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

Percentage Accurate: 67.3% → 88.5%

Time: 4.5s

Alternatives: 16

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-309}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z} - \frac{x}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\left(-\frac{\mathsf{fma}\left(a, \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}, \left(t - x\right) \cdot y\right) - \left(t - x\right) \cdot a}{z}\right) + t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -4e-309)
     (fma (- y z) (- (/ t (- a z)) (/ x (- a z))) x)
     (if (<= t_1 0.0)
       (+
        (-
         (/
          (- (fma a (/ (* (- t x) (- y a)) z) (* (- t x) y)) (* (- t x) a))
          z))
        t)
       (if (<= t_1 2e+253) t_1 (fma (- y z) (/ (- t x) (- a z)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -4e-309) {
		tmp = fma((y - z), ((t / (a - z)) - (x / (a - z))), x);
	} else if (t_1 <= 0.0) {
		tmp = -((fma(a, (((t - x) * (y - a)) / z), ((t - x) * y)) - ((t - x) * a)) / z) + t;
	} else if (t_1 <= 2e+253) {
		tmp = t_1;
	} else {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -4e-309)
		tmp = fma(Float64(y - z), Float64(Float64(t / Float64(a - z)) - Float64(x / Float64(a - z))), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(-Float64(Float64(fma(a, Float64(Float64(Float64(t - x) * Float64(y - a)) / z), Float64(Float64(t - x) * y)) - Float64(Float64(t - x) * a)) / z)) + t);
	elseif (t_1 <= 2e+253)
		tmp = t_1;
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-309], N[(N[(y - z), $MachinePrecision] * N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[((-N[(N[(N[(a * N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], If[LessEqual[t$95$1, 2e+253], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -3.9999999999999977e-309

   1. Initial program 67.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.7

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

   3. Applied rewrites 79.7%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. sub-div N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 79.3

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

   5. Applied rewrites 79.3%

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

   if -3.9999999999999977e-309 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 39.6%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.9999999999999999e253

   1. Initial program 67.3%

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

   if 1.9999999999999999e253 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 67.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.7

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

   3. Applied rewrites 79.7%

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

Alternative 2: 88.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-309}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z} - \frac{x}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -4e-309)
     (fma (- y z) (- (/ t (- a z)) (/ x (- a z))) x)
     (if (<= t_1 0.0)
       (+ (- (/ (* (- t x) (- y a)) z)) t)
       (if (<= t_1 2e+253) t_1 (fma (- y z) (/ (- t x) (- a z)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -4e-309) {
		tmp = fma((y - z), ((t / (a - z)) - (x / (a - z))), x);
	} else if (t_1 <= 0.0) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else if (t_1 <= 2e+253) {
		tmp = t_1;
	} else {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -4e-309)
		tmp = fma(Float64(y - z), Float64(Float64(t / Float64(a - z)) - Float64(x / Float64(a - z))), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	elseif (t_1 <= 2e+253)
		tmp = t_1;
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-309], N[(N[(y - z), $MachinePrecision] * N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], If[LessEqual[t$95$1, 2e+253], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -3.9999999999999977e-309

   1. Initial program 67.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.7

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

   3. Applied rewrites 79.7%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. sub-div N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 79.3

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

   5. Applied rewrites 79.3%

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

   if -3.9999999999999977e-309 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.9999999999999999e253

   1. Initial program 67.3%

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

   if 1.9999999999999999e253 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 67.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.7

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

   3. Applied rewrites 79.7%

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

Alternative 3: 88.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-309}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+253}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -4e-309)
     t_1
     (if (<= t_2 0.0)
       (+ (- (/ (* (- t x) (- y a)) z)) t)
       (if (<= t_2 2e+253) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -4e-309) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else if (t_2 <= 2e+253) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -4e-309)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	elseif (t_2 <= 2e+253)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-309], t$95$1, If[LessEqual[t$95$2, 0.0], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], If[LessEqual[t$95$2, 2e+253], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -3.9999999999999977e-309 or 1.9999999999999999e253 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 67.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.7

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

   3. Applied rewrites 79.7%

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

   if -3.9999999999999977e-309 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.9999999999999999e253

