Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Percentage Accurate: 98.1% → 96.9%

Time: 3.4s

Alternatives: 15

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Fortran

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) / (a - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	x + (y * ((z - t) / (a - t)))
END code

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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) / (a - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	x + (y * ((z - t) / (a - t)))
END code

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (fma (- t z) (/ y (- t a)) x))

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	((t - z) * (y / (t - a))) + x
END code

Derivation

1. Initial program 98.1%

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

3. Applied rewrites 95.8%

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

Alternative 2: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t\_1 \leq 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 1.02:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z - a}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))))
  (if (<= t_1 -50.0)
    (+ x (/ (* y z) (- a t)))
    (if (<= t_1 1e-7)
      (fma (- z t) (/ y a) x)
      (if (<= t_1 1.02)
        (fma y (- 1.0 (/ (- z a) t)) x)
        (fma y (/ z (- a t)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -50.0) {
		tmp = x + ((y * z) / (a - t));
	} else if (t_1 <= 1e-7) {
		tmp = fma((z - t), (y / a), x);
	} else if (t_1 <= 1.02) {
		tmp = fma(y, (1.0 - ((z - a) / t)), x);
	} else {
		tmp = fma(y, (z / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	elseif (t_1 <= 1e-7)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	elseif (t_1 <= 1.02)
		tmp = fma(y, Float64(1.0 - Float64(Float64(z - a) / t)), x);
	else
		tmp = fma(y, Float64(z / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-7], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1.02], N[(y * N[(1.0 - N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET tmp_2 = IF (t_1 <= (1020000000000000017763568394002504646778106689453125e-51)) THEN ((y * ((1) - ((z - a) / t))) + x) ELSE ((y * (z / (a - t))) + x) ENDIF IN
		LET tmp_1 = IF (t_1 <= (999999999999999954748111825886258685613938723690807819366455078125e-73)) THEN (((z - t) * (y / a)) + x) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-50)) THEN (x + ((y * z) / (a - t))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -50

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 73.9%

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

   if -50 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999995e-8

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.1%

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

   6. Applied rewrites 61.1%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.02

   1. Initial program 98.1%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 60.8%

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

   6. Applied rewrites 60.8%

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

   if 1.02 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.8%

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

   6. Applied rewrites 76.8%

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

Alternative 3: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 1.02:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))))
  (if (<= t_1 -50.0)
    (+ x (/ (* y z) (- a t)))
    (if (<= t_1 1e-9)
      (fma (- z t) (/ y a) x)
      (if (<= t_1 1.02)
        (fma y (- 1.0 (/ z t)) x)
        (fma y (/ z (- a t)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -50.0) {
		tmp = x + ((y * z) / (a - t));
	} else if (t_1 <= 1e-9) {
		tmp = fma((z - t), (y / a), x);
	} else if (t_1 <= 1.02) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else {
		tmp = fma(y, (z / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	elseif (t_1 <= 1e-9)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	elseif (t_1 <= 1.02)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	else
		tmp = fma(y, Float64(z / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-9], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1.02], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET tmp_2 = IF (t_1 <= (1020000000000000017763568394002504646778106689453125e-51)) THEN ((y * ((1) - (z / t))) + x) ELSE ((y * (z / (a - t))) + x) ENDIF IN
		LET tmp_1 = IF (t_1 <= (10000000000000000622815914577798564188970686927859787829220294952392578125e-82)) THEN (((z - t) * (y / a)) + x) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-50)) THEN (x + ((y * z) / (a - t))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -50

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 73.9%

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

   if -50 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e-9

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.1%

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

   6. Applied rewrites 61.1%

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

   if 1.0000000000000001e-9 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.02

