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

Percentage Accurate: 68.0% → 85.2%

Time: 7.8s

Alternatives: 14

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t - x\right) \cdot \frac{y - a}{z}, -1, t\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (* (- t x) (/ (- y a) z)) -1.0 t)))
   (if (<= z -4e+63)
     t_1
     (if (<= z 4.2) (fma (- y z) (/ (- t x) (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) * ((y - a) / z)), -1.0, t);
	double tmp;
	if (z <= -4e+63) {
		tmp = t_1;
	} else if (z <= 4.2) {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) * Float64(Float64(y - a) / z)), -1.0, t)
	tmp = 0.0
	if (z <= -4e+63)
		tmp = t_1;
	elseif (z <= 4.2)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * -1.0 + t), $MachinePrecision]}, If[LessEqual[z, -4e+63], t$95$1, If[LessEqual[z, 4.2], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000023e63 or 4.20000000000000018 < z

   1. Initial program 42.4%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 24.8

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

   4. Applied rewrites 24.8%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
   6. 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 78.1

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

   7. Applied rewrites 78.1%

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

   if -4.00000000000000023e63 < z < 4.20000000000000018

   1. Initial program 88.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 90.9

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

   3. Applied rewrites 90.9%

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

Alternative 2: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-300)
     t_1
     (if (<= t_2 0.0) (+ t (- (/ (* (- t x) (- y a)) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-300) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + -(((t - x) * (y - a)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-300)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-300], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + (-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999996e-300 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 86.1

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

   3. Applied rewrites 86.1%

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

   if -4.99999999999999996e-300 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 5.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 5.3

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

   3. Applied rewrites 5.3%

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

   4. Taylor expanded in z around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower-neg.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 98.9

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

   6. Applied rewrites 98.9%

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

Alternative 3: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-300) t_1 (if (<= t_2 0.0) (+ t (* x (/ y z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-300) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-300)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-300], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999996e-300 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 86.1

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

   3. Applied rewrites 86.1%

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

   if -4.99999999999999996e-300 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 5.0%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 98.9%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 69.7

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

   7. Applied rewrites 69.7%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 69.9

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

   10. Applied rewrites 69.9%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 69.7

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

   13. Applied rewrites 69.7%

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

Alternative 4: 45.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-179}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -1.65e-62)
     t_1
     (if (<= z -1.8e-200)
       x
       (if (<= z 1.9e-179) (* (/ (- t x) a) y) (if (<= z 1.65e-48) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.65e-62) {
		tmp = t_1;
	} else if (z <= -1.8e-200) {
		tmp = x;
	} else if (z <= 1.9e-179) {
		tmp = ((t - x) / a) * y;
	} else if (z <= 1.65e-48) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-1.65d-62)) then
        tmp = t_1
    else if (z <= (-1.8d-200)) then
        tmp = x
    else if (z <= 1.9d-179) then
        tmp = ((t - x) / a) * y
    else if (z <= 1.65d-48) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.65e-62) {
		tmp = t_1;
	} else if (z <= -1.8e-200) {
		tmp = x;
	} else if (z <= 1.9e-179) {
		tmp = ((t - x) / a) * y;
	} else if (z <= 1.65e-48) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -1.65e-62:
		tmp = t_1
	elif z <= -1.8e-200:
		tmp = x
	elif z <= 1.9e-179:
		tmp = ((t - x) / a) * y
	elif z <= 1.65e-48:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.65e-62)
		tmp = t_1;
	elseif (z <= -1.8e-200)
		tmp = x;
	elseif (z <= 1.9e-179)
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	elseif (z <= 1.65e-48)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.65e-62)
		tmp = t_1;
	elseif (z <= -1.8e-200)
		tmp = x;
	elseif (z <= 1.9e-179)
		tmp = ((t - x) / a) * y;
	elseif (z <= 1.65e-48)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-62], t$95$1, If[LessEqual[z, -1.8e-200], x, If[LessEqual[z, 1.9e-179], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 1.65e-48], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000002e-62 or 1.65e-48 < z

