Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.7% → 90.3%

Time: 4.6s

Alternatives: 15

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: 80.7% 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: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-241}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{\left(a + \frac{t \cdot y}{x}\right) - \left(y + \frac{a \cdot t}{x}\right)}{z}, \frac{t}{x}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-266)
     t_1
     (if (<= t_1 2e-241)
       (*
        (fma -1.0 (/ (- (+ a (/ (* t y) x)) (+ y (/ (* a t) x))) z) (/ t x))
        x)
       (fma (/ (- x t) (- z a)) (- y z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-266) {
		tmp = t_1;
	} else if (t_1 <= 2e-241) {
		tmp = fma(-1.0, (((a + ((t * y) / x)) - (y + ((a * t) / x))) / z), (t / x)) * x;
	} else {
		tmp = fma(((x - t) / (z - a)), (y - z), 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 <= -5e-266)
		tmp = t_1;
	elseif (t_1 <= 2e-241)
		tmp = Float64(fma(-1.0, Float64(Float64(Float64(a + Float64(Float64(t * y) / x)) - Float64(y + Float64(Float64(a * t) / x))) / z), Float64(t / x)) * x);
	else
		tmp = fma(Float64(Float64(x - t) / Float64(z - a)), Float64(y - z), 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, -5e-266], t$95$1, If[LessEqual[t$95$1, 2e-241], N[(N[(-1.0 * N[(N[(N[(a + N[(N[(t * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(y + N[(N[(a * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(t / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * 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)))) < -4.99999999999999992e-266

   1. Initial program 90.4%

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

   if -4.99999999999999992e-266 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999999e-241

   1. Initial program 10.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 16.5%

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

   5. Taylor expanded in z around -inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 85.4

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

   7. Applied rewrites 85.4%

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

   if 1.9999999999999999e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.5%

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

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. sub-negate-rev N/A

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

      12. frac-2neg-rev N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 91.5

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

   3. Applied rewrites 91.5%

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

Alternative 2: 89.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-241}:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-266)
     t_1
     (if (<= t_1 2e-241)
       (+ (- (/ (* (- t x) (- y a)) z)) t)
       (fma (/ (- x t) (- z a)) (- y z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-266) {
		tmp = t_1;
	} else if (t_1 <= 2e-241) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else {
		tmp = fma(((x - t) / (z - a)), (y - z), 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 <= -5e-266)
		tmp = t_1;
	elseif (t_1 <= 2e-241)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	else
		tmp = fma(Float64(Float64(x - t) / Float64(z - a)), Float64(y - z), 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, -5e-266], t$95$1, If[LessEqual[t$95$1, 2e-241], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * 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)))) < -4.99999999999999992e-266

   1. Initial program 90.4%

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

   if -4.99999999999999992e-266 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999999e-241

   1. Initial program 10.5%

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

   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. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 76.4

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

   4. Applied rewrites 76.4%

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

   if 1.9999999999999999e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.5%

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

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. sub-negate-rev N/A

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

      12. frac-2neg-rev N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 91.5

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

   3. Applied rewrites 91.5%

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

Alternative 3: 89.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-241}:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -5e-266)
     t_1
     (if (<= t_2 2e-241) (+ (- (/ (* (- t x) (- y a)) z)) 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 <= -5e-266) {
		tmp = t_1;
	} else if (t_2 <= 2e-241) {
		tmp = -(((t - x) * (y - a)) / z) + 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 <= -5e-266)
		tmp = t_1;
	elseif (t_2 <= 2e-241)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + 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, -5e-266], t$95$1, If[LessEqual[t$95$2, 2e-241], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $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)))) < -4.99999999999999992e-266 or 1.9999999999999999e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.0%

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

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. sub-negate-rev N/A

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

      12. frac-2neg-rev N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 91.0

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

   3. Applied rewrites 91.0%

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

   if -4.99999999999999992e-266 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999999e-241

   1. Initial program 10.5%

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

   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. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 76.4