   1. Initial program 67.3%

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

Alternative 4: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-309}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{elif}\;t\_2 \leq 10^{-76}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -4e-309)
     t_1
     (if (<= t_2 0.0)
       (+ (- (/ (* (- t x) (- y a)) z)) t)
       (if (<= t_2 1e-76) (+ x (/ (* (- y z) t) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -4e-309) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else if (t_2 <= 1e-76) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -4e-309)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	elseif (t_2 <= 1e-76)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-309], t$95$1, If[LessEqual[t$95$2, 0.0], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], If[LessEqual[t$95$2, 1e-76], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -3.9999999999999977e-309 or 9.99999999999999927e-77 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 67.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.7

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

   3. Applied rewrites 79.7%

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

   if -3.9999999999999977e-309 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.99999999999999927e-77

   1. Initial program 67.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.0%

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

Alternative 5: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t - x}{z} \cdot y\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ (- t x) z) y))))
   (if (<= z -3.2e-44)
     t_1
     (if (<= z 2.7e-60)
       (fma (- t x) (/ (- y z) a) x)
       (if (<= z 1.32e+178) (fma (- y z) (/ t (- a z)) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) / z) * y);
	double tmp;
	if (z <= -3.2e-44) {
		tmp = t_1;
	} else if (z <= 2.7e-60) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else if (z <= 1.32e+178) {
		tmp = fma((y - z), (t / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) / z) * y))
	tmp = 0.0
	if (z <= -3.2e-44)
		tmp = t_1;
	elseif (z <= 2.7e-60)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	elseif (z <= 1.32e+178)
		tmp = fma(Float64(y - z), Float64(t / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-44], t$95$1, If[LessEqual[z, 2.7e-60], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.32e+178], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999995e-44 or 1.3200000000000001e178 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 47.7

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

   7. Applied rewrites 47.7%

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

   if -3.19999999999999995e-44 < z < 2.7e-60

   1. Initial program 67.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 53.1

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

   4. Applied rewrites 53.1%

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

   if 2.7e-60 < z < 1.3200000000000001e178

   1. Initial program 67.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.7

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 63.2%

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

Alternative 6: 70.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t - x}{z} \cdot y\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ (- t x) z) y))))
   (if (<= z -3.2e-44)
     t_1
     (if (<= z 7.5e+160) (fma (- t x) (/ (- y z) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) / z) * y);
	double tmp;
	if (z <= -3.2e-44) {
		tmp = t_1;
	} else if (z <= 7.5e+160) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) / z) * y))
	tmp = 0.0
	if (z <= -3.2e-44)
		tmp = t_1;
	elseif (z <= 7.5e+160)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-44], t$95$1, If[LessEqual[z, 7.5e+160], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999995e-44 or 7.50000000000000028e160 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 47.7

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

   7. Applied rewrites 47.7%

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

   if -3.19999999999999995e-44 < z < 7.50000000000000028e160

   1. Initial program 67.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 53.1

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

   4. Applied rewrites 53.1%

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

Alternative 7: 69.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t - x}{z} \cdot y\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ (- t x) z) y))))
   (if (<= z -3.2e-44) t_1 (if (<= z 1.06e-17) (fma (- t x) (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) / z) * y);
	double tmp;
	if (z <= -3.2e-44) {
		tmp = t_1;
	} else if (z <= 1.06e-17) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) / z) * y))
	tmp = 0.0
	if (z <= -3.2e-44)
		tmp = t_1;
	elseif (z <= 1.06e-17)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-44], t$95$1, If[LessEqual[z, 1.06e-17], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999995e-44 or 1.06000000000000006e-17 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 47.7

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

   7. Applied rewrites 47.7%

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

   if -3.19999999999999995e-44 < z < 1.06000000000000006e-17

   1. Initial program 67.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.7

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 49.0

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

   6. Applied rewrites 49.0%

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

Alternative 8: 52.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+180}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+180)
   (+ x (- t x))
   (if (<= z -5.5e-14)
     (/ (* (- y a) x) z)
     (if (<= z 1.7e+185) (fma (- t x) (/ y a) x) (* (- x) (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+180) {
		tmp = x + (t - x);
	} else if (z <= -5.5e-14) {
		tmp = ((y - a) * x) / z;
	} else if (z <= 1.7e+185) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = -x * ((a - y) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+180)
		tmp = Float64(x + Float64(t - x));
	elseif (z <= -5.5e-14)
		tmp = Float64(Float64(Float64(y - a) * x) / z);
	elseif (z <= 1.7e+185)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = Float64(Float64(-x) * Float64(Float64(a - y) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+180], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-14], N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.7e+185], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[((-x) * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.0000000000000001e180