   1. Initial program 51.9%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 55.1%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 56.3

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

   7. Applied rewrites 56.3%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 48.1

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

   10. Applied rewrites 48.1%

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

   if -1.65000000000000002e-62 < z < -1.8000000000000001e-200 or 1.89999999999999987e-179 < z < 1.65e-48

   1. Initial program 89.2%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 34.1%

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

   if -1.8000000000000001e-200 < z < 1.89999999999999987e-179

   1. Initial program 92.8%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 91.8

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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 52.5

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

   7. Applied rewrites 52.5%

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

Alternative 5: 53.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+76}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e+87)
   x
   (if (<= a 4.1e-13)
     (+ t (* x (/ y z)))
     (if (<= a 1.1e+76) (* (/ (- t x) a) y) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+87) {
		tmp = x;
	} else if (a <= 4.1e-13) {
		tmp = t + (x * (y / z));
	} else if (a <= 1.1e+76) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.35d+87)) then
        tmp = x
    else if (a <= 4.1d-13) then
        tmp = t + (x * (y / z))
    else if (a <= 1.1d+76) then
        tmp = ((t - x) / a) * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+87) {
		tmp = x;
	} else if (a <= 4.1e-13) {
		tmp = t + (x * (y / z));
	} else if (a <= 1.1e+76) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e+87:
		tmp = x
	elif a <= 4.1e-13:
		tmp = t + (x * (y / z))
	elif a <= 1.1e+76:
		tmp = ((t - x) / a) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e+87)
		tmp = x;
	elseif (a <= 4.1e-13)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 1.1e+76)
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.35e+87)
		tmp = x;
	elseif (a <= 4.1e-13)
		tmp = t + (x * (y / z));
	elseif (a <= 1.1e+76)
		tmp = ((t - x) / a) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e+87], x, If[LessEqual[a, 4.1e-13], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+76], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.35000000000000003e87 or 1.1e76 < a

   1. Initial program 68.2%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 49.0%

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

   if -1.35000000000000003e87 < a < 4.1000000000000002e-13

   1. Initial program 67.6%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 57.9%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 65.3

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

   7. Applied rewrites 65.3%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 59.5

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

   10. Applied rewrites 59.5%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 58.7

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

   13. Applied rewrites 58.7%

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

   if 4.1000000000000002e-13 < a < 1.1e76

   1. Initial program 69.4%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 55.9

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

   4. Applied rewrites 55.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 35.2

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

   7. Applied rewrites 35.2%

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

Alternative 6: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(-\frac{y \cdot \left(t - x\right)}{z}\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.75:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (- (/ (* y (- t x)) z)))))
   (if (<= z -3e-62) t_1 (if (<= z 3.75) (fma (- t x) (/ (- y z) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + -((y * (t - x)) / z);
	double tmp;
	if (z <= -3e-62) {
		tmp = t_1;
	} else if (z <= 3.75) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(-Float64(Float64(y * Float64(t - x)) / z)))
	tmp = 0.0
	if (z <= -3e-62)
		tmp = t_1;
	elseif (z <= 3.75)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + (-N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -3e-62], t$95$1, If[LessEqual[z, 3.75], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000001e-62 or 3.75 < z

   1. Initial program 49.5%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 56.1%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 57.2

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

   7. Applied rewrites 57.2%

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

   if -3.0000000000000001e-62 < z < 3.75

   1. Initial program 90.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 80.3

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

   4. Applied rewrites 80.3%

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

Alternative 7: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e-29)
   (* t (/ (- y z) (- a z)))
   (if (<= z 3.95e+30) (fma (- t x) (/ (- y z) a) x) (+ t (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e-29) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 3.95e+30) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e-29)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 3.95e+30)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	else
		tmp = Float64(t + Float64(x * Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e-29], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.95e+30], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000005e-29

