Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 94.5%

Time: 5.3s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.4% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{-1}{z - a} \cdot \left(y - z\right), x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (* (/ -1.0 (- z a)) (- y z)) x))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-273)
     t_1
     (if (<= t_2 0.0) (fma (/ (- y a) z) (- x t) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((-1.0 / (z - a)) * (y - z)), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-273) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = fma(((y - a) / z), (x - t), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(-1.0 / Float64(z - a)) * Float64(y - z)), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-273)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(Float64(y - a) / z), Float64(x - t), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(-1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-273], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-273 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 84.8

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

   3. Applied rewrites 84.8%

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

   if -1e-273 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lift--.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lift-*.f64 N/A

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

      14. +-commutative N/A

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

   8. Applied rewrites 53.4%

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

Alternative 2: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;x - \left(z - y\right) \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{z - a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-273)
     (- x (* (- z y) (/ (- x t) (- z a))))
     (if (<= t_1 0.0)
       (fma (/ (- y a) z) (- x t) t)
       (+ x (/ (- z y) (/ (- z a) (- t 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 <= -1e-273) {
		tmp = x - ((z - y) * ((x - t) / (z - a)));
	} else if (t_1 <= 0.0) {
		tmp = fma(((y - a) / z), (x - t), t);
	} else {
		tmp = x + ((z - y) / ((z - a) / (t - x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-273)
		tmp = Float64(x - Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(z - a))));
	elseif (t_1 <= 0.0)
		tmp = fma(Float64(Float64(y - a) / z), Float64(x - t), t);
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(z - a) / Float64(t - x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-273], N[(x - N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-273

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 80.4

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

      10. lift-/.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 80.4

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

   3. Applied rewrites 80.4%

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

   if -1e-273 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lift--.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lift-*.f64 N/A

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

      14. +-commutative N/A

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

   8. Applied rewrites 53.4%

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

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

   1. Initial program 80.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip N/A

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

      4. mult-flip-rev N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. distribute-frac-neg N/A

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

      14. frac-2neg-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 N/A

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

      19. lower-/.f64 N/A

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

      20. lift--.f64 N/A

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

      21. sub-negate-rev N/A

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

      22. lower--.f64 80.5

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

   3. Applied rewrites 80.5%

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

Alternative 3: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - t}{z - a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;x - \left(z - y\right) \cdot t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x t) (- z a))) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-273)
     (- x (* (- z y) t_1))
     (if (<= t_2 0.0) (fma (/ (- y a) z) (- x t) t) (fma t_1 (- y z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - t) / (z - a);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-273) {
		tmp = x - ((z - y) * t_1);
	} else if (t_2 <= 0.0) {
		tmp = fma(((y - a) / z), (x - t), t);
	} else {
		tmp = fma(t_1, (y - z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - t) / Float64(z - a))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-273)
		tmp = Float64(x - Float64(Float64(z - y) * t_1));
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(Float64(y - a) / z), Float64(x - t), t);
	else
		tmp = fma(t_1, Float64(y - z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-273], N[(x - N[(N[(z - y), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision], N[(t$95$1 * N[(y - z), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-273

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 80.4

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

      10. lift-/.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 80.4

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

   3. Applied rewrites 80.4%

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

   if -1e-273 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lift--.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lift-*.f64 N/A

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

      14. +-commutative N/A

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

   8. Applied rewrites 53.4%

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

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

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 80.5

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 80.5

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

   3. Applied rewrites 80.5%

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

Alternative 4: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x t) (- z a)) (- y z) x))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-273)
     t_1
     (if (<= t_2 0.0) (fma (/ (- y a) z) (- x t) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - t) / (z - a)), (y - z), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-273) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = fma(((y - a) / z), (x - t), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - t) / Float64(z - a)), Float64(y - z), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-273)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(Float64(y - a) / z), Float64(x - t), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-273], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-273 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 80.5

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 80.5

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

   3. Applied rewrites 80.5%

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

   if -1e-273 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lift--.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lift-*.f64 N/A