   1. Initial program 67.3%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 19.1

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

   4. Applied rewrites 19.1%

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

   if -8.0000000000000001e180 < z < -5.49999999999999991e-14

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 19.9

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

   7. Applied rewrites 19.9%

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

   if -5.49999999999999991e-14 < z < 1.70000000000000009e185

   1. Initial program 67.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 79.7

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 49.0

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

   6. Applied rewrites 49.0%

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

   if 1.70000000000000009e185 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 23.3

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

   7. Applied rewrites 23.3%

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

Alternative 9: 50.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+180}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+180)
   (+ x (- t x))
   (if (<= z -5.5e-14)
     (/ (* (- y a) x) z)
     (if (<= z 3e+183) (fma y (/ (- t x) a) x) (* (- x) (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+180) {
		tmp = x + (t - x);
	} else if (z <= -5.5e-14) {
		tmp = ((y - a) * x) / z;
	} else if (z <= 3e+183) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = -x * ((a - y) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+180)
		tmp = Float64(x + Float64(t - x));
	elseif (z <= -5.5e-14)
		tmp = Float64(Float64(Float64(y - a) * x) / z);
	elseif (z <= 3e+183)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = Float64(Float64(-x) * Float64(Float64(a - y) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+180], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-14], N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3e+183], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[((-x) * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.0000000000000001e180

   1. Initial program 67.3%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 19.1

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

   4. Applied rewrites 19.1%

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

   if -8.0000000000000001e180 < z < -5.49999999999999991e-14

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 19.9

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

   7. Applied rewrites 19.9%

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

   if -5.49999999999999991e-14 < z < 2.99999999999999996e183

   1. Initial program 67.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 47.8

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

   4. Applied rewrites 47.8%

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

   if 2.99999999999999996e183 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 23.3

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

   7. Applied rewrites 23.3%

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

Alternative 10: 46.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-232}:\\ \;\;\;\;x + \left(-x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-147}:\\ \;\;\;\;\left(-x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.45e+139)
   (* t (/ (- y z) a))
   (if (<= t -1.4e-232)
     (+ x (* (- x) (/ y a)))
     (if (<= t 2.25e-147) (* (- x) (/ (- a y) z)) (+ x (/ (* t y) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+139) {
		tmp = t * ((y - z) / a);
	} else if (t <= -1.4e-232) {
		tmp = x + (-x * (y / a));
	} else if (t <= 2.25e-147) {
		tmp = -x * ((a - y) / z);
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.45d+139)) then
        tmp = t * ((y - z) / a)
    else if (t <= (-1.4d-232)) then
        tmp = x + (-x * (y / a))
    else if (t <= 2.25d-147) then
        tmp = -x * ((a - y) / z)
    else
        tmp = x + ((t * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+139) {
		tmp = t * ((y - z) / a);
	} else if (t <= -1.4e-232) {
		tmp = x + (-x * (y / a));
	} else if (t <= 2.25e-147) {
		tmp = -x * ((a - y) / z);
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.45e+139:
		tmp = t * ((y - z) / a)
	elif t <= -1.4e-232:
		tmp = x + (-x * (y / a))
	elif t <= 2.25e-147:
		tmp = -x * ((a - y) / z)
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.45e+139)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (t <= -1.4e-232)
		tmp = Float64(x + Float64(Float64(-x) * Float64(y / a)));
	elseif (t <= 2.25e-147)
		tmp = Float64(Float64(-x) * Float64(Float64(a - y) / z));
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.45e+139)
		tmp = t * ((y - z) / a);
	elseif (t <= -1.4e-232)
		tmp = x + (-x * (y / a));
	elseif (t <= 2.25e-147)
		tmp = -x * ((a - y) / z);
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.45e+139], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.4e-232], N[(x + N[((-x) * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e-147], N[((-x) * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4499999999999999e139