   1. Initial program 49.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 69.9

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

   3. Applied rewrites 69.9%

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

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. 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 60.0

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

   6. Applied rewrites 60.0%

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

   if -6.0000000000000005e-29 < z < 3.94999999999999981e30

   1. Initial program 89.8%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 77.7

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

   4. Applied rewrites 77.7%

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

   if 3.94999999999999981e30 < z

   1. Initial program 41.4%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 58.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 58.2

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

   7. Applied rewrites 58.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 59.4

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

   10. Applied rewrites 59.4%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 60.3

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

   13. Applied rewrites 60.3%

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

Alternative 8: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-105}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e-105)
   (* t (/ (- y z) (- a z)))
   (if (<= z 3.95e+30) (fma (- t x) (/ y a) x) (+ t (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e-105) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 3.95e+30) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e-105)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 3.95e+30)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = Float64(t + Float64(x * Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e-105], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.95e+30], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.10000000000000007e-105

   1. Initial program 56.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 73.8

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

   3. Applied rewrites 73.8%

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

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. 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 57.7

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

   6. Applied rewrites 57.7%

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

   if -5.10000000000000007e-105 < z < 3.94999999999999981e30

   1. Initial program 90.0%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 79.5

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

   4. Applied rewrites 79.5%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 76.3%

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

   if 3.94999999999999981e30 < z

   1. Initial program 41.4%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 58.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 58.2

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

   7. Applied rewrites 58.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 59.4

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

   10. Applied rewrites 59.4%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 60.3

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

   13. Applied rewrites 60.3%

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

Alternative 9: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-29}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e-29)
   (+ t (/ (* x y) z))
   (if (<= z 3.95e+30) (fma (- t x) (/ y a) x) (+ t (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-29) {
		tmp = t + ((x * y) / z);
	} else if (z <= 3.95e+30) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e-29)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (z <= 3.95e+30)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = Float64(t + Float64(x * Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e-29], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.95e+30], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999993e-29

   1. Initial program 49.1%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 56.3%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 57.8

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

   7. Applied rewrites 57.8%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 53.6

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

   10. Applied rewrites 53.6%

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

   if -2.49999999999999993e-29 < z < 3.94999999999999981e30

   1. Initial program 89.8%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 77.8

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

   4. Applied rewrites 77.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 74.5%

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

   if 3.94999999999999981e30 < z

   1. Initial program 41.4%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 58.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 58.2

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

   7. Applied rewrites 58.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 59.4

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

   10. Applied rewrites 59.4%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 60.3

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

   13. Applied rewrites 60.3%

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

Alternative 10: 64.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-29}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e-29)
   (+ t (/ (* x y) z))
   (if (<= z 3.95e+30) (fma y (/ (- t x) a) x) (+ t (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-29) {
		tmp = t + ((x * y) / z);
	} else if (z <= 3.95e+30) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e-29)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (z <= 3.95e+30)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = Float64(t + Float64(x * Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e-29], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.95e+30], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999993e-29

   1. Initial program 49.1%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 56.3%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 57.8

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

   7. Applied rewrites 57.8%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 53.6

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

   10. Applied rewrites 53.6%

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

   if -2.49999999999999993e-29 < z < 3.94999999999999981e30

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 72.8

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

   4. Applied rewrites 72.8%

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

   if 3.94999999999999981e30 < z

   1. Initial program 41.4%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 58.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 58.2