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

   4. Applied rewrites 76.4%

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

Alternative 4: 79.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-266}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-241}:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (* (- y z) (/ t (- a z))))))
   (if (<= t_1 (- INFINITY))
     (* (- t x) (/ y (- a z)))
     (if (<= t_1 -5e-266)
       t_2
       (if (<= t_1 2e-241)
         (+ (- (/ (* (- t x) (- y a)) z)) t)
         (if (<= t_1 2e+304) t_2 (/ (* (- t x) y) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (t - x) * (y / (a - z));
	} else if (t_1 <= -5e-266) {
		tmp = t_2;
	} else if (t_1 <= 2e-241) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else if (t_1 <= 2e+304) {
		tmp = t_2;
	} else {
		tmp = ((t - x) * y) / (a - z);
	}
	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 t_2 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (t - x) * (y / (a - z));
	} else if (t_1 <= -5e-266) {
		tmp = t_2;
	} else if (t_1 <= 2e-241) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else if (t_1 <= 2e+304) {
		tmp = t_2;
	} else {
		tmp = ((t - x) * y) / (a - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + ((y - z) * (t / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (t - x) * (y / (a - z))
	elif t_1 <= -5e-266:
		tmp = t_2
	elif t_1 <= 2e-241:
		tmp = -(((t - x) * (y - a)) / z) + t
	elif t_1 <= 2e+304:
		tmp = t_2
	else:
		tmp = ((t - x) * y) / (a - z)
	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))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (t_1 <= -5e-266)
		tmp = t_2;
	elseif (t_1 <= 2e-241)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	elseif (t_1 <= 2e+304)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(t - x) * y) / Float64(a - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + ((y - z) * (t / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (t - x) * (y / (a - z));
	elseif (t_1 <= -5e-266)
		tmp = t_2;
	elseif (t_1 <= 2e-241)
		tmp = -(((t - x) * (y - a)) / z) + t;
	elseif (t_1 <= 2e+304)
		tmp = t_2;
	else
		tmp = ((t - x) * y) / (a - z);
	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]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-266], t$95$2, If[LessEqual[t$95$1, 2e-241], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], If[LessEqual[t$95$1, 2e+304], t$95$2, N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $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 85.2%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 91.0

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

   4. Applied rewrites 91.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 91.0

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

   6. Applied rewrites 91.0%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999992e-266 or 1.9999999999999999e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999999e304

   1. Initial program 92.2%

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

   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 77.8%

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

   if -4.99999999999999992e-266 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999999e-241

   1. Initial program 10.5%

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

   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. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower--.f64 76.4

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

   4. Applied rewrites 76.4%

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

   if 1.9999999999999999e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.2%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 28.9

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

   4. Applied rewrites 28.9%

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

Alternative 5: 74.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-266}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-187}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (* (- y z) (/ t (- a z))))))
   (if (<= t_1 (- INFINITY))
     (* (- t x) (/ y (- a z)))
     (if (<= t_1 -5e-266)
       t_2
       (if (<= t_1 5e-187)
         (/ (* (- y z) t) (- a z))
         (if (<= t_1 2e+304) t_2 (/ (* (- t x) y) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (t - x) * (y / (a - z));
	} else if (t_1 <= -5e-266) {
		tmp = t_2;
	} else if (t_1 <= 5e-187) {
		tmp = ((y - z) * t) / (a - z);
	} else if (t_1 <= 2e+304) {
		tmp = t_2;
	} else {
		tmp = ((t - x) * y) / (a - z);
	}
	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 t_2 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (t - x) * (y / (a - z));
	} else if (t_1 <= -5e-266) {
		tmp = t_2;
	} else if (t_1 <= 5e-187) {
		tmp = ((y - z) * t) / (a - z);
	} else if (t_1 <= 2e+304) {
		tmp = t_2;
	} else {
		tmp = ((t - x) * y) / (a - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + ((y - z) * (t / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (t - x) * (y / (a - z))
	elif t_1 <= -5e-266:
		tmp = t_2
	elif t_1 <= 5e-187:
		tmp = ((y - z) * t) / (a - z)
	elif t_1 <= 2e+304:
		tmp = t_2
	else:
		tmp = ((t - x) * y) / (a - z)
	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))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (t_1 <= -5e-266)
		tmp = t_2;
	elseif (t_1 <= 5e-187)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (t_1 <= 2e+304)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(t - x) * y) / Float64(a - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + ((y - z) * (t / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (t - x) * (y / (a - z));
	elseif (t_1 <= -5e-266)
		tmp = t_2;
	elseif (t_1 <= 5e-187)
		tmp = ((y - z) * t) / (a - z);
	elseif (t_1 <= 2e+304)
		tmp = t_2;
	else
		tmp = ((t - x) * y) / (a - z);
	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]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-266], t$95$2, If[LessEqual[t$95$1, 5e-187], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+304], t$95$2, N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $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 85.2%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 91.0