   1. Initial program 98.1%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 60.8%

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

   6. Applied rewrites 60.8%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 67.0%

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

   if 1.02 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.8%

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

   6. Applied rewrites 76.8%

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

Alternative 4: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 1.02:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (fma y (/ z (- a t)) x)))
  (if (<= t_1 -50.0)
    t_2
    (if (<= t_1 1e-9)
      (fma (- z t) (/ y a) x)
      (if (<= t_1 1.02) (fma y (- 1.0 (/ z t)) x) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = fma(y, (z / (a - t)), x);
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_2;
	} else if (t_1 <= 1e-9) {
		tmp = fma((z - t), (y / a), x);
	} else if (t_1 <= 1.02) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = fma(y, Float64(z / Float64(a - t)), x)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_2;
	elseif (t_1 <= 1e-9)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	elseif (t_1 <= 1.02)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$2, If[LessEqual[t$95$1, 1e-9], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1.02], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$2]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET t_2 = ((y * (z / (a - t))) + x) IN
			LET tmp_2 = IF (t_1 <= (1020000000000000017763568394002504646778106689453125e-51)) THEN ((y * ((1) - (z / t))) + x) ELSE t_2 ENDIF IN
			LET tmp_1 = IF (t_1 <= (10000000000000000622815914577798564188970686927859787829220294952392578125e-82)) THEN (((z - t) * (y / a)) + x) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-50)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -50 or 1.02 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.8%

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

   6. Applied rewrites 76.8%

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

   if -50 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e-9

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.1%

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

   6. Applied rewrites 61.1%

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

   if 1.0000000000000001e-9 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.02

   1. Initial program 98.1%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 60.8%

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

   6. Applied rewrites 60.8%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 67.0%

      \[\leadsto \mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 1.02:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (fma y (/ z (- a t)) x)))
  (if (<= t_1 -50.0)
    t_2
    (if (<= t_1 1e-9)
      (fma y (/ (- z t) a) x)
      (if (<= t_1 1.02) (fma y (- 1.0 (/ z t)) x) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = fma(y, (z / (a - t)), x);
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_2;
	} else if (t_1 <= 1e-9) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 1.02) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = fma(y, Float64(z / Float64(a - t)), x)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_2;
	elseif (t_1 <= 1e-9)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 1.02)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$2, If[LessEqual[t$95$1, 1e-9], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1.02], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$2]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET t_2 = ((y * (z / (a - t))) + x) IN
			LET tmp_2 = IF (t_1 <= (1020000000000000017763568394002504646778106689453125e-51)) THEN ((y * ((1) - (z / t))) + x) ELSE t_2 ENDIF IN
			LET tmp_1 = IF (t_1 <= (10000000000000000622815914577798564188970686927859787829220294952392578125e-82)) THEN ((y * ((z - t) / a)) + x) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-50)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -50 or 1.02 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.8%

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

   6. Applied rewrites 76.8%

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

   if -50 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e-9

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.1%

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

   6. Applied rewrites 60.1%

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

   if 1.0000000000000001e-9 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.02

   1. Initial program 98.1%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 60.8%

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

   6. Applied rewrites 60.8%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 67.0%

      \[\leadsto \mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 1.02:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (fma y (/ z (- a t)) x)))
  (if (<= t_1 -50.0)
    t_2
    (if (<= t_1 1e-9)
      (fma y (/ (- z t) a) x)
      (if (<= t_1 1.02) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = fma(y, (z / (a - t)), x);
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_2;
	} else if (t_1 <= 1e-9) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 1.02) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = fma(y, Float64(z / Float64(a - t)), x)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_2;
	elseif (t_1 <= 1e-9)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 1.02)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$2, If[LessEqual[t$95$1, 1e-9], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1.02], N[(x + y), $MachinePrecision], t$95$2]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET t_2 = ((y * (z / (a - t))) + x) IN
			LET tmp_2 = IF (t_1 <= (1020000000000000017763568394002504646778106689453125e-51)) THEN (x + y) ELSE t_2 ENDIF IN
			LET tmp_1 = IF (t_1 <= (10000000000000000622815914577798564188970686927859787829220294952392578125e-82)) THEN ((y * ((z - t) / a)) + x) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-50)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -50 or 1.02 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.8%

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

   6. Applied rewrites 76.8%

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

   if -50 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e-9

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.1%

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

   6. Applied rewrites 60.1%

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

   if 1.0000000000000001e-9 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.02

