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

Percentage Accurate: 67.8% → 90.6%

Time: 4.5s

Alternatives: 18

Speedup: 0.8×

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: 67.8% 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: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-266}:\\ \;\;\;\;\mathsf{fma}\left(y - x, t\_1, x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right) + y\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))) (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -1e-266)
     (fma (- y x) t_1 x)
     (if (<= t_2 0.0)
       (+ (- (/ (* (- y x) (- z a)) t)) y)
       (+ x (* (- y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -1e-266) {
		tmp = fma((y - x), t_1, x);
	} else if (t_2 <= 0.0) {
		tmp = -(((y - x) * (z - a)) / t) + y;
	} else {
		tmp = x + ((y - x) * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e-266)
		tmp = fma(Float64(y - x), t_1, x);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-Float64(Float64(Float64(y - x) * Float64(z - a)) / t)) + y);
	else
		tmp = Float64(x + Float64(Float64(y - x) * t_1));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999998e-267

   1. Initial program 72.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. negate-sub2 N/A

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

      14. negate-sub2 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 90.4

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

   3. Applied rewrites 90.4%

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

   if -9.9999999999999998e-267 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.2%

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

   2. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 94.5%

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

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

   1. Initial program 73.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-div N/A

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

      11. negate-sub2 N/A

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

      12. negate-sub2 N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lower--.f64 90.2

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

   3. Applied rewrites 90.2%

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

Alternative 2: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - x, \frac{t - z}{t - a}, x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right) + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y x) (/ (- t z) (- t a)) x))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -1e-266)
     t_1
     (if (<= t_2 0.0) (+ (- (/ (* (- y x) (- z a)) t)) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - x), ((t - z) / (t - a)), x);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -1e-266) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = -(((y - x) * (z - a)) / t) + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - x), Float64(Float64(t - z) / Float64(t - a)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e-266)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-Float64(Float64(Float64(y - x) * Float64(z - a)) / t)) + y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $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-266], t$95$1, If[LessEqual[t$95$2, 0.0], N[((-N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + y), $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))) < -9.9999999999999998e-267 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 72.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. negate-sub2 N/A

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

      14. negate-sub2 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 90.3

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

   3. Applied rewrites 90.3%

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

   if -9.9999999999999998e-267 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.2%

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

   2. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 94.5%

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

Alternative 3: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - x, \frac{z - t}{a}, x\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+38}:\\ \;\;\;\;\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right) + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y x) (/ (- z t) a) x)))
   (if (<= a -1e+32)
     t_1
     (if (<= a 4.8e+38) (+ (- (/ (* (- y x) (- z a)) t)) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - x), ((z - t) / a), x);
	double tmp;
	if (a <= -1e+32) {
		tmp = t_1;
	} else if (a <= 4.8e+38) {
		tmp = -(((y - x) * (z - a)) / t) + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - x), Float64(Float64(z - t) / a), x)
	tmp = 0.0
	if (a <= -1e+32)
		tmp = t_1;
	elseif (a <= 4.8e+38)
		tmp = Float64(Float64(-Float64(Float64(Float64(y - x) * Float64(z - a)) / t)) + y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1e+32], t$95$1, If[LessEqual[a, 4.8e+38], N[((-N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.00000000000000005e32 or 4.80000000000000035e38 < a