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

   4. Applied rewrites 91.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 91.0

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

   6. Applied rewrites 91.0%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999992e-266 or 4.9999999999999996e-187 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999999e304

   1. Initial program 92.6%

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

   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 78.0%

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

   if -4.99999999999999992e-266 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999996e-187

   1. Initial program 16.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 37.0

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

   4. Applied rewrites 37.0%

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

   if 1.9999999999999999e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.6%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 29.1

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

   4. Applied rewrites 29.1%

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

Alternative 6: 67.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -1.3e-64)
     t_1
     (if (<= a 1.55e-34) (* t (/ (- y z) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / a), x);
	double tmp;
	if (a <= -1.3e-64) {
		tmp = t_1;
	} else if (a <= 1.55e-34) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -1.3e-64)
		tmp = t_1;
	elseif (a <= 1.55e-34)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.3e-64], t$95$1, If[LessEqual[a, 1.55e-34], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e-64 or 1.5499999999999999e-34 < a

   1. Initial program 86.9%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 71.2

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

   4. Applied rewrites 71.2%

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

   if -1.3e-64 < a < 1.5499999999999999e-34

   1. Initial program 72.2%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 70.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 63.4

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

   7. Applied rewrites 63.4%

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

Alternative 7: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8200000000000:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;\frac{t - x}{a - z} \cdot y\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+22}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8200000000000.0)
   (+ x (* (- y z) (/ t a)))
   (if (<= a -3.1e-90)
     (* (/ (- t x) (- a z)) y)
     (if (<= a 1.65e+22) (* t (/ (- y z) (- a z))) (fma y (/ (- t x) a) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8200000000000.0) {
		tmp = x + ((y - z) * (t / a));
	} else if (a <= -3.1e-90) {
		tmp = ((t - x) / (a - z)) * y;
	} else if (a <= 1.65e+22) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = fma(y, ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8200000000000.0)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	elseif (a <= -3.1e-90)
		tmp = Float64(Float64(Float64(t - x) / Float64(a - z)) * y);
	elseif (a <= 1.65e+22)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8200000000000.0], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.1e-90], N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 1.65e+22], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.2e12

   1. Initial program 88.3%

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

   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 78.4%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 67.6%

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

   if -8.2e12 < a < -3.1000000000000001e-90

   1. Initial program 79.8%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 45.0

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

   4. Applied rewrites 45.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 47.7

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

   6. Applied rewrites 47.7%

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

   if -3.1000000000000001e-90 < a < 1.6499999999999999e22

   1. Initial program 72.6%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 70.8%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 63.4

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

   7. Applied rewrites 63.4%

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

   if 1.6499999999999999e22 < a

   1. Initial program 88.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 67.1

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

   4. Applied rewrites 67.1%

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

Alternative 8: 60.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= x -1.02e+114)
     t_1
     (if (<= x 6.5e+182) (* t (/ (- y z) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (x <= -1.02e+114) {
		tmp = t_1;
	} else if (x <= 6.5e+182) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (x <= -1.02e+114)
		tmp = t_1;
	elseif (x <= 6.5e+182)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -1.02e+114], t$95$1, If[LessEqual[x, 6.5e+182], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999999e114 or 6.4999999999999998e182 < x

   1. Initial program 70.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 54.2

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

   4. Applied rewrites 54.2%

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

   if -1.01999999999999999e114 < x < 6.4999999999999998e182

   1. Initial program 84.1%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 83.0%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 62.1

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

   7. Applied rewrites 62.1%

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

Alternative 9: 54.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-196}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-145}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{-z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{t}{x} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- t x) a) x)))
   (if (<= a -3.8e-72)
     t_1
     (if (<= a -1.6e-196)
       t
       (if (<= a 3e-145)
         (/ (* (- t x) y) (- z))
         (if (<= a 1.5e-75) (* (/ t x) x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - x) / a), x);
	double tmp;
	if (a <= -3.8e-72) {
		tmp = t_1;
	} else if (a <= -1.6e-196) {
		tmp = t;
	} else if (a <= 3e-145) {
		tmp = ((t - x) * y) / -z;
	} else if (a <= 1.5e-75) {
		tmp = (t / x) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -3.8e-72)
		tmp = t_1;
	elseif (a <= -1.6e-196)
		tmp = t;
	elseif (a <= 3e-145)
		tmp = Float64(Float64(Float64(t - x) * y) / Float64(-z));
	elseif (a <= 1.5e-75)
		tmp = Float64(Float64(t / x) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.8e-72], t$95$1, If[LessEqual[a, -1.6e-196], t, If[LessEqual[a, 3e-145], N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[a, 1.5e-75], N[(N[(t / x), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.80000000000000002e-72 or 1.4999999999999999e-75 < a