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

      14. +-commutative N/A

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

   8. Applied rewrites 53.4%

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

Alternative 5: 78.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := \mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-143}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z)))))
        (t_2 (fma (/ (- y a) z) (- x t) t)))
   (if (<= z -9e+22)
     t_2
     (if (<= z -1.8e-191)
       t_1
       (if (<= z 1.2e-143)
         (fma (- t x) (/ y a) x)
         (if (<= z 1.55e+75) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double t_2 = fma(((y - a) / z), (x - t), t);
	double tmp;
	if (z <= -9e+22) {
		tmp = t_2;
	} else if (z <= -1.8e-191) {
		tmp = t_1;
	} else if (z <= 1.2e-143) {
		tmp = fma((t - x), (y / a), x);
	} else if (z <= 1.55e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	t_2 = fma(Float64(Float64(y - a) / z), Float64(x - t), t)
	tmp = 0.0
	if (z <= -9e+22)
		tmp = t_2;
	elseif (z <= -1.8e-191)
		tmp = t_1;
	elseif (z <= 1.2e-143)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	elseif (z <= 1.55e+75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -9e+22], t$95$2, If[LessEqual[z, -1.8e-191], t$95$1, If[LessEqual[z, 1.2e-143], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.55e+75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999996e22 or 1.5500000000000001e75 < z

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lift--.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lift-*.f64 N/A

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

      14. +-commutative N/A

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

   8. Applied rewrites 53.4%

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

   if -8.9999999999999996e22 < z < -1.8000000000000001e-191 or 1.1999999999999999e-143 < z < 1.5500000000000001e75

   1. Initial program 80.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 64.0%

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

   if -1.8000000000000001e-191 < z < 1.1999999999999999e-143

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 84.8

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

   3. Applied rewrites 84.8%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   6. Applied rewrites 48.8%

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

Alternative 6: 77.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-143}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+22)
   (fma (/ (- y a) z) (- x t) t)
   (if (<= z 1.8e-143)
     (+ x (* (- y z) (/ (- t x) a)))
     (if (<= z 1.55e+75)
       (+ x (* (- y z) (/ t (- a z))))
       (- t (/ (- t x) (/ z (- y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+22) {
		tmp = fma(((y - a) / z), (x - t), t);
	} else if (z <= 1.8e-143) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (z <= 1.55e+75) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+22)
		tmp = fma(Float64(Float64(y - a) / z), Float64(x - t), t);
	elseif (z <= 1.8e-143)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	elseif (z <= 1.55e+75)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+22], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[z, 1.8e-143], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+75], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5999999999999996e22

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lift--.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lift-*.f64 N/A

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

      14. +-commutative N/A

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

   8. Applied rewrites 53.4%

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

   if -6.5999999999999996e22 < z < 1.7999999999999999e-143

   1. Initial program 80.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.8%

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

   if 1.7999999999999999e-143 < z < 1.5500000000000001e75

   1. Initial program 80.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 64.0%

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

   if 1.5500000000000001e75 < z

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip N/A

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

      4. mult-flip-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 53.4

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

   8. Applied rewrites 53.4%

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

Alternative 7: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-143}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y a) z) (- x t) t)))
   (if (<= z -6.6e+22)
     t_1
     (if (<= z 1.8e-143)
       (+ x (* (- y z) (/ (- t x) a)))
       (if (<= z 1.55e+75) (+ 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 - a) / z), (x - t), t);
	double tmp;
	if (z <= -6.6e+22) {
		tmp = t_1;
	} else if (z <= 1.8e-143) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (z <= 1.55e+75) {
		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(Float64(y - a) / z), Float64(x - t), t)
	tmp = 0.0
	if (z <= -6.6e+22)
		tmp = t_1;
	elseif (z <= 1.8e-143)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	elseif (z <= 1.55e+75)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(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[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -6.6e+22], t$95$1, If[LessEqual[z, 1.8e-143], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+75], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999996e22 or 1.5500000000000001e75 < z