   1. Initial program 68.2%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 78.1

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

   4. Applied rewrites 78.1%

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

   if -1.00000000000000005e32 < a < 4.80000000000000035e38

   1. Initial program 67.6%

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

   2. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 69.9%

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

Alternative 4: 67.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{a - t} \cdot z\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{t - a} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- y x) (- a t)) z)))
   (if (<= z -7.8e+43)
     t_1
     (if (<= z 2.9e-12) (+ (* (- y x) (/ t (- t a))) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) / (a - t)) * z;
	double tmp;
	if (z <= -7.8e+43) {
		tmp = t_1;
	} else if (z <= 2.9e-12) {
		tmp = ((y - x) * (t / (t - a))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y - x) / (a - t)) * z
    if (z <= (-7.8d+43)) then
        tmp = t_1
    else if (z <= 2.9d-12) then
        tmp = ((y - x) * (t / (t - a))) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) / (a - t)) * z;
	double tmp;
	if (z <= -7.8e+43) {
		tmp = t_1;
	} else if (z <= 2.9e-12) {
		tmp = ((y - x) * (t / (t - a))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - x) / (a - t)) * z
	tmp = 0
	if z <= -7.8e+43:
		tmp = t_1
	elif z <= 2.9e-12:
		tmp = ((y - x) * (t / (t - a))) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) / Float64(a - t)) * z)
	tmp = 0.0
	if (z <= -7.8e+43)
		tmp = t_1;
	elseif (z <= 2.9e-12)
		tmp = Float64(Float64(Float64(y - x) * Float64(t / Float64(t - a))) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - x) / (a - t)) * z;
	tmp = 0.0;
	if (z <= -7.8e+43)
		tmp = t_1;
	elseif (z <= 2.9e-12)
		tmp = ((y - x) * (t / (t - a))) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -7.8e+43], t$95$1, If[LessEqual[z, 2.9e-12], N[(N[(N[(y - x), $MachinePrecision] * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000001e43 or 2.9000000000000002e-12 < z

   1. Initial program 69.4%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 58.3

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

   4. Applied rewrites 58.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. sub-div N/A

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

      10. frac-2neg N/A

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

      11. mul-1-neg N/A

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

      12. negate-sub2 N/A

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

      13. associate-*r/ N/A

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

      14. lower-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. mul-1-neg N/A

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

      17. negate-sub2 N/A

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

      18. frac-2neg N/A

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

      19. lower-/.f64 N/A

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

      20. lift--.f64 N/A

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

      21. lift--.f64 70.2

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

   6. Applied rewrites 70.2%

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

   if -7.8000000000000001e43 < z < 2.9000000000000002e-12

   1. Initial program 66.5%

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

   2. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. negate-sub2 N/A

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

      4. frac-2neg-rev N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 53.0

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

   4. Applied rewrites 53.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 53.0

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 65.7

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

   6. Applied rewrites 65.7%

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

Alternative 5: 67.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{a - t} \cdot z\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{t}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- y x) (- a t)) z)))
   (if (<= z -7.8e+43)
     t_1
     (if (<= z 2.9e-12) (fma (- y x) (/ t (- t a)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) / (a - t)) * z;
	double tmp;
	if (z <= -7.8e+43) {
		tmp = t_1;
	} else if (z <= 2.9e-12) {
		tmp = fma((y - x), (t / (t - a)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) / Float64(a - t)) * z)
	tmp = 0.0
	if (z <= -7.8e+43)
		tmp = t_1;
	elseif (z <= 2.9e-12)
		tmp = fma(Float64(y - x), Float64(t / Float64(t - a)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -7.8e+43], t$95$1, If[LessEqual[z, 2.9e-12], N[(N[(y - x), $MachinePrecision] * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000001e43 or 2.9000000000000002e-12 < z

   1. Initial program 69.4%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 58.3

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

   4. Applied rewrites 58.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. sub-div N/A

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

      10. frac-2neg N/A

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

      11. mul-1-neg N/A

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

      12. negate-sub2 N/A

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

      13. associate-*r/ N/A

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

      14. lower-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. mul-1-neg N/A

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

      17. negate-sub2 N/A

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

      18. frac-2neg N/A

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

      19. lower-/.f64 N/A

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

      20. lift--.f64 N/A

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

      21. lift--.f64 70.2

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

   6. Applied rewrites 70.2%

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

   if -7.8000000000000001e43 < z < 2.9000000000000002e-12

   1. Initial program 66.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-div N/A

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

      11. negate-sub2 N/A

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

      12. negate-sub2 N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lower--.f64 79.2