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

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

Alternative 7: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \mathsf{fma}\left(y, \frac{z}{a - t}, x\right)\\ \mathbf{if}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 1.02:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (fma y (/ z (- a t)) x)))
  (if (<= t_1 1e-9) t_2 (if (<= t_1 1.02) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = fma(y, (z / (a - t)), x);
	double tmp;
	if (t_1 <= 1e-9) {
		tmp = t_2;
	} else if (t_1 <= 1.02) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = fma(y, Float64(z / Float64(a - t)), x)
	tmp = 0.0
	if (t_1 <= 1e-9)
		tmp = t_2;
	elseif (t_1 <= 1.02)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-9], t$95$2, If[LessEqual[t$95$1, 1.02], N[(x + y), $MachinePrecision], t$95$2]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET t_2 = ((y * (z / (a - t))) + x) IN
			LET tmp_1 = IF (t_1 <= (1020000000000000017763568394002504646778106689453125e-51)) THEN (x + y) ELSE t_2 ENDIF IN
			LET tmp = IF (t_1 <= (10000000000000000622815914577798564188970686927859787829220294952392578125e-82)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e-9 or 1.02 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.8%

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

   6. Applied rewrites 76.8%

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

   if 1.0000000000000001e-9 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.02

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

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

Alternative 8: 84.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+104}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 5000000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))))
  (if (<= t_1 -1e+104)
    (* z (/ y (- a t)))
    (if (<= t_1 1e-9)
      (+ x (* z (/ y a)))
      (if (<= t_1 5000000000000.0) (+ x y) (* (/ z (- a t)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -1e+104) {
		tmp = z * (y / (a - t));
	} else if (t_1 <= 1e-9) {
		tmp = x + (z * (y / a));
	} else if (t_1 <= 5000000000000.0) {
		tmp = x + y;
	} else {
		tmp = (z / (a - t)) * y;
	}
	return tmp;
}

Fortran

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 = (z - t) / (a - t)
    if (t_1 <= (-1d+104)) then
        tmp = z * (y / (a - t))
    else if (t_1 <= 1d-9) then
        tmp = x + (z * (y / a))
    else if (t_1 <= 5000000000000.0d0) then
        tmp = x + y
    else
        tmp = (z / (a - t)) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -1e+104) {
		tmp = z * (y / (a - t));
	} else if (t_1 <= 1e-9) {
		tmp = x + (z * (y / a));
	} else if (t_1 <= 5000000000000.0) {
		tmp = x + y;
	} else {
		tmp = (z / (a - t)) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -1e+104:
		tmp = z * (y / (a - t))
	elif t_1 <= 1e-9:
		tmp = x + (z * (y / a))
	elif t_1 <= 5000000000000.0:
		tmp = x + y
	else:
		tmp = (z / (a - t)) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -1e+104)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t_1 <= 1e-9)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t_1 <= 5000000000000.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z / Float64(a - t)) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -1e+104)
		tmp = z * (y / (a - t));
	elseif (t_1 <= 1e-9)
		tmp = x + (z * (y / a));
	elseif (t_1 <= 5000000000000.0)
		tmp = x + y;
	else
		tmp = (z / (a - t)) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+104], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-9], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5000000000000.0], N[(x + y), $MachinePrecision], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET tmp_2 = IF (t_1 <= (5e12)) THEN (x + y) ELSE ((z / (a - t)) * y) ENDIF IN
		LET tmp_1 = IF (t_1 <= (10000000000000000622815914577798564188970686927859787829220294952392578125e-82)) THEN (x + (z * (y / a))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-100000000000000000191567508573466873621595512726519201115280351459937932420398875596123614510818032353280)) THEN (z * (y / (a - t))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -1e104

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 62.0%

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

   6. Applied rewrites 62.0%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 26.2%

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

   11. Applied rewrites 28.3%

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

   if -1e104 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e-9

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.5%

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

   6. Applied rewrites 62.1%

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

   if 1.0000000000000001e-9 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5e12

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

      \[\leadsto x + y \]

   if 5e12 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 62.0%

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

   6. Applied rewrites 62.0%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 26.2%

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

   11. Applied rewrites 28.3%

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

Alternative 9: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+104}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 5000000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))))
  (if (<= t_1 -1e+104)
    (* z (/ y (- a t)))
    (if (<= t_1 1e-9)
      (fma y (/ z a) x)
      (if (<= t_1 5000000000000.0) (+ x y) (* (/ z (- a t)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -1e+104) {
		tmp = z * (y / (a - t));
	} else if (t_1 <= 1e-9) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 5000000000000.0) {
		tmp = x + y;
	} else {
		tmp = (z / (a - t)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -1e+104)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t_1 <= 1e-9)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 5000000000000.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z / Float64(a - t)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+104], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-9], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5000000000000.0], N[(x + y), $MachinePrecision], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET tmp_2 = IF (t_1 <= (5e12)) THEN (x + y) ELSE ((z / (a - t)) * y) ENDIF IN
		LET tmp_1 = IF (t_1 <= (10000000000000000622815914577798564188970686927859787829220294952392578125e-82)) THEN ((y * (z / a)) + x) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-100000000000000000191567508573466873621595512726519201115280351459937932420398875596123614510818032353280)) THEN (z * (y / (a - t))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -1e104