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lift--.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lift-*.f64 N/A

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

      14. +-commutative N/A

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

   8. Applied rewrites 53.4%

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

   if -6.5999999999999996e22 < z < 1.7999999999999999e-143

   1. Initial program 80.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.8%

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

   if 1.7999999999999999e-143 < z < 1.5500000000000001e75

   1. Initial program 80.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 64.0%

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

Alternative 8: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y a) z) (- x t) t)))
   (if (<= z -7e+22)
     t_1
     (if (<= z 1.1e+30) (+ x (/ (* y (- t x)) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - a) / z), (x - t), t);
	double tmp;
	if (z <= -7e+22) {
		tmp = t_1;
	} else if (z <= 1.1e+30) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - a) / z), Float64(x - t), t)
	tmp = 0.0
	if (z <= -7e+22)
		tmp = t_1;
	elseif (z <= 1.1e+30)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -7e+22], t$95$1, If[LessEqual[z, 1.1e+30], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7e22 or 1.1e30 < z

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lift--.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lift-*.f64 N/A

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

      14. +-commutative N/A

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

   8. Applied rewrites 53.4%

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

   if -7e22 < z < 1.1e30

   1. Initial program 80.4%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 55.3

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

   4. Applied rewrites 55.3%

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

Alternative 9: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 250:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y a) z) (- x t) t)))
   (if (<= z -6.6e+22) t_1 (if (<= z 250.0) (fma (- t x) (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - a) / z), (x - t), t);
	double tmp;
	if (z <= -6.6e+22) {
		tmp = t_1;
	} else if (z <= 250.0) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - a) / z), Float64(x - t), t)
	tmp = 0.0
	if (z <= -6.6e+22)
		tmp = t_1;
	elseif (z <= 250.0)
		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[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -6.6e+22], t$95$1, If[LessEqual[z, 250.0], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999996e22 or 250 < z

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lift--.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lift-*.f64 N/A

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

      14. +-commutative N/A

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

   8. Applied rewrites 53.4%

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

   if -6.5999999999999996e22 < z < 250

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 84.8

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

   3. Applied rewrites 84.8%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   6. Applied rewrites 48.8%

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

Alternative 10: 70.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 250:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (- t x) (/ y z)))))
   (if (<= z -7e+22) t_1 (if (<= z 250.0) (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) * (y / z));
	double tmp;
	if (z <= -7e+22) {
		tmp = t_1;
	} else if (z <= 250.0) {
		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(t - x) * Float64(y / z)))
	tmp = 0.0
	if (z <= -7e+22)
		tmp = t_1;
	elseif (z <= 250.0)
		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[(t - x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+22], t$95$1, If[LessEqual[z, 250.0], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7e22 or 250 < z

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 49.1

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

   9. Applied rewrites 49.1%

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

   if -7e22 < z < 250

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 84.8

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

   3. Applied rewrites 84.8%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   6. Applied rewrites 48.8%

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

Alternative 11: 63.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* t (/ (- y a) z)))))
   (if (<= z -8.8e+27) t_1 (if (<= z 9.4e+30) (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 * ((y - a) / z));
	double tmp;
	if (z <= -8.8e+27) {
		tmp = t_1;
	} else if (z <= 9.4e+30) {
		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(t * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -8.8e+27)
		tmp = t_1;
	elseif (z <= 9.4e+30)
		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[(t * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+27], t$95$1, If[LessEqual[z, 9.4e+30], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.7999999999999995e27 or 9.39999999999999979e30 < z