   1. Initial program 86.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 61.4

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

   4. Applied rewrites 61.4%

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

   if -3.80000000000000002e-72 < a < -1.6e-196

   1. Initial program 70.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 36.3%

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

   if -1.6e-196 < a < 2.99999999999999992e-145

   1. Initial program 70.8%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 56.1

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

   4. Applied rewrites 56.1%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 48.8

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

   7. Applied rewrites 48.8%

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

   if 2.99999999999999992e-145 < a < 1.4999999999999999e-75

   1. Initial program 77.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 62.0%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 27.0

         \[\leadsto \frac{t}{x} \cdot x \]

   7. Applied rewrites 27.0%

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

Alternative 10: 43.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+139}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-13}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -8.6e+139)
   (* (/ (- t x) a) y)
   (if (<= y 2.9e-13) (+ x t) (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8.6e+139) {
		tmp = ((t - x) / a) * y;
	} else if (y <= 2.9e-13) {
		tmp = x + t;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-8.6d+139)) then
        tmp = ((t - x) / a) * y
    else if (y <= 2.9d-13) then
        tmp = x + t
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8.6e+139) {
		tmp = ((t - x) / a) * y;
	} else if (y <= 2.9e-13) {
		tmp = x + t;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -8.6e+139:
		tmp = ((t - x) / a) * y
	elif y <= 2.9e-13:
		tmp = x + t
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -8.6e+139)
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	elseif (y <= 2.9e-13)
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -8.6e+139)
		tmp = ((t - x) / a) * y;
	elseif (y <= 2.9e-13)
		tmp = x + t;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -8.6e+139], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 2.9e-13], N[(x + t), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5999999999999996e139

   1. Initial program 90.0%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 64.7

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

   4. Applied rewrites 64.7%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 80.8

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

   6. Applied rewrites 80.8%

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

   7. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 50.2

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

   9. Applied rewrites 50.2%

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

   if -8.5999999999999996e139 < y < 2.8999999999999998e-13

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 24.4

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

   4. Applied rewrites 24.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 43.7%

      \[\leadsto x + t \]

   if 2.8999999999999998e-13 < y

   1. Initial program 87.3%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 56.7

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

   4. Applied rewrites 56.7%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 37.9

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

   7. Applied rewrites 37.9%

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

Alternative 11: 43.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -335000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-13}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -335000000.0) t_1 (if (<= y 2.9e-13) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -335000000.0) {
		tmp = t_1;
	} else if (y <= 2.9e-13) {
		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 = t * (y / (a - z))
    if (y <= (-335000000.0d0)) then
        tmp = t_1
    else if (y <= 2.9d-13) 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 = t * (y / (a - z));
	double tmp;
	if (y <= -335000000.0) {
		tmp = t_1;
	} else if (y <= 2.9e-13) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -335000000.0:
		tmp = t_1
	elif y <= 2.9e-13:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -335000000.0)
		tmp = t_1;
	elseif (y <= 2.9e-13)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -335000000.0)
		tmp = t_1;
	elseif (y <= 2.9e-13)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -335000000.0], t$95$1, If[LessEqual[y, 2.9e-13], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.35e8 or 2.8999999999999998e-13 < y