   1. Initial program 67.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 53.1

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

   4. Applied rewrites 53.1%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 23.1

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

   7. Applied rewrites 23.1%

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

   if -1.4499999999999999e139 < t < -1.39999999999999996e-232

   1. Initial program 67.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 43.8

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

   4. Applied rewrites 43.8%

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

   5. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 32.8

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

   7. Applied rewrites 32.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 36.5

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

   9. Applied rewrites 36.5%

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

   if -1.39999999999999996e-232 < t < 2.24999999999999986e-147

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 23.3

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

   7. Applied rewrites 23.3%

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

   if 2.24999999999999986e-147 < t

   1. Initial program 67.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 43.8

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

   4. Applied rewrites 43.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 37.9%

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

Alternative 11: 45.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{-z}{a}, x\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-158}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+91)
   (fma t (/ (- z) a) x)
   (if (<= a -2.2e-150)
     (* y (/ (- t x) a))
     (if (<= a 5.6e-158) (* (/ (- x t) z) y) (+ x (/ (* t y) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+91) {
		tmp = fma(t, (-z / a), x);
	} else if (a <= -2.2e-150) {
		tmp = y * ((t - x) / a);
	} else if (a <= 5.6e-158) {
		tmp = ((x - t) / z) * y;
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e+91)
		tmp = fma(t, Float64(Float64(-z) / a), x);
	elseif (a <= -2.2e-150)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= 5.6e-158)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e+91], N[(t * N[((-z) / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, -2.2e-150], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e-158], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.6e91

   1. Initial program 67.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 53.1

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

   4. Applied rewrites 53.1%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(t - x, \frac{-1 \cdot z}{a}, x\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 30.4

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

   7. Applied rewrites 30.4%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 29.9%

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

   if -3.6e91 < a < -2.1999999999999999e-150

   1. Initial program 67.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 53.1

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

   4. Applied rewrites 53.1%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 26.3

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

   7. Applied rewrites 26.3%

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

   if -2.1999999999999999e-150 < a < 5.60000000000000004e-158

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 25.9

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

   7. Applied rewrites 25.9%

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

   if 5.60000000000000004e-158 < a

   1. Initial program 67.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 43.8

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

   4. Applied rewrites 43.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 37.9%

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

Alternative 12: 42.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t \cdot y}{a}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-158}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* t y) a))))
   (if (<= a -1.2e+39)
     t_1
     (if (<= a -2.2e-150)
       (* y (/ (- t x) a))
       (if (<= a 5.6e-158) (* (/ (- x t) z) y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * y) / a);
	double tmp;
	if (a <= -1.2e+39) {
		tmp = t_1;
	} else if (a <= -2.2e-150) {
		tmp = y * ((t - x) / a);
	} else if (a <= 5.6e-158) {
		tmp = ((x - t) / z) * y;
	} 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 = x + ((t * y) / a)
    if (a <= (-1.2d+39)) then
        tmp = t_1
    else if (a <= (-2.2d-150)) then
        tmp = y * ((t - x) / a)
    else if (a <= 5.6d-158) then
        tmp = ((x - t) / z) * y
    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 = x + ((t * y) / a);
	double tmp;
	if (a <= -1.2e+39) {
		tmp = t_1;
	} else if (a <= -2.2e-150) {
		tmp = y * ((t - x) / a);
	} else if (a <= 5.6e-158) {
		tmp = ((x - t) / z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t * y) / a)
	tmp = 0
	if a <= -1.2e+39:
		tmp = t_1
	elif a <= -2.2e-150:
		tmp = y * ((t - x) / a)
	elif a <= 5.6e-158:
		tmp = ((x - t) / z) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t * y) / a))
	tmp = 0.0
	if (a <= -1.2e+39)
		tmp = t_1;
	elseif (a <= -2.2e-150)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= 5.6e-158)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t * y) / a);
	tmp = 0.0;
	if (a <= -1.2e+39)
		tmp = t_1;
	elseif (a <= -2.2e-150)
		tmp = y * ((t - x) / a);
	elseif (a <= 5.6e-158)
		tmp = ((x - t) / z) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e+39], t$95$1, If[LessEqual[a, -2.2e-150], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e-158], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2e39 or 5.60000000000000004e-158 < a