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.1

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

   4. Applied rewrites 46.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-flip-reverse N/A

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

      5. lower--.f64 46.1

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 53.4

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

   6. Applied rewrites 53.4%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 36.3%

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

   if -8.7999999999999995e27 < z < 9.39999999999999979e30

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 84.8

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

   3. Applied rewrites 84.8%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   6. Applied rewrites 48.8%

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

Alternative 12: 60.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-8}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ y a) x)))
   (if (<= a -3.8e+47) t_1 (if (<= a 6e-8) (* (- x t) (/ y (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), (y / a), x);
	double tmp;
	if (a <= -3.8e+47) {
		tmp = t_1;
	} else if (a <= 6e-8) {
		tmp = (x - t) * (y / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(y / a), x)
	tmp = 0.0
	if (a <= -3.8e+47)
		tmp = t_1;
	elseif (a <= 6e-8)
		tmp = Float64(Float64(x - t) * Float64(y / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.8e+47], t$95$1, If[LessEqual[a, 6e-8], N[(N[(x - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.8000000000000003e47 or 5.99999999999999946e-8 < a

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 84.8

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

   3. Applied rewrites 84.8%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   6. Applied rewrites 48.8%

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

   if -3.8000000000000003e47 < a < 5.99999999999999946e-8

   1. Initial program 80.4%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.5

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

   4. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 41.5

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. frac-2neg N/A

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

      14. lift-/.f64 41.9

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

   6. Applied rewrites 41.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 43.4

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

   8. Applied rewrites 43.4%

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

Alternative 13: 57.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-23}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e-23)
   (+ x t)
   (if (<= z 2.15e+68) (fma (- t x) (/ y a) x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-23) {
		tmp = x + t;
	} else if (z <= 2.15e+68) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e-23)
		tmp = Float64(x + t);
	elseif (z <= 2.15e+68)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e-23], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.15e+68], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999988e-23 or 2.1500000000000001e68 < z

   1. Initial program 80.4%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 19.8

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

   4. Applied rewrites 19.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 33.7%

      \[\leadsto x + t \]

   if -1.59999999999999988e-23 < z < 2.1500000000000001e68

   1. Initial program 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 84.8

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

   3. Applied rewrites 84.8%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   6. Applied rewrites 48.8%

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

Alternative 14: 44.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-295}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 400000000:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (/ (* y (- x t)) z)
     (if (<= t_1 -1e-295)
       (+ x t)
       (if (<= t_1 0.0)
         (/ (* x (- y a)) z)
         (if (<= t_1 400000000.0)
           (* y (/ t (- a z)))
           (if (<= t_1 4e+301) (+ x t) (/ (* x y) (- z a)))))))))

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 <= -((double) INFINITY)) {
		tmp = (y * (x - t)) / z;
	} else if (t_1 <= -1e-295) {
		tmp = x + t;
	} else if (t_1 <= 0.0) {
		tmp = (x * (y - a)) / z;
	} else if (t_1 <= 400000000.0) {
		tmp = y * (t / (a - z));
	} else if (t_1 <= 4e+301) {
		tmp = x + t;
	} else {
		tmp = (x * y) / (z - a);
	}
	return tmp;
}

Java

public static 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 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * (x - t)) / z;
	} else if (t_1 <= -1e-295) {
		tmp = x + t;
	} else if (t_1 <= 0.0) {
		tmp = (x * (y - a)) / z;
	} else if (t_1 <= 400000000.0) {
		tmp = y * (t / (a - z));
	} else if (t_1 <= 4e+301) {
		tmp = x + t;
	} else {
		tmp = (x * y) / (z - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y * (x - t)) / z
	elif t_1 <= -1e-295:
		tmp = x + t
	elif t_1 <= 0.0:
		tmp = (x * (y - a)) / z
	elif t_1 <= 400000000.0:
		tmp = y * (t / (a - z))
	elif t_1 <= 4e+301:
		tmp = x + t
	else:
		tmp = (x * y) / (z - a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (t_1 <= -1e-295)
		tmp = Float64(x + t);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (t_1 <= 400000000.0)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (t_1 <= 4e+301)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(x * y) / Float64(z - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y * (x - t)) / z;
	elseif (t_1 <= -1e-295)
		tmp = x + t;
	elseif (t_1 <= 0.0)
		tmp = (x * (y - a)) / z;
	elseif (t_1 <= 400000000.0)
		tmp = y * (t / (a - z));
	elseif (t_1 <= 4e+301)
		tmp = x + t;
	else
		tmp = (x * y) / (z - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e-295], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 400000000.0], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+301], N[(x + t), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0

