Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

analyze19.0ms (1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.3s (68.8%)

Results

1.2s	8256×	body	256	valid
22.0ms	370×	body	256	invalid

Bogosity

preprocess81.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

308×	`fma-def`
60×	`fma-neg`
48×	`sub-neg`
32×	`distribute-lft-neg-in`
32×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	56
1	37	56
2	70	56
3	144	56
4	242	56
5	329	56
6	422	56
7	476	56
8	490	56
9	493	56

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (+.f64 (*.f64 (neg.f64 x) (neg.f64 x)) y))
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 y)))
(sqrt.f64 (+.f64 (*.f64 y y) x))

Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (fma.f64 x x y))
(sqrt.f64 (+.f64 (*.f64 (neg.f64 x) (neg.f64 x)) y))
(sqrt.f64 (fma.f64 x x y))
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 y)))
(sqrt.f64 (fma.f64 x x (neg.f64 y)))
(sqrt.f64 (-.f64 (*.f64 x x) y))
(sqrt.f64 (+.f64 (*.f64 y y) x))
(sqrt.f64 (fma.f64 y y x))

Symmetry

(abs x)

Compiler

Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	11	13

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))

Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (fma.f64 x x y))

eval0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Accurracy

69.5%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize25.0ms (1.4%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 19 to 6 computations (68.4% saved)

series3.0ms (0.1%)

Counts

1 → 16

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	x	@	0	(sqrt.f64 (+.f64 (*.f64 x x) y))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 (*.f64 x x) y))
0.0ms	y	@	-inf	(sqrt.f64 (+.f64 (*.f64 x x) y))
0.0ms	y	@	0	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite60.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1692×	`pow1`
1568×	`add-exp-log`
1568×	`log1p-expm1-u`
1568×	`expm1-log1p-u`
1534×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	169	11
2	2210	11

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))

Outputs
(-.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 y))) 1)
(*.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(*.f64 1 (hypot.f64 x (sqrt.f64 y)))
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(*.f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (sqrt.f64 (-.f64 (.f64 x x) y)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(pow.f64 (fma.f64 x x y) 1/2)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)
(pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
(fabs.f64 (hypot.f64 x (sqrt.f64 y)))
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))

simplify73.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1528×	`times-frac`
1390×	`fma-neg`
1162×	`associate-/l*`
740×	`associate-/r*`
678×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	1280
1	270	1160
2	702	1056
3	2399	1020
4	7661	1020

Stop Event

1×	node limit

Counts

40 → 68

Calls

Call 1

Inputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y)))
(+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6))) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(*.f64 -1 x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(-.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 y))) 1)
(*.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(*.f64 1 (hypot.f64 x (sqrt.f64 y)))
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(*.f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (sqrt.f64 (-.f64 (.f64 x x) y)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(pow.f64 (fma.f64 x x y) 1/2)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)
(pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
(fabs.f64 (hypot.f64 x (sqrt.f64 y)))
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))
(hypot.f64 x (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) x)
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))

Outputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))
(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (sqrt.f64 y))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y)))
(fma.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x)) (sqrt.f64 y)))
(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 -1/8 (pow.f64 x 4)) (sqrt.f64 y)))
(+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6))) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))))
(fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6)) (fma.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (sqrt.f64 y))))
(fma.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(fma.f64 1/2 (/.f64 y x) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 y x) (neg.f64 x))
(-.f64 (*.f64 (/.f64 y x) -1/2) x)
(neg.f64 (fma.f64 1/2 (/.f64 y x) x))
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (fma.f64 -1 x (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) 1/8)))
(fma.f64 (/.f64 y x) -1/2 (-.f64 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8) x))
(-.f64 (fma.f64 (/.f64 y x) -1/2 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8)) x)
(-.f64 (.f64 (/.f64 y x) (+.f64 -1/2 (.f64 (/.f64 y x) (/.f64 1/8 x)))) x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 y x) (fma.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1 x (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) 1/8))))
(fma.f64 (/.f64 y x) -1/2 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (-.f64 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8) x)))
(fma.f64 (/.f64 y x) -1/2 (-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8 (/.f64 (*.f64 (pow.f64 y 3) -1/16) (pow.f64 x 5))) x))
(fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (-.f64 (.f64 (/.f64 y x) (+.f64 -1/2 (.f64 (/.f64 y x) (/.f64 1/8 x)))) x))
(fma.f64 (/.f64 y x) (+.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 1/8 x))) (-.f64 (/.f64 (pow.f64 y 3) (/.f64 (pow.f64 x 5) -1/16)) x))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(fma.f64 1/2 (/.f64 y x) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(-.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 y))) 1)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 1 (hypot.f64 x (sqrt.f64 y)))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 y) x)) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))
(*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 y) x)) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(pow.f64 (cbrt.f64 (fma.f64 x x y)) 3/2)
(*.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
(pow.f64 (cbrt.f64 (fma.f64 x x y)) 3/2)
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (sqrt.f64 (-.f64 (.f64 x x) y)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 y 3) (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (hypot.f64 (pow.f64 x 3) (pow.f64 y 3/2)) (sqrt.f64 (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4))))
(/.f64 (hypot.f64 (pow.f64 x 3) (pow.f64 y 3/2)) (sqrt.f64 (fma.f64 y (fma.f64 x (neg.f64 x) y) (pow.f64 x 4))))
(pow.f64 (fma.f64 x x y) 1/2)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(fabs.f64 (hypot.f64 x (sqrt.f64 y)))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(hypot.f64 x (sqrt.f64 y))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(hypot.f64 (sqrt.f64 y) x)
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))
(+.f64 1 (-.f64 (hypot.f64 x (sqrt.f64 y)) 1))
(+.f64 (hypot.f64 x (sqrt.f64 y)) 0)
(hypot.f64 (sqrt.f64 y) x)

eval17.0ms (0.9%)

Compiler: Compiled 950 to 526 computations (44.6% saved)

prune22.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	4	69

Accurracy

100.0%

Counts

69 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.3%	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	36.7%	(sqrt.f64 y)
	66.1%	x
▶	66.3%	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	36.7%	(sqrt.f64 y)
	66.1%	x

Compiler

Compiled 48 to 32 computations (33.3% saved)

localize38.0ms (2%)

Compiler: Compiled 24 to 11 computations (54.2% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	2	2
Done	1	1
Total	4	4

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.3%	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	36.7%	(sqrt.f64 y)
	66.1%	x
✓	66.3%	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	36.7%	(sqrt.f64 y)
	66.1%	x

Compiler

Compiled 48 to 32 computations (33.3% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.3%	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	36.7%	(sqrt.f64 y)
	66.1%	x
✓	66.3%	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	36.7%	(sqrt.f64 y)
	66.1%	x

Compiler

Compiled 48 to 32 computations (33.3% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune20.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.3%	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	36.7%	(sqrt.f64 y)
	66.1%	x

Compiler

Compiled 42 to 26 computations (38.1% saved)

regimes42.0ms (2.3%)

Counts

4 → 2

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(sqrt.f64 y)
(sqrt.f64 (+.f64 (*.f64 x x) y))

Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
x

Calls

5 calls:

14.0ms	y
8.0ms	x
7.0ms	(+.f64 (*.f64 x x) y)
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
5.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
86.1%	4	`y`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 44 to 26 computations (40.9% saved)

regimes26.0ms (1.4%)

Counts

3 → 4

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(sqrt.f64 y)

Outputs
(sqrt.f64 y)
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(sqrt.f64 y)
(+.f64 (*.f64 1/2 (/.f64 y x)) x)

Calls

1 calls:

25.0ms

Results

Accuracy	Segments	Branch
88.8%	4	`x`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes7.0ms (0.4%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)

Outputs
(+.f64 (*.f64 1/2 (/.f64 y x)) x)

Calls

2 calls:

3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
66.3%	1	`y`
66.3%	1	`x`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes6.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

2 calls:

3.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
66.1%	1	`y`
66.1%	1	`x`

Compiler

Compiled 9 to 6 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.627748983500114e+242	2.130883025176852e+249

Compiler

Compiled 13 to 9 computations (30.8% saved)

bsearch54.0ms (2.9%)

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	5.17611850576376e-24	1.0995754703497294e-23
30.0ms	2.6144159990173133e-36	1.787979612559998e-32
14.0ms	1.076554812205187e-53	1.04079152815416e-50

Results

46.0ms	336×	body	256	valid
3.0ms	51×	body	256	invalid

Compiler

Compiled 328 to 240 computations (26.8% saved)

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

4×	`not-or`
4×	`+-commutative`
4×	`if-if-or-not`
2×	`not-not`
2×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	116
1	36	116
2	39	116
3	42	114
4	43	114
5	44	114

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) 500000000000000037325287824915847887316397650059807796581517200060057728567899618146074726653749664037239515660064971095733796417287170413167982256753295033075394319374559417709018509763611443472490620259742323283073361279494542304167694696448) (sqrt.f64 (+.f64 (.f64 x x) y)) x)
(if (<=.f64 x 8424983333484575/842498333348457493583344221469363458551160763204392890034487820288) (sqrt.f64 y) (if (<=.f64 x 3507603929594167/23384026197294446691258957323460528314494920687616) (+.f64 (.f64 1/2 (/.f64 y x)) x) (if (<=.f64 x 552958846246525/85070591730234615865843651857942052864) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x))))
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
x

Outputs
(if (<=.f64 (.f64 x x) 500000000000000037325287824915847887316397650059807796581517200060057728567899618146074726653749664037239515660064971095733796417287170413167982256753295033075394319374559417709018509763611443472490620259742323283073361279494542304167694696448) (sqrt.f64 (+.f64 (.f64 x x) y)) x)
(if (<=.f64 x 8424983333484575/842498333348457493583344221469363458551160763204392890034487820288) (sqrt.f64 y) (if (<=.f64 x 3507603929594167/23384026197294446691258957323460528314494920687616) (+.f64 (.f64 1/2 (/.f64 y x)) x) (if (<=.f64 x 552958846246525/85070591730234615865843651857942052864) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x))))
(if (<=.f64 x 8424983333484575/842498333348457493583344221469363458551160763204392890034487820288) (sqrt.f64 y) (if (or (<=.f64 x 3507603929594167/23384026197294446691258957323460528314494920687616) (not (<=.f64 x 552958846246525/85070591730234615865843651857942052864))) (+.f64 x (*.f64 1/2 (/.f64 y x))) (sqrt.f64 y)))
(if (or (<=.f64 x 8424983333484575/842498333348457493583344221469363458551160763204392890034487820288) (and (not (<=.f64 x 3507603929594167/23384026197294446691258957323460528314494920687616)) (<=.f64 x 552958846246525/85070591730234615865843651857942052864))) (sqrt.f64 y) (+.f64 x (*.f64 1/2 (/.f64 y x))))
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 x (*.f64 1/2 (/.f64 y x)))
x

Compiler

Compiled 51 to 33 computations (35.3% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess61.0ms (3.3%)

Compiler: Compiled 198 to 116 computations (41.4% saved)

analyze19.0ms (1%)

sample1.3s (68.8%)

preprocess81.0ms (4.4%)

simplify3.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize25.0ms (1.4%)

series3.0ms (0.1%)

rewrite60.0ms (3.3%)

simplify73.0ms (4%)

eval17.0ms (0.9%)

prune22.0ms (1.2%)

localize38.0ms (2%)

eval0.0ms (0%)

prune3.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune20.0ms (1.1%)

regimes42.0ms (2.3%)

regimes26.0ms (1.4%)

regimes7.0ms (0.4%)

regimes6.0ms (0.3%)

bsearch0.0ms (0%)

bsearch54.0ms (2.9%)

simplify9.0ms (0.5%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess61.0ms (3.3%)

Profiling