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 62.0%

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

   6. Applied rewrites 62.0%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 26.2%

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

   11. Applied rewrites 28.3%

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

   if -1e104 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e-9

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 62.0%

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

   6. Applied rewrites 62.0%

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

   if 1.0000000000000001e-9 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5e12

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

      \[\leadsto x + y \]

   if 5e12 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 62.0%

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

   6. Applied rewrites 62.0%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 26.2%

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

   11. Applied rewrites 28.3%

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

Alternative 10: 83.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 5000000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* z (/ y (- a t)))))
  (if (<= t_1 -1e+104)
    t_2
    (if (<= t_1 1e-9)
      (fma y (/ z a) x)
      (if (<= t_1 5000000000000.0) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = z * (y / (a - t));
	double tmp;
	if (t_1 <= -1e+104) {
		tmp = t_2;
	} else if (t_1 <= 1e-9) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 5000000000000.0) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e+104)
		tmp = t_2;
	elseif (t_1 <= 1e-9)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 5000000000000.0)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+104], t$95$2, If[LessEqual[t$95$1, 1e-9], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5000000000000.0], N[(x + y), $MachinePrecision], t$95$2]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET t_2 = (z * (y / (a - t))) IN
			LET tmp_2 = IF (t_1 <= (5e12)) THEN (x + y) ELSE t_2 ENDIF IN
			LET tmp_1 = IF (t_1 <= (10000000000000000622815914577798564188970686927859787829220294952392578125e-82)) THEN ((y * (z / a)) + x) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-100000000000000000191567508573466873621595512726519201115280351459937932420398875596123614510818032353280)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -1e104 or 5e12 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 62.0%

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

   6. Applied rewrites 62.0%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 26.2%

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

   11. Applied rewrites 28.3%

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

   if -1e104 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e-9

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 62.0%

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

   6. Applied rewrites 62.0%

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

   if 1.0000000000000001e-9 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5e12

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

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

Alternative 11: 81.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{if}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 1.02:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (fma y (/ z a) x)))
  (if (<= t_1 1e-9) t_2 (if (<= t_1 1.02) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = fma(y, (z / a), x);
	double tmp;
	if (t_1 <= 1e-9) {
		tmp = t_2;
	} else if (t_1 <= 1.02) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = fma(y, Float64(z / a), x)
	tmp = 0.0
	if (t_1 <= 1e-9)
		tmp = t_2;
	elseif (t_1 <= 1.02)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-9], t$95$2, If[LessEqual[t$95$1, 1.02], N[(x + y), $MachinePrecision], t$95$2]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET t_2 = ((y * (z / a)) + x) IN
			LET tmp_1 = IF (t_1 <= (1020000000000000017763568394002504646778106689453125e-51)) THEN (x + y) ELSE t_2 ENDIF IN
			LET tmp = IF (t_1 <= (10000000000000000622815914577798564188970686927859787829220294952392578125e-82)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e-9 or 1.02 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 62.0%

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

   6. Applied rewrites 62.0%

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

   if 1.0000000000000001e-9 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.02

