= t 7.5e+86) (fma (/ z a) (- y x) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) / (a - t)) * y;
	double tmp;
	if (t <= -7.5e-34) {
		tmp = t_1;
	} else if (t <= 7.5e+86) {
		tmp = fma((z / a), (y - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) / Float64(a - t)) * y)
	tmp = 0.0
	if (t <= -7.5e-34)
		tmp = t_1;
	elseif (t <= 7.5e+86)
		tmp = fma(Float64(z / a), Float64(y - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t, -7.5e-34], t$95$1, If[LessEqual[t, 7.5e+86], N[(N[(z / a), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5000000000000004e-34 or 7.4999999999999997e86 < t

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 51.2

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

      14. lift-/.f64 N/A

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

      15. frac-2neg N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lift--.f64 N/A

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

      22. lower-/.f64 51.2

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

   6. Applied rewrites 51.2%

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

   if -7.5000000000000004e-34 < t < 7.4999999999999997e86

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 48.0

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

   6. Applied rewrites 48.0%

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

Alternative 9: 61.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- a t)))))
   (if (<= t -7.5e-34) t_1 (if (<= t 9.6e+86) (fma (/ z a) (- y x) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double tmp;
	if (t <= -7.5e-34) {
		tmp = t_1;
	} else if (t <= 9.6e+86) {
		tmp = fma((z / a), (y - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t <= -7.5e-34)
		tmp = t_1;
	elseif (t <= 9.6e+86)
		tmp = fma(Float64(z / a), Float64(y - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e-34], t$95$1, If[LessEqual[t, 9.6e+86], N[(N[(z / a), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5000000000000004e-34 or 9.6000000000000001e86 < t

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 45.9

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

   6. Applied rewrites 45.9%

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

   if -7.5000000000000004e-34 < t < 9.6000000000000001e86

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 48.0

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

   6. Applied rewrites 48.0%

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

Alternative 10: 57.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{a}, y - x, x\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z a) (- y x) x)))
   (if (<= z -1.95e-57) t_1 (if (<= z 1.9e+94) (fma (/ t (- t a)) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / a), (y - x), x);
	double tmp;
	if (z <= -1.95e-57) {
		tmp = t_1;
	} else if (z <= 1.9e+94) {
		tmp = fma((t / (t - a)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / a), Float64(y - x), x)
	tmp = 0.0
	if (z <= -1.95e-57)
		tmp = t_1;
	elseif (z <= 1.9e+94)
		tmp = fma(Float64(t / Float64(t - a)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / a), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.95e-57], t$95$1, If[LessEqual[z, 1.9e+94], N[(N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000003e-57 or 1.8999999999999998e94 < z

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 48.0

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

   6. Applied rewrites 48.0%

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

   if -1.95000000000000003e-57 < z < 1.8999999999999998e94

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 46.0%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 44.7%

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

Alternative 11: 57.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{x} \cdot x\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y x) x)))
   (if (<= t -4.7e+151)
     t_1
     (if (<= t 2.05e+103) (fma (/ z a) (- y x) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / x) * x;
	double tmp;
	if (t <= -4.7e+151) {
		tmp = t_1;
	} else if (t <= 2.05e+103) {
		tmp = fma((z / a), (y - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / x) * x)
	tmp = 0.0
	if (t <= -4.7e+151)
		tmp = t_1;
	elseif (t <= 2.05e+103)
		tmp = fma(Float64(z / a), Float64(y - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / x), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -4.7e+151], t$95$1, If[LessEqual[t, 2.05e+103], N[(N[(z / a), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.69999999999999989e151 or 2.0500000000000001e103 < t

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. sum-to-mult N/A

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

      3. lower-*.f64 N/A

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

   3. Applied rewrites 62.8%

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

   4. Taylor expanded in t around inf

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

      1. lower-/.f64 22.5

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

   6. Applied rewrites 22.5%

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

   if -4.69999999999999989e151 < t < 2.0500000000000001e103

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 48.0

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

   6. Applied rewrites 48.0%

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

Alternative 12: 49.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{x} \cdot x\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y x) x)))
   (if (<= t -4.7e+151) t_1 (if (<= t 2.05e+103) (fma (/ z a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / x) * x;
	double tmp;
	if (t <= -4.7e+151) {
		tmp = t_1;
	} else if (t <= 2.05e+103) {
		tmp = fma((z / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / x) * x)
	tmp = 0.0
	if (t <= -4.7e+151)
		tmp = t_1;
	elseif (t <= 2.05e+103)
		tmp = fma(Float64(z / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / x), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -4.7e+151], t$95$1, If[LessEqual[t, 2.05e+103], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.69999999999999989e151 or 2.0500000000000001e103 < t