   1. Initial program 80.4%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.5

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

   4. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 41.5

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. frac-2neg N/A

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

      14. lift-/.f64 41.9

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

   6. Applied rewrites 41.9%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 23.8

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

   9. Applied rewrites 23.8%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000006e-295 or 4e8 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000021e301

   1. Initial program 80.4%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 19.8

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

   4. Applied rewrites 19.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 33.7%

      \[\leadsto x + t \]

   if -1.00000000000000006e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.4%

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

   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. lower-+.f64 N/A

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      2. lower-*.f64 N/A

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      3. lower-/.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{\color{blue}{z}} \]

      4. lower--.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

      5. lower-*.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

      6. lower--.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

      8. lower--.f64 46.1

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

   4. Applied rewrites 46.1%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

   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. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(y - a\right)}{z} \]

      3. lower--.f64 19.8

         \[\leadsto \frac{x \cdot \left(y - a\right)}{z} \]

   7. Applied rewrites 19.8%

      \[\leadsto \frac{x \cdot \left(y - a\right)}{\color{blue}{z}} \]

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4e8

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto y \cdot \frac{t}{\color{blue}{a - z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto y \cdot \frac{t}{a - \color{blue}{z}} \]

      2. lower--.f64 23.1

         \[\leadsto y \cdot \frac{t}{a - z} \]

   7. Applied rewrites 23.1%

      \[\leadsto y \cdot \frac{t}{\color{blue}{a - z}} \]

   if 4.00000000000000021e301 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. sub-negate-rev N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      9. lift--.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      12. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      13. frac-2neg N/A

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

      14. lift-/.f64 41.9

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

   6. Applied rewrites 41.9%

      \[\leadsto \frac{x - t}{z - a} \cdot \color{blue}{y} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{\color{blue}{z - a}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{z - \color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{z - a} \]

      3. lower--.f64 21.1

         \[\leadsto \frac{x \cdot y}{z - a} \]

   9. Applied rewrites 21.1%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z - a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 15: 43.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-295}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq 10^{-53}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 400000000:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (/ (* y (- x t)) z)
     (if (<= t_1 -1e-295)
       (+ x t)
       (if (<= t_1 1e-53)
         (/ (* x (- y a)) z)
         (if (<= t_1 400000000.0)
           (/ (* t y) (- a z))
           (if (<= t_1 4e+301) (+ x t) (/ (* x y) (- z a)))))))))

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 <= -((double) INFINITY)) {
		tmp = (y * (x - t)) / z;
	} else if (t_1 <= -1e-295) {
		tmp = x + t;
	} else if (t_1 <= 1e-53) {
		tmp = (x * (y - a)) / z;
	} else if (t_1 <= 400000000.0) {
		tmp = (t * y) / (a - z);
	} else if (t_1 <= 4e+301) {
		tmp = x + t;
	} else {
		tmp = (x * y) / (z - a);
	}
	return tmp;
}