   1. Initial program 67.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 43.8

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

   4. Applied rewrites 43.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 37.9%

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

   if -1.2e39 < a < -2.1999999999999999e-150

   1. Initial program 67.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 53.1

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

   4. Applied rewrites 53.1%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 26.3

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

   7. Applied rewrites 26.3%

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

   if -2.1999999999999999e-150 < a < 5.60000000000000004e-158

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 25.9

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

   7. Applied rewrites 25.9%

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

Alternative 13: 40.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+86}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+214}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= y -3.1e+199)
     t_1
     (if (<= y -1.02e+86)
       (* (/ (- x t) z) y)
       (if (<= y 6e+214) (+ x t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (y <= -3.1e+199) {
		tmp = t_1;
	} else if (y <= -1.02e+86) {
		tmp = ((x - t) / z) * y;
	} else if (y <= 6e+214) {
		tmp = x + t;
	} 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 * ((t - x) / a)
    if (y <= (-3.1d+199)) then
        tmp = t_1
    else if (y <= (-1.02d+86)) then
        tmp = ((x - t) / z) * y
    else if (y <= 6d+214) then
        tmp = x + t
    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 * ((t - x) / a);
	double tmp;
	if (y <= -3.1e+199) {
		tmp = t_1;
	} else if (y <= -1.02e+86) {
		tmp = ((x - t) / z) * y;
	} else if (y <= 6e+214) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if y <= -3.1e+199:
		tmp = t_1
	elif y <= -1.02e+86:
		tmp = ((x - t) / z) * y
	elif y <= 6e+214:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (y <= -3.1e+199)
		tmp = t_1;
	elseif (y <= -1.02e+86)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (y <= 6e+214)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (y <= -3.1e+199)
		tmp = t_1;
	elseif (y <= -1.02e+86)
		tmp = ((x - t) / z) * y;
	elseif (y <= 6e+214)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+199], t$95$1, If[LessEqual[y, -1.02e+86], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 6e+214], N[(x + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999986e199 or 6.0000000000000002e214 < y

   1. Initial program 67.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 53.1

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

   4. Applied rewrites 53.1%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 26.3

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

   7. Applied rewrites 26.3%

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

   if -3.09999999999999986e199 < y < -1.01999999999999996e86

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 25.9

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

   7. Applied rewrites 25.9%

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

   if -1.01999999999999996e86 < y < 6.0000000000000002e214

   1. Initial program 67.3%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 19.1

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

   4. Applied rewrites 19.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 39.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+86}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+204}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.02e+86)
   (* (/ (- x t) z) y)
   (if (<= y 6e+204) (+ x t) (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.02e+86) {
		tmp = ((x - t) / z) * y;
	} else if (y <= 6e+204) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.02d+86)) then
        tmp = ((x - t) / z) * y
    else if (y <= 6d+204) then
        tmp = x + t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.02e+86) {
		tmp = ((x - t) / z) * y;
	} else if (y <= 6e+204) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.02e+86:
		tmp = ((x - t) / z) * y
	elif y <= 6e+204:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.02e+86)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (y <= 6e+204)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.02e+86)
		tmp = ((x - t) / z) * y;
	elseif (y <= 6e+204)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.02e+86], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 6e+204], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.01999999999999996e86

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 25.9

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

   7. Applied rewrites 25.9%

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

   if -1.01999999999999996e86 < y < 5.99999999999999965e204

   1. Initial program 67.3%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 19.1

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

   4. Applied rewrites 19.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]

   if 5.99999999999999965e204 < y

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 23.3

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

   7. Applied rewrites 23.3%

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

   8. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 19.2

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

   10. Applied rewrites 19.2%

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

Alternative 15: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+204}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= y -1.12e+111) t_1 (if (<= y 6e+204) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (y <= -1.12e+111) {
		tmp = t_1;
	} else if (y <= 6e+204) {
		tmp = x + t;
	} 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 = x * (y / z)
    if (y <= (-1.12d+111)) then
        tmp = t_1
    else if (y <= 6d+204) then
        tmp = x + t
    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 = x * (y / z);
	double tmp;
	if (y <= -1.12e+111) {
		tmp = t_1;
	} else if (y <= 6e+204) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if y <= -1.12e+111:
		tmp = t_1
	elif y <= 6e+204:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (y <= -1.12e+111)
		tmp = t_1;
	elseif (y <= 6e+204)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (y <= -1.12e+111)
		tmp = t_1;
	elseif (y <= 6e+204)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+111], t$95$1, If[LessEqual[y, 6e+204], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.11999999999999995e111 or 5.99999999999999965e204 < y

   1. Initial program 67.3%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 46.9

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

   4. Applied rewrites 46.9%

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

   5. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 23.3

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

   7. Applied rewrites 23.3%

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

   8. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 19.2

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

   10. Applied rewrites 19.2%

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

   if -1.11999999999999995e111 < y < 5.99999999999999965e204

   1. Initial program 67.3%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 19.1

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

   4. Applied rewrites 19.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 33.6% accurate, 4.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + t), $MachinePrecision]

Derivation

1. Initial program 67.3%

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

2. Taylor expanded in z around inf

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

   1. lift--.f64 19.1

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

4. Applied rewrites 19.1%

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

5. Taylor expanded in x around 0

   \[\leadsto x + t \]
6. Step-by-step derivation

7. Applied rewrites 33.6%

   \[\leadsto x + t \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025127 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y z) (- t x)) (- a z))))