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. sum-to-mult N/A

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

      3. lower-*.f64 N/A

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

   3. Applied rewrites 62.8%

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

   4. Taylor expanded in t around inf

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

      1. lower-/.f64 22.5

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

   6. Applied rewrites 22.5%

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

   if -4.69999999999999989e151 < t < 2.0500000000000001e103

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 48.0

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

   6. Applied rewrites 48.0%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 39.7%

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

Alternative 13: 36.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{x} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+45) (* 1.0 x) (if (<= a 3.25e-12) (* (/ y x) x) (* 1.0 x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+45) {
		tmp = 1.0 * x;
	} else if (a <= 3.25e-12) {
		tmp = (y / x) * x;
	} else {
		tmp = 1.0 * 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 <= (-1.2d+45)) then
        tmp = 1.0d0 * x
    else if (a <= 3.25d-12) then
        tmp = (y / x) * x
    else
        tmp = 1.0d0 * 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 <= -1.2e+45) {
		tmp = 1.0 * x;
	} else if (a <= 3.25e-12) {
		tmp = (y / x) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+45:
		tmp = 1.0 * x
	elif a <= 3.25e-12:
		tmp = (y / x) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+45)
		tmp = Float64(1.0 * x);
	elseif (a <= 3.25e-12)
		tmp = Float64(Float64(y / x) * x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e+45)
		tmp = 1.0 * x;
	elseif (a <= 3.25e-12)
		tmp = (y / x) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+45], N[(1.0 * x), $MachinePrecision], If[LessEqual[a, 3.25e-12], N[(N[(y / x), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.19999999999999995e45 or 3.2500000000000001e-12 < a

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   5. Applied rewrites 66.2%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 24.2%

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

   if -1.19999999999999995e45 < a < 3.2500000000000001e-12

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. sum-to-mult N/A

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

      3. lower-*.f64 N/A

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

   3. Applied rewrites 62.8%

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

   4. Taylor expanded in t around inf

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

      1. lower-/.f64 22.5

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

   6. Applied rewrites 22.5%

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

Alternative 14: 27.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.9 \cdot 10^{+147}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 4.9e+147) (* 1.0 x) (* (/ z a) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 4.9e+147) {
		tmp = 1.0 * x;
	} else {
		tmp = (z / a) * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= 4.9d+147) then
        tmp = 1.0d0 * x
    else
        tmp = (z / a) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 4.9e+147) {
		tmp = 1.0 * x;
	} else {
		tmp = (z / a) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 4.9e+147:
		tmp = 1.0 * x
	else:
		tmp = (z / a) * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 4.9e+147)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(z / a) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 4.9e+147)
		tmp = 1.0 * x;
	else
		tmp = (z / a) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 4.9e+147], N[(1.0 * x), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.8999999999999998e147

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   5. Applied rewrites 66.2%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 24.2%

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

   if 4.8999999999999998e147 < z

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.2

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

   7. Applied rewrites 16.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 18.7

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

   9. Applied rewrites 18.7%

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

Alternative 15: 27.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.9 \cdot 10^{+147}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 4.9e+147) (* 1.0 x) (* z (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 4.9e+147) {
		tmp = 1.0 * x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= 4.9d+147) then
        tmp = 1.0d0 * x
    else
        tmp = z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 4.9e+147) {
		tmp = 1.0 * x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 4.9e+147:
		tmp = 1.0 * x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 4.9e+147)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 4.9e+147)
		tmp = 1.0 * x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 4.9e+147], N[(1.0 * x), $MachinePrecision], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.8999999999999998e147

   1. Initial program 67.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 83.4

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

   3. Applied rewrites 83.4%

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

   5. Applied rewrites 66.2%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 24.2%

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

   if 4.8999999999999998e147 < z

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.2

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

   7. Applied rewrites 16.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 17.8

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

   9. Applied rewrites 17.8%

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

Alternative 16: 24.2% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z, double t, double a) {
	return 1.0 * x;
}

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 = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 1.0 * x;
}

Python

def code(x, y, z, t, a):
	return 1.0 * x

Julia

function code(x, y, z, t, a)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 67.5%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. frac-2neg N/A

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

   9. lift--.f64 N/A

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

   10. sub-negate-rev N/A

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

   11. lower-/.f64 N/A

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

   12. lower--.f64 N/A

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

   13. lift--.f64 N/A

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

   14. sub-negate-rev N/A

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

   15. lower--.f64 83.4

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

3. Applied rewrites 83.4%

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

5. Applied rewrites 66.2%

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

6. Taylor expanded in a around inf

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

8. Applied rewrites 24.2%

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

Reproduce

herbie shell --seed 2025142 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y x) (- z t)) (- a t))))