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

   3. Applied rewrites 79.2%

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

   4. Taylor expanded in z around 0

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

      1. frac-2neg N/A

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

      2. negate-sub2 N/A

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

      3. negate-sub2 N/A

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

      4. associate-/l* N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 65.7

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

   6. Applied rewrites 65.7%

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

Alternative 6: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{a - t} \cdot z\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- y x) (- a t)) z)))
   (if (<= z -2.1e+86)
     t_1
     (if (<= z -2.6e-60)
       (* y (/ (- z t) (- a t)))
       (if (<= z 2.9e-12) (+ x (* t (/ y (- t a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) / (a - t)) * z;
	double tmp;
	if (z <= -2.1e+86) {
		tmp = t_1;
	} else if (z <= -2.6e-60) {
		tmp = y * ((z - t) / (a - t));
	} else if (z <= 2.9e-12) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y - x) / (a - t)) * z
    if (z <= (-2.1d+86)) then
        tmp = t_1
    else if (z <= (-2.6d-60)) then
        tmp = y * ((z - t) / (a - t))
    else if (z <= 2.9d-12) then
        tmp = x + (t * (y / (t - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) / (a - t)) * z;
	double tmp;
	if (z <= -2.1e+86) {
		tmp = t_1;
	} else if (z <= -2.6e-60) {
		tmp = y * ((z - t) / (a - t));
	} else if (z <= 2.9e-12) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - x) / (a - t)) * z
	tmp = 0
	if z <= -2.1e+86:
		tmp = t_1
	elif z <= -2.6e-60:
		tmp = y * ((z - t) / (a - t))
	elif z <= 2.9e-12:
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) / Float64(a - t)) * z)
	tmp = 0.0
	if (z <= -2.1e+86)
		tmp = t_1;
	elseif (z <= -2.6e-60)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (z <= 2.9e-12)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - x) / (a - t)) * z;
	tmp = 0.0;
	if (z <= -2.1e+86)
		tmp = t_1;
	elseif (z <= -2.6e-60)
		tmp = y * ((z - t) / (a - t));
	elseif (z <= 2.9e-12)
		tmp = x + (t * (y / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.1e+86], t$95$1, If[LessEqual[z, -2.6e-60], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-12], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0999999999999999e86 or 2.9000000000000002e-12 < z

   1. Initial program 69.5%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 58.9

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

   4. Applied rewrites 58.9%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. sub-div N/A

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

      10. frac-2neg N/A

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

      11. mul-1-neg N/A

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

      12. negate-sub2 N/A

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

      13. associate-*r/ N/A

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

      14. lower-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. mul-1-neg N/A

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

      17. negate-sub2 N/A

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

      18. frac-2neg N/A

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

      19. lower-/.f64 N/A

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

      20. lift--.f64 N/A

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

      21. lift--.f64 71.2

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

   6. Applied rewrites 71.2%

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

   if -2.0999999999999999e86 < z < -2.5999999999999998e-60

   1. Initial program 71.0%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 47.9

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

   4. Applied rewrites 47.9%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lift--.f64 49.6

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

   7. Applied rewrites 49.6%

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

   if -2.5999999999999998e-60 < z < 2.9000000000000002e-12

   1. Initial program 65.5%

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

   2. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. negate-sub2 N/A

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

      4. frac-2neg-rev N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 55.1

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

   4. Applied rewrites 55.1%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 62.8

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

   7. Applied rewrites 62.8%

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

Alternative 7: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -28000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-184}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{y - x}{a - t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -28000000.0)
     t_1
     (if (<= t 3.6e-184)
       (fma z (/ (- y x) a) x)
       (if (<= t 3.8e+71) (* (/ (- y x) (- a t)) z) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -28000000.0) {
		tmp = t_1;
	} else if (t <= 3.6e-184) {
		tmp = fma(z, ((y - x) / a), x);
	} else if (t <= 3.8e+71) {
		tmp = ((y - x) / (a - t)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -28000000.0)
		tmp = t_1;
	elseif (t <= 3.6e-184)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	elseif (t <= 3.8e+71)
		tmp = Float64(Float64(Float64(y - x) / Float64(a - t)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -28000000.0], t$95$1, If[LessEqual[t, 3.6e-184], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 3.8e+71], N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e7 or 3.8000000000000001e71 < t