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

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

Alternative 12: 72.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{y \cdot z}{a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-42}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+107}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (/ (* y z) a)))
  (if (<= t_1 -1e+103)
    t_2
    (if (<= t_1 2e-42) (* x 1.0) (if (<= t_1 5e+107) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (y * z) / a;
	double tmp;
	if (t_1 <= -1e+103) {
		tmp = t_2;
	} else if (t_1 <= 2e-42) {
		tmp = x * 1.0;
	} else if (t_1 <= 5e+107) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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) :: t_2
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    t_2 = (y * z) / a
    if (t_1 <= (-1d+103)) then
        tmp = t_2
    else if (t_1 <= 2d-42) then
        tmp = x * 1.0d0
    else if (t_1 <= 5d+107) then
        tmp = x + y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (y * z) / a;
	double tmp;
	if (t_1 <= -1e+103) {
		tmp = t_2;
	} else if (t_1 <= 2e-42) {
		tmp = x * 1.0;
	} else if (t_1 <= 5e+107) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = (y * z) / a
	tmp = 0
	if t_1 <= -1e+103:
		tmp = t_2
	elif t_1 <= 2e-42:
		tmp = x * 1.0
	elif t_1 <= 5e+107:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(y * z) / a)
	tmp = 0.0
	if (t_1 <= -1e+103)
		tmp = t_2;
	elseif (t_1 <= 2e-42)
		tmp = Float64(x * 1.0);
	elseif (t_1 <= 5e+107)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = (y * z) / a;
	tmp = 0.0;
	if (t_1 <= -1e+103)
		tmp = t_2;
	elseif (t_1 <= 2e-42)
		tmp = x * 1.0;
	elseif (t_1 <= 5e+107)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+103], t$95$2, If[LessEqual[t$95$1, 2e-42], N[(x * 1.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+107], N[(x + y), $MachinePrecision], t$95$2]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (a - t)) IN
		LET t_2 = ((y * z) / a) IN
			LET tmp_2 = IF (t_1 <= (500000000000000016999495856501412297471987359856449023856715357418937635861600416646370808190366722960654336)) THEN (x + y) ELSE t_2 ENDIF IN
			LET tmp_1 = IF (t_1 <= (200000000000000007524625871377379968058902433453275290835288395066001500595069327282634990631972526265675645269770388523511428502388298511505126953125e-191)) THEN (x * (1)) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-10000000000000000019156750857346687362159551272651920111528035145993793242039887559612361451081803235328)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -1e103 or 5.0000000000000002e107 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 62.0%

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

   6. Applied rewrites 62.0%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 26.2%

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

   10. Taylor expanded in t around 0

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

   12. Applied rewrites 18.4%

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

   if -1e103 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.0000000000000001e-42

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot 1 \]
   6. Step-by-step derivation

   7. Applied rewrites 51.3%

      \[\leadsto x \cdot 1 \]

   if 2.0000000000000001e-42 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5.0000000000000002e107

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

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

Alternative 13: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 1.7911263122038114 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= (/ (- z t) (- a t)) 1.7911263122038114e-38) (* x 1.0) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) / (a - t)) <= 1.7911263122038114e-38) {
		tmp = x * 1.0;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

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 - t) / (a - t)) <= 1.7911263122038114d-38) then
        tmp = x * 1.0d0
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) / (a - t)) <= 1.7911263122038114e-38) {
		tmp = x * 1.0;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) / (a - t)) <= 1.7911263122038114e-38:
		tmp = x * 1.0
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z - t) / Float64(a - t)) <= 1.7911263122038114e-38)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) / (a - t)) <= 1.7911263122038114e-38)
		tmp = x * 1.0;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], 1.7911263122038114e-38], N[(x * 1.0), $MachinePrecision], N[(x + y), $MachinePrecision]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp = IF (((z - t) / (a - t)) <= (17911263122038113614022299391481853749243922013103198506950602435491052738411005562298008890597810112421672812388351303525269031524658203125e-177)) THEN (x * (1)) ELSE (x + y) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.7911263122038114e-38

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot 1 \]
   6. Step-by-step derivation

   7. Applied rewrites 51.3%

      \[\leadsto x \cdot 1 \]

   if 1.7911263122038114e-38 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

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

Alternative 14: 61.3% accurate, 4.3× speedup

Math

\[x + y \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (+ x y))

C

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

Fortran

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	x + y
END code

Derivation

1. Initial program 98.1%

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

2. Taylor expanded in t around inf

   \[\leadsto x + y \]
3. Step-by-step derivation

4. Applied rewrites 61.3%

   \[\leadsto x + y \]
5. Add Preprocessing

Alternative 15: 18.7% accurate, 15.6× speedup

Math

\[y \]

FPCore

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

C

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

Fortran

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 = y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	y
END code

Derivation

1. Initial program 98.1%

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

2. Taylor expanded in t around inf

   \[\leadsto x + y \]
3. Step-by-step derivation

4. Applied rewrites 61.3%

   \[\leadsto x + y \]

5. Taylor expanded in x around 0

   \[\leadsto y \]
6. Step-by-step derivation

7. Applied rewrites 18.7%

   \[\leadsto y \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64
  (+ x (* y (/ (- z t) (- a t)))))