Java

public static 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 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * (x - t)) / z;
	} else if (t_1 <= -1e-295) {
		tmp = x + t;
	} else if (t_1 <= 1e-53) {
		tmp = (x * (y - a)) / z;
	} else if (t_1 <= 400000000.0) {
		tmp = (t * y) / (a - z);
	} else if (t_1 <= 4e+301) {
		tmp = x + t;
	} else {
		tmp = (x * y) / (z - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y * (x - t)) / z
	elif t_1 <= -1e-295:
		tmp = x + t
	elif t_1 <= 1e-53:
		tmp = (x * (y - a)) / z
	elif t_1 <= 400000000.0:
		tmp = (t * y) / (a - z)
	elif t_1 <= 4e+301:
		tmp = x + t
	else:
		tmp = (x * y) / (z - a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (t_1 <= -1e-295)
		tmp = Float64(x + t);
	elseif (t_1 <= 1e-53)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (t_1 <= 400000000.0)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	elseif (t_1 <= 4e+301)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(x * y) / Float64(z - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y * (x - t)) / z;
	elseif (t_1 <= -1e-295)
		tmp = x + t;
	elseif (t_1 <= 1e-53)
		tmp = (x * (y - a)) / z;
	elseif (t_1 <= 400000000.0)
		tmp = (t * y) / (a - z);
	elseif (t_1 <= 4e+301)
		tmp = x + t;
	else
		tmp = (x * y) / (z - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e-295], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 1e-53], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 400000000.0], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+301], N[(x + t), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. sub-negate-rev N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      9. lift--.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      12. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      13. frac-2neg N/A

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

      14. lift-/.f64 41.9

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

   6. Applied rewrites 41.9%

      \[\leadsto \frac{x - t}{z - a} \cdot \color{blue}{y} \]

   7. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      3. lower--.f64 23.8

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

   9. Applied rewrites 23.8%

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000006e-295 or 4e8 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000021e301

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.8

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.8%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.7%

      \[\leadsto x + t \]

   if -1.00000000000000006e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000003e-53

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-+.f64 N/A

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      2. lower-*.f64 N/A

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      3. lower-/.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{\color{blue}{z}} \]

      4. lower--.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

      5. lower-*.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

      6. lower--.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

      8. lower--.f64 46.1

         \[\leadsto t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \]

   4. Applied rewrites 46.1%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

   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. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(y - a\right)}{z} \]

      3. lower--.f64 19.8

         \[\leadsto \frac{x \cdot \left(y - a\right)}{z} \]

   7. Applied rewrites 19.8%

      \[\leadsto \frac{x \cdot \left(y - a\right)}{\color{blue}{z}} \]

   if 1.00000000000000003e-53 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4e8

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot y}{a - \color{blue}{z}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t \cdot y}{a - z} \]

      3. lower--.f64 21.3

         \[\leadsto \frac{t \cdot y}{a - z} \]

   7. Applied rewrites 21.3%

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]

   if 4.00000000000000021e301 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. sub-negate-rev N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      9. lift--.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      12. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      13. frac-2neg N/A

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

      14. lift-/.f64 41.9

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

   6. Applied rewrites 41.9%

      \[\leadsto \frac{x - t}{z - a} \cdot \color{blue}{y} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{\color{blue}{z - a}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{z - \color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{z - a} \]

      3. lower--.f64 21.1

         \[\leadsto \frac{x \cdot y}{z - a} \]

   9. Applied rewrites 21.1%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z - a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 16: 43.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-31}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e-31) (+ x t) (if (<= z 5.3e-25) (* y (/ (- t x) a)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e-31) {
		tmp = x + t;
	} else if (z <= 5.3e-25) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1d-31)) then
        tmp = x + t
    else if (z <= 5.3d-25) then
        tmp = y * ((t - x) / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e-31) {
		tmp = x + t;
	} else if (z <= 5.3e-25) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e-31:
		tmp = x + t
	elif z <= 5.3e-25:
		tmp = y * ((t - x) / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e-31)
		tmp = Float64(x + t);
	elseif (z <= 5.3e-25)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e-31)
		tmp = x + t;
	elseif (z <= 5.3e-25)
		tmp = y * ((t - x) / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e-31], N[(x + t), $MachinePrecision], If[LessEqual[z, 5.3e-25], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e-31 or 5.2999999999999997e-25 < z

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.8

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.8%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.7%

      \[\leadsto x + t \]

   if -1e-31 < z < 5.2999999999999997e-25

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto y \cdot \frac{t - x}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto y \cdot \frac{t - x}{a} \]

      2. lower--.f64 25.8

         \[\leadsto y \cdot \frac{t - x}{a} \]