   1. Initial program 42.6%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 20.0

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

   4. Applied rewrites 20.0%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lift--.f64 61.0

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

   7. Applied rewrites 61.0%

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

   if -2.8e7 < t < 3.6000000000000001e-184

   1. Initial program 89.9%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 74.8

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

   4. Applied rewrites 74.8%

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

   if 3.6000000000000001e-184 < t < 3.8000000000000001e71

   1. Initial program 83.4%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 45.3

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

   4. Applied rewrites 45.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. sub-div N/A

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

      10. frac-2neg N/A

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

      11. mul-1-neg N/A

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

      12. negate-sub2 N/A

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

      13. associate-*r/ N/A

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

      14. lower-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. mul-1-neg N/A

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

      17. negate-sub2 N/A

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

      18. frac-2neg N/A

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

      19. lower-/.f64 N/A

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

      20. lift--.f64 N/A

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

      21. lift--.f64 47.8

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

   6. Applied rewrites 47.8%

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

Alternative 8: 64.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -28000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-70}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+71}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -28000000.0)
     t_1
     (if (<= t 6e-70)
       (fma z (/ (- y x) a) x)
       (if (<= t 3.8e+71) (* (- y x) (/ z (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -28000000.0) {
		tmp = t_1;
	} else if (t <= 6e-70) {
		tmp = fma(z, ((y - x) / a), x);
	} else if (t <= 3.8e+71) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -28000000.0)
		tmp = t_1;
	elseif (t <= 6e-70)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	elseif (t <= 3.8e+71)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -28000000.0], t$95$1, If[LessEqual[t, 6e-70], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 3.8e+71], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e7 or 3.8000000000000001e71 < t

   1. Initial program 42.6%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 20.0

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

   4. Applied rewrites 20.0%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lift--.f64 61.0

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

   7. Applied rewrites 61.0%

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

   if -2.8e7 < t < 6.0000000000000003e-70

   1. Initial program 89.7%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 73.4

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

   4. Applied rewrites 73.4%

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

   if 6.0000000000000003e-70 < t < 3.8000000000000001e71

   1. Initial program 79.2%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 42.0

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

   4. Applied rewrites 42.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 46.0

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

   6. Applied rewrites 46.0%

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

Alternative 9: 63.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -28000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -28000000.0)
     t_1
     (if (<= t 1.75e+52) (fma z (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -28000000.0) {
		tmp = t_1;
	} else if (t <= 1.75e+52) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -28000000.0)
		tmp = t_1;
	elseif (t <= 1.75e+52)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -28000000.0], t$95$1, If[LessEqual[t, 1.75e+52], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e7 or 1.75e52 < t

   1. Initial program 43.4%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 20.6

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

   4. Applied rewrites 20.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lift--.f64 60.7

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

   7. Applied rewrites 60.7%

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

   if -2.8e7 < t < 1.75e52

   1. Initial program 88.1%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 69.0

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

   4. Applied rewrites 69.0%

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

Alternative 10: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+176) y (if (<= t 5e+99) (fma z (/ (- y x) a) x) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+176) {
		tmp = y;
	} else if (t <= 5e+99) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+176)
		tmp = y;
	elseif (t <= 5e+99)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+176], y, If[LessEqual[t, 5e+99], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -4.59999999999999992e176 or 5.00000000000000008e99 < t