   1. Initial program 87.5%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 57.4

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

   4. Applied rewrites 57.4%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 39.2

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

   7. Applied rewrites 39.2%

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

   if -3.35e8 < y < 2.8999999999999998e-13

   1. Initial program 73.7%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 26.0

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

   4. Applied rewrites 26.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 46.3%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 42.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;t\_1 \leq -0.005:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-241}:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-x\right) \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (/ (* t y) a)
     (if (<= t_1 -0.005)
       (+ x t)
       (if (<= t_1 2e-241)
         t
         (if (<= t_1 2e+304) (+ x t) (/ (* (- x) y) 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 = (t * y) / a;
	} else if (t_1 <= -0.005) {
		tmp = x + t;
	} else if (t_1 <= 2e-241) {
		tmp = t;
	} else if (t_1 <= 2e+304) {
		tmp = x + t;
	} else {
		tmp = (-x * y) / 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 = (t * y) / a;
	} else if (t_1 <= -0.005) {
		tmp = x + t;
	} else if (t_1 <= 2e-241) {
		tmp = t;
	} else if (t_1 <= 2e+304) {
		tmp = x + t;
	} else {
		tmp = (-x * y) / 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 = (t * y) / a
	elif t_1 <= -0.005:
		tmp = x + t
	elif t_1 <= 2e-241:
		tmp = t
	elif t_1 <= 2e+304:
		tmp = x + t
	else:
		tmp = (-x * y) / 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(t * y) / a);
	elseif (t_1 <= -0.005)
		tmp = Float64(x + t);
	elseif (t_1 <= 2e-241)
		tmp = t;
	elseif (t_1 <= 2e+304)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(Float64(-x) * y) / 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 = (t * y) / a;
	elseif (t_1 <= -0.005)
		tmp = x + t;
	elseif (t_1 <= 2e-241)
		tmp = t;
	elseif (t_1 <= 2e+304)
		tmp = x + t;
	else
		tmp = (-x * y) / 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[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$1, -0.005], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 2e-241], t, If[LessEqual[t$95$1, 2e+304], N[(x + t), $MachinePrecision], N[(N[((-x) * y), $MachinePrecision] / a), $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 85.2%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 57.4

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

   4. Applied rewrites 57.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 46.6

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

   7. Applied rewrites 46.6%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -0.0050000000000000001 or 1.9999999999999999e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999999e304

   1. Initial program 94.5%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 25.1

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

   4. Applied rewrites 25.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 46.0%

      \[\leadsto x + t \]

   if -0.0050000000000000001 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999999e-241

   1. Initial program 41.6%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 33.1%

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

   if 1.9999999999999999e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.5%

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

   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. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 29.0

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

   4. Applied rewrites 29.0%

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

   5. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 13.8

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

   7. Applied rewrites 13.8%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 7.9%

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

Alternative 13: 42.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot y}{a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -0.005:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-241}:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t y) a)) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -0.005)
       (+ x t)
       (if (<= t_2 2e-241) t (if (<= t_2 5e+307) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -0.005) {
		tmp = x + t;
	} else if (t_2 <= 2e-241) {
		tmp = t;
	} else if (t_2 <= 5e+307) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -0.005) {
		tmp = x + t;
	} else if (t_2 <= 2e-241) {
		tmp = t;
	} else if (t_2 <= 5e+307) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * y) / a
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -0.005:
		tmp = x + t
	elif t_2 <= 2e-241:
		tmp = t
	elif t_2 <= 5e+307:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * y) / a)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -0.005)
		tmp = Float64(x + t);
	elseif (t_2 <= 2e-241)
		tmp = t;
	elseif (t_2 <= 5e+307)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * y) / a;
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -0.005)
		tmp = x + t;
	elseif (t_2 <= 2e-241)
		tmp = t;
	elseif (t_2 <= 5e+307)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * y), $MachinePrecision] / a), $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, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -0.005], N[(x + t), $MachinePrecision], If[LessEqual[t$95$2, 2e-241], t, If[LessEqual[t$95$2, 5e+307], N[(x + t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 5e307 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 57.7

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

   4. Applied rewrites 57.7%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 45.9

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

   7. Applied rewrites 45.9%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -0.0050000000000000001 or 1.9999999999999999e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e307

   1. Initial program 94.5%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 25.1

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

   4. Applied rewrites 25.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 46.1%

      \[\leadsto x + t \]

   if -0.0050000000000000001 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999999e-241

   1. Initial program 41.6%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 33.1%

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

Alternative 14: 38.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e-12) t (if (<= z 1.2e-9) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e-12) {
		tmp = t;
	} else if (z <= 1.2e-9) {
		tmp = x;
	} else {
		tmp = 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 <= (-3.4d-12)) then
        tmp = t
    else if (z <= 1.2d-9) then
        tmp = x
    else
        tmp = 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 <= -3.4e-12) {
		tmp = t;
	} else if (z <= 1.2e-9) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e-12:
		tmp = t
	elif z <= 1.2e-9:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e-12)
		tmp = t;
	elseif (z <= 1.2e-9)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e-12)
		tmp = t;
	elseif (z <= 1.2e-9)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e-12], t, If[LessEqual[z, 1.2e-9], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000001e-12 or 1.2e-9 < z

   1. Initial program 70.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 41.4%

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

   if -3.4000000000000001e-12 < z < 1.2e-9

   1. Initial program 91.6%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 35.2%

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

Alternative 15: 25.0% accurate, 17.9× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.7%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 25.0%

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

Reproduce

herbie shell --seed 2025128 
(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)))))