   7. Applied rewrites 25.8%

      \[\leadsto y \cdot \frac{t - x}{\color{blue}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 40.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-295}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq 10^{-231}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+301}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (/ (* y (- x t)) z)
     (if (<= t_1 -1e-295)
       (+ x t)
       (if (<= t_1 1e-231)
         (* y (/ x z))
         (if (<= t_1 4e+301) (+ x t) (/ (* x y) (- z a))))))))

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 <= -((double) INFINITY)) {
		tmp = (y * (x - t)) / z;
	} else if (t_1 <= -1e-295) {
		tmp = x + t;
	} else if (t_1 <= 1e-231) {
		tmp = y * (x / z);
	} else if (t_1 <= 4e+301) {
		tmp = x + t;
	} else {
		tmp = (x * y) / (z - a);
	}
	return tmp;
}

Java

public static 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 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * (x - t)) / z;
	} else if (t_1 <= -1e-295) {
		tmp = x + t;
	} else if (t_1 <= 1e-231) {
		tmp = y * (x / z);
	} else if (t_1 <= 4e+301) {
		tmp = x + t;
	} else {
		tmp = (x * y) / (z - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y * (x - t)) / z
	elif t_1 <= -1e-295:
		tmp = x + t
	elif t_1 <= 1e-231:
		tmp = y * (x / z)
	elif t_1 <= 4e+301:
		tmp = x + t
	else:
		tmp = (x * y) / (z - a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (t_1 <= -1e-295)
		tmp = Float64(x + t);
	elseif (t_1 <= 1e-231)
		tmp = Float64(y * Float64(x / z));
	elseif (t_1 <= 4e+301)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(x * y) / Float64(z - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y * (x - t)) / z;
	elseif (t_1 <= -1e-295)
		tmp = x + t;
	elseif (t_1 <= 1e-231)
		tmp = y * (x / z);
	elseif (t_1 <= 4e+301)
		tmp = x + t;
	else
		tmp = (x * y) / (z - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e-295], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 1e-231], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+301], N[(x + t), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. sub-negate-rev N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      9. lift--.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      12. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      13. frac-2neg N/A

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

      14. lift-/.f64 41.9

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

   6. Applied rewrites 41.9%

      \[\leadsto \frac{x - t}{z - a} \cdot \color{blue}{y} \]

   7. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

      3. lower--.f64 23.8

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z} \]

   9. Applied rewrites 23.8%

      \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z}} \]

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000006e-295 or 9.9999999999999999e-232 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000021e301

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.8

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.8%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.7%

      \[\leadsto x + t \]

   if -1.00000000000000006e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999999e-232

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in z around -inf

      \[\leadsto y \cdot \left(-1 \cdot \color{blue}{\frac{t - x}{z}}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \frac{t - x}{\color{blue}{z}}\right) \]

      2. lower-/.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \frac{t - x}{z}\right) \]

      3. lower--.f64 25.6

         \[\leadsto y \cdot \left(-1 \cdot \frac{t - x}{z}\right) \]

   7. Applied rewrites 25.6%

      \[\leadsto y \cdot \left(-1 \cdot \color{blue}{\frac{t - x}{z}}\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto y \cdot \frac{x}{z} \]
   9. Step-by-step derivation

      1. lower-/.f64 17.8

         \[\leadsto y \cdot \frac{x}{z} \]

   10. Applied rewrites 17.8%

       \[\leadsto y \cdot \frac{x}{z} \]

   if 4.00000000000000021e301 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. sub-negate-rev N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      9. lift--.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{a - z} \cdot y \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      12. lift--.f64 N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(x - t\right)\right)}{\mathsf{neg}\left(\left(z - a\right)\right)} \cdot y \]

      13. frac-2neg N/A

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

      14. lift-/.f64 41.9

          \[\leadsto \frac{x - t}{z - a} \cdot y \]

   6. Applied rewrites 41.9%

      \[\leadsto \frac{x - t}{z - a} \cdot \color{blue}{y} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{\color{blue}{z - a}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{z - \color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{z - a} \]