   1. Initial program 32.1%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 53.1%

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

   if -4.59999999999999992e176 < t < 5.00000000000000008e99

   1. Initial program 81.3%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 60.1

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

   4. Applied rewrites 60.1%

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

Alternative 11: 50.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+176)
   y
   (if (<= t 3e-68)
     (fma z (/ y a) x)
     (if (<= t 3.8e+71) (/ (* (- y x) z) (- t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+176) {
		tmp = y;
	} else if (t <= 3e-68) {
		tmp = fma(z, (y / a), x);
	} else if (t <= 3.8e+71) {
		tmp = ((y - x) * z) / -t;
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+176)
		tmp = y;
	elseif (t <= 3e-68)
		tmp = fma(z, Float64(y / a), x);
	elseif (t <= 3.8e+71)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(-t));
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+176], y, If[LessEqual[t, 3e-68], N[(z * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 3.8e+71], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / (-t)), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.59999999999999992e176 or 3.8000000000000001e71 < t

   1. Initial program 35.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 50.9%

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

   if -4.59999999999999992e176 < t < 3e-68

   1. Initial program 82.3%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.4

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

   4. Applied rewrites 63.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 52.5%

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

   if 3e-68 < t < 3.8000000000000001e71

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 41.6

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

   4. Applied rewrites 41.6%

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

   5. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 30.8

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

   7. Applied rewrites 30.8%

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

Alternative 12: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{t - a} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+176)
   y
   (if (<= t 2.3e-44)
     (fma z (/ y a) x)
     (if (<= t 3.8e+71) (* (/ z (- t a)) x) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+176) {
		tmp = y;
	} else if (t <= 2.3e-44) {
		tmp = fma(z, (y / a), x);
	} else if (t <= 3.8e+71) {
		tmp = (z / (t - a)) * x;
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+176)
		tmp = y;
	elseif (t <= 2.3e-44)
		tmp = fma(z, Float64(y / a), x);
	elseif (t <= 3.8e+71)
		tmp = Float64(Float64(z / Float64(t - a)) * x);
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+176], y, If[LessEqual[t, 2.3e-44], N[(z * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 3.8e+71], N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.59999999999999992e176 or 3.8000000000000001e71 < t

   1. Initial program 35.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 50.9%

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

   if -4.59999999999999992e176 < t < 2.29999999999999998e-44

   1. Initial program 82.4%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.3

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

   4. Applied rewrites 63.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 52.5%

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

   if 2.29999999999999998e-44 < t < 3.8000000000000001e71

   1. Initial program 77.5%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 40.1

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

   4. Applied rewrites 40.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. mul-1-neg N/A

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

      7. negate-sub2 N/A

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

      8. frac-2neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 36.7

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

   7. Applied rewrites 36.7%

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

   8. Taylor expanded in x around inf

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 24.5

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

   10. Applied rewrites 24.5%

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

Alternative 13: 49.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+176) y (if (<= t 7.4e+34) (fma z (/ y a) x) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+176) {
		tmp = y;
	} else if (t <= 7.4e+34) {
		tmp = fma(z, (y / a), x);
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+176)
		tmp = y;
	elseif (t <= 7.4e+34)
		tmp = fma(z, Float64(y / a), x);
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+176], y, If[LessEqual[t, 7.4e+34], N[(z * N[(y / a), $MachinePrecision] + x), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -4.59999999999999992e176 or 7.40000000000000017e34 < t