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

   7. Applied rewrites 58.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 59.4

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

   10. Applied rewrites 59.4%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 60.3

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

   13. Applied rewrites 60.3%

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

Alternative 11: 56.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-50}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e-50)
   (+ t (/ (* x y) z))
   (if (<= z 3.05e+26) (+ x (/ (* t y) a)) (+ t (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-50) {
		tmp = t + ((x * y) / z);
	} else if (z <= 3.05e+26) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d-50)) then
        tmp = t + ((x * y) / z)
    else if (z <= 3.05d+26) then
        tmp = x + ((t * y) / a)
    else
        tmp = t + (x * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-50) {
		tmp = t + ((x * y) / z);
	} else if (z <= 3.05e+26) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e-50:
		tmp = t + ((x * y) / z)
	elif z <= 3.05e+26:
		tmp = x + ((t * y) / a)
	else:
		tmp = t + (x * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e-50)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	elseif (z <= 3.05e+26)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(t + Float64(x * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e-50)
		tmp = t + ((x * y) / z);
	elseif (z <= 3.05e+26)
		tmp = x + ((t * y) / a);
	else
		tmp = t + (x * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e-50], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.05e+26], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999984e-50

   1. Initial program 51.6%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 55.4%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 57.2

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 52.5

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

   10. Applied rewrites 52.5%

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

   if -2.49999999999999984e-50 < z < 3.0500000000000001e26

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 70.4

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

   4. Applied rewrites 70.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 57.9%

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

   if 3.0500000000000001e26 < z

   1. Initial program 41.8%

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

   2. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   4. Applied rewrites 58.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 58.1

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

   7. Applied rewrites 58.1%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 59.4

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

   10. Applied rewrites 59.4%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 60.2

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

   13. Applied rewrites 60.2%

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

Alternative 12: 45.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a} \cdot y\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+98}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- t x) a) y)))
   (if (<= y -1.1e+111) t_1 (if (<= y 5.1e+98) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) / a) * y;
	double tmp;
	if (y <= -1.1e+111) {
		tmp = t_1;
	} else if (y <= 5.1e+98) {
		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 - x) / a) * y
    if (y <= (-1.1d+111)) then
        tmp = t_1
    else if (y <= 5.1d+98) 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 - x) / a) * y;
	double tmp;
	if (y <= -1.1e+111) {
		tmp = t_1;
	} else if (y <= 5.1e+98) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((t - x) / a) * y
	tmp = 0
	if y <= -1.1e+111:
		tmp = t_1
	elif y <= 5.1e+98:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t - x) / a) * y)
	tmp = 0.0
	if (y <= -1.1e+111)
		tmp = t_1;
	elseif (y <= 5.1e+98)
		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 - x) / a) * y;
	tmp = 0.0;
	if (y <= -1.1e+111)
		tmp = t_1;
	elseif (y <= 5.1e+98)
		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[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.1e+111], t$95$1, If[LessEqual[y, 5.1e+98], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.09999999999999999e111 or 5.09999999999999988e98 < y

   1. Initial program 69.5%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 57.0

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

   4. Applied rewrites 57.0%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 48.6

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

   7. Applied rewrites 48.6%

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

   if -1.09999999999999999e111 < y < 5.09999999999999988e98

   1. Initial program 67.1%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 24.0

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

   4. Applied rewrites 24.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 43.4%

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

Alternative 13: 37.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e+87) x (if (<= a 1.8e-12) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e+87) {
		tmp = x;
	} else if (a <= 1.8e-12) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.25d+87)) then
        tmp = x
    else if (a <= 1.8d-12) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e+87) {
		tmp = x;
	} else if (a <= 1.8e-12) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.25e+87:
		tmp = x
	elif a <= 1.8e-12:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.25e+87)
		tmp = x;
	elseif (a <= 1.8e-12)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.25e+87)
		tmp = x;
	elseif (a <= 1.8e-12)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e+87], x, If[LessEqual[a, 1.8e-12], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.24999999999999995e87 or 1.8e-12 < a

   1. Initial program 68.4%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 43.8%

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

   if -1.24999999999999995e87 < a < 1.8e-12

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 32.9%

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

Alternative 14: 25.0% accurate, 29.0× 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 68.0%

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

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

Developer Target 1: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025106 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))