      3. lower--.f64 21.1

         \[\leadsto \frac{x \cdot y}{z - a} \]

   9. Applied rewrites 21.1%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z - a}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 18: 37.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-139}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e-139) (+ x t) (if (<= z 6.2e-25) (/ (* t y) (- a z)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e-139) {
		tmp = x + t;
	} else if (z <= 6.2e-25) {
		tmp = (t * y) / (a - z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.3d-139)) then
        tmp = x + t
    else if (z <= 6.2d-25) then
        tmp = (t * y) / (a - z)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e-139) {
		tmp = x + t;
	} else if (z <= 6.2e-25) {
		tmp = (t * y) / (a - z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e-139:
		tmp = x + t
	elif z <= 6.2e-25:
		tmp = (t * y) / (a - z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e-139)
		tmp = Float64(x + t);
	elseif (z <= 6.2e-25)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e-139)
		tmp = x + t;
	elseif (z <= 6.2e-25)
		tmp = (t * y) / (a - z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e-139], N[(x + t), $MachinePrecision], If[LessEqual[z, 6.2e-25], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e-139 or 6.19999999999999989e-25 < z

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.8

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.8%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.7%

      \[\leadsto x + t \]

   if -3.3e-139 < z < 6.19999999999999989e-25

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot y}{a - \color{blue}{z}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t \cdot y}{a - z} \]

      3. lower--.f64 21.3

         \[\leadsto \frac{t \cdot y}{a - z} \]

   7. Applied rewrites 21.3%

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 35.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.04 \cdot 10^{+223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+204}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= y -1.04e+223) t_1 (if (<= y 1.2e+204) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / z);
	double tmp;
	if (y <= -1.04e+223) {
		tmp = t_1;
	} else if (y <= 1.2e+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 = y * (x / z)
    if (y <= (-1.04d+223)) then
        tmp = t_1
    else if (y <= 1.2d+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 = y * (x / z);
	double tmp;
	if (y <= -1.04e+223) {
		tmp = t_1;
	} else if (y <= 1.2e+204) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (x / z)
	tmp = 0
	if y <= -1.04e+223:
		tmp = t_1
	elif y <= 1.2e+204:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -1.04e+223)
		tmp = t_1;
	elseif (y <= 1.2e+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 = y * (x / z);
	tmp = 0.0;
	if (y <= -1.04e+223)
		tmp = t_1;
	elseif (y <= 1.2e+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[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.04e+223], t$95$1, If[LessEqual[y, 1.2e+204], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04e223 or 1.2e204 < y

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in z around -inf

      \[\leadsto y \cdot \left(-1 \cdot \color{blue}{\frac{t - x}{z}}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \frac{t - x}{\color{blue}{z}}\right) \]

      2. lower-/.f64 N/A

         \[\leadsto y \cdot \left(-1 \cdot \frac{t - x}{z}\right) \]

      3. lower--.f64 25.6

         \[\leadsto y \cdot \left(-1 \cdot \frac{t - x}{z}\right) \]

   7. Applied rewrites 25.6%

      \[\leadsto y \cdot \left(-1 \cdot \color{blue}{\frac{t - x}{z}}\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto y \cdot \frac{x}{z} \]
   9. Step-by-step derivation

      1. lower-/.f64 17.8

         \[\leadsto y \cdot \frac{x}{z} \]

   10. Applied rewrites 17.8%

       \[\leadsto y \cdot \frac{x}{z} \]

   if -1.04e223 < y < 1.2e204

   1. Initial program 80.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.8

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.8%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.7%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 33.7% 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 80.4%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Step-by-step derivation

   1. lower--.f64 19.8

      \[\leadsto x + \left(t - \color{blue}{x}\right) \]

4. Applied rewrites 19.8%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]

5. Taylor expanded in x around 0

   \[\leadsto x + t \]
6. Step-by-step derivation

7. Applied rewrites 33.7%

   \[\leadsto x + t \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025149 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))