   1. Initial program 38.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 49.2%

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

   if -4.59999999999999992e176 < t < 7.40000000000000017e34

   1. Initial program 82.4%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 61.9

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

   4. Applied rewrites 61.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 51.4%

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

Alternative 14: 37.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+112}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-272}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e+112)
   y
   (if (<= t 1.85e-272)
     (/ (* y z) a)
     (if (<= t 1.35e-70) x (if (<= t 3.8e+71) (* (/ z t) x) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+112) {
		tmp = y;
	} else if (t <= 1.85e-272) {
		tmp = (y * z) / a;
	} else if (t <= 1.35e-70) {
		tmp = x;
	} else if (t <= 3.8e+71) {
		tmp = (z / t) * x;
	} else {
		tmp = 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 (t <= (-4.4d+112)) then
        tmp = y
    else if (t <= 1.85d-272) then
        tmp = (y * z) / a
    else if (t <= 1.35d-70) then
        tmp = x
    else if (t <= 3.8d+71) then
        tmp = (z / t) * x
    else
        tmp = 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 (t <= -4.4e+112) {
		tmp = y;
	} else if (t <= 1.85e-272) {
		tmp = (y * z) / a;
	} else if (t <= 1.35e-70) {
		tmp = x;
	} else if (t <= 3.8e+71) {
		tmp = (z / t) * x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e+112:
		tmp = y
	elif t <= 1.85e-272:
		tmp = (y * z) / a
	elif t <= 1.35e-70:
		tmp = x
	elif t <= 3.8e+71:
		tmp = (z / t) * x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e+112)
		tmp = y;
	elseif (t <= 1.85e-272)
		tmp = Float64(Float64(y * z) / a);
	elseif (t <= 1.35e-70)
		tmp = x;
	elseif (t <= 3.8e+71)
		tmp = Float64(Float64(z / t) * x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.4e+112)
		tmp = y;
	elseif (t <= 1.85e-272)
		tmp = (y * z) / a;
	elseif (t <= 1.35e-70)
		tmp = x;
	elseif (t <= 3.8e+71)
		tmp = (z / t) * x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e+112], y, If[LessEqual[t, 1.85e-272], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 1.35e-70], x, If[LessEqual[t, 3.8e+71], N[(N[(z / t), $MachinePrecision] * x), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.3999999999999999e112 or 3.8000000000000001e71 < t

   1. Initial program 36.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 49.1%

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

   if -4.3999999999999999e112 < t < 1.8499999999999998e-272

   1. Initial program 84.1%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.9

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

   4. Applied rewrites 63.9%

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

   5. Taylor expanded in x 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 22.6

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

   7. Applied rewrites 22.6%

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

   if 1.8499999999999998e-272 < t < 1.3500000000000001e-70

   1. Initial program 90.6%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 36.5%

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

   if 1.3500000000000001e-70 < t < 3.8000000000000001e71

   1. Initial program 79.3%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 42.1

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

   4. Applied rewrites 42.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. mul-1-neg N/A

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

      7. negate-sub2 N/A

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

      8. frac-2neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 37.8

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

   7. Applied rewrites 37.8%

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

   8. Taylor expanded in x around inf

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 24.9

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

   10. Applied rewrites 24.9%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 19.9%

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

Alternative 15: 35.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+112}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e+112)
   y
   (if (<= t 4.4e-101) (* y (/ z a)) (if (<= t 3.8e+71) (* (/ z t) x) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+112) {
		tmp = y;
	} else if (t <= 4.4e-101) {
		tmp = y * (z / a);
	} else if (t <= 3.8e+71) {
		tmp = (z / t) * x;
	} else {
		tmp = 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 (t <= (-4.4d+112)) then
        tmp = y
    else if (t <= 4.4d-101) then
        tmp = y * (z / a)
    else if (t <= 3.8d+71) then
        tmp = (z / t) * x
    else
        tmp = 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 (t <= -4.4e+112) {
		tmp = y;
	} else if (t <= 4.4e-101) {
		tmp = y * (z / a);
	} else if (t <= 3.8e+71) {
		tmp = (z / t) * x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e+112:
		tmp = y
	elif t <= 4.4e-101:
		tmp = y * (z / a)
	elif t <= 3.8e+71:
		tmp = (z / t) * x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e+112)
		tmp = y;
	elseif (t <= 4.4e-101)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 3.8e+71)
		tmp = Float64(Float64(z / t) * x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.4e+112)
		tmp = y;
	elseif (t <= 4.4e-101)
		tmp = y * (z / a);
	elseif (t <= 3.8e+71)
		tmp = (z / t) * x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e+112], y, If[LessEqual[t, 4.4e-101], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+71], N[(N[(z / t), $MachinePrecision] * x), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3999999999999999e112 or 3.8000000000000001e71 < t

   1. Initial program 36.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 49.1%

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

   if -4.3999999999999999e112 < t < 4.3999999999999998e-101

   1. Initial program 86.1%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 67.8

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

   4. Applied rewrites 67.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lift--.f64 44.5

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

   7. Applied rewrites 44.5%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 27.5

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

   10. Applied rewrites 27.5%

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

   if 4.3999999999999998e-101 < t < 3.8000000000000001e71

   1. Initial program 80.6%

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

   2. Taylor expanded in z around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 43.5

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

   4. Applied rewrites 43.5%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. mul-1-neg N/A

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

      7. negate-sub2 N/A

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

      8. frac-2neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 38.9

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

   7. Applied rewrites 38.9%

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

   8. Taylor expanded in x around inf

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 25.5

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

   10. Applied rewrites 25.5%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 20.4%

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

Alternative 16: 34.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+112}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-272}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e+112)
   y
   (if (<= t 1.85e-272) (/ (* y z) a) (if (<= t 7.8e+33) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+112) {
		tmp = y;
	} else if (t <= 1.85e-272) {
		tmp = (y * z) / a;
	} else if (t <= 7.8e+33) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-4.4d+112)) then
        tmp = y
    else if (t <= 1.85d-272) then
        tmp = (y * z) / a
    else if (t <= 7.8d+33) then
        tmp = x
    else
        tmp = 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 (t <= -4.4e+112) {
		tmp = y;
	} else if (t <= 1.85e-272) {
		tmp = (y * z) / a;
	} else if (t <= 7.8e+33) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e+112:
		tmp = y
	elif t <= 1.85e-272:
		tmp = (y * z) / a
	elif t <= 7.8e+33:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e+112)
		tmp = y;
	elseif (t <= 1.85e-272)
		tmp = Float64(Float64(y * z) / a);
	elseif (t <= 7.8e+33)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.4e+112)
		tmp = y;
	elseif (t <= 1.85e-272)
		tmp = (y * z) / a;
	elseif (t <= 7.8e+33)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e+112], y, If[LessEqual[t, 1.85e-272], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 7.8e+33], x, y]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3999999999999999e112 or 7.8000000000000004e33 < t

   1. Initial program 38.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 47.7%

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

   if -4.3999999999999999e112 < t < 1.8499999999999998e-272

   1. Initial program 84.1%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.9

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

   4. Applied rewrites 63.9%

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

   5. Taylor expanded in x 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 22.6

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

   7. Applied rewrites 22.6%

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

   if 1.8499999999999998e-272 < t < 7.8000000000000004e33

   1. Initial program 88.3%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 34.2%

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

Alternative 17: 33.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+176) y (if (<= t 7.8e+33) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+176) {
		tmp = y;
	} else if (t <= 7.8e+33) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-4.6d+176)) then
        tmp = y
    else if (t <= 7.8d+33) then
        tmp = x
    else
        tmp = 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 (t <= -4.6e+176) {
		tmp = y;
	} else if (t <= 7.8e+33) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.6e+176:
		tmp = y
	elif t <= 7.8e+33:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+176)
		tmp = y;
	elseif (t <= 7.8e+33)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.6e+176)
		tmp = y;
	elseif (t <= 7.8e+33)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+176], y, If[LessEqual[t, 7.8e+33], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -4.59999999999999992e176 or 7.8000000000000004e33 < t

   1. Initial program 38.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 49.1%

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

   if -4.59999999999999992e176 < t < 7.8000000000000004e33

   1. Initial program 82.4%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 31.2%

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

Alternative 18: 24.9% accurate, 17.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.8%

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

2. Taylor expanded in a around inf

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

4. Applied rewrites 24.9%

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

Reproduce

herbie shell --seed 2025110 
(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))))