Details

analyze84.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	56.2%	18.8%	6
37.5%	40.6%	22%	7
46.8%	31.2%	22%	8
54.6%	21.9%	23.5%	9
60.1%	16.4%	23.5%	10
64.4%	11.3%	24.3%	11
67.3%	8.4%	24.3%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample780.0ms (37.6%)

Results

757.0ms	8256×	body	256	valid
9.0ms	92×	body	256	invalid

preprocess18.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

8×	`fma-def_binary64`
4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`associate-+r+_binary64`
2×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	26	16
3	30	16
4	32	16
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`associate-+r+_binary64`
1×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	11	8
2	15	8
3	17	8
4	18	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 15 to 7 computations (53.3% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
▶	0.0b	(+.f64 y (fma.f64 x x y))

Compiler

Compiled 17 to 9 computations (47.1% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (fma.f64 x x y))

Compiler

Compiled 14 to 4 computations (71.4% saved)

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite53.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`pow1_binary64`
577×	`add-log-exp_binary64`
577×	`log1p-expm1-u_binary64`
577×	`expm1-log1p-u_binary64`
564×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	109	8
2	1535	8

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

Inputs
(+.f64 y (fma.f64 x x y))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 y (fma.f64 x x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 y y) (-.f64 y (fma.f64 x x y))) (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2) (cbrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) (sqrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (fma.f64 y y (.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (/.f64 1 (-.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 y y (.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y))) (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 y (fma.f64 x x y)) (-.f64 (.f64 y y) (pow.f64 (fma.f64 x x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y y (.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (.f64 y y) (.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))) (neg.f64 (fma.f64 y y (.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 y y) (pow.f64 (fma.f64 x x y) 2))) (neg.f64 (-.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x x y) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 y (fma.f64 x x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 y y) (-.f64 y (fma.f64 x x y))) (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2) (cbrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) (sqrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (fma.f64 y y (*.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (/.f64 1 (-.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 y y (*.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y))) (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 y (fma.f64 x x y)) (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y y (*.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (*.f64 y y) (*.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))) (neg.f64 (fma.f64 y y (*.f64 (fma.f64 x x y) (-.f64 (fma.f64 x x y) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2))) (neg.f64 (-.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x x y) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)))))

simplify166.0ms (8%)

Algorithm

1×	egg-herbie

Rules

1366×	`sqr-pow_binary64`
695×	`pow-sqr_binary64`
617×	`cube-prod_binary64`
611×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	168
1	15	168
2	25	168
3	36	168
4	65	168
5	167	168
6	587	168
7	1453	168
8	1637	168
9	1821	168
10	2029	168
11	2324	168
12	2717	168
13	3202	168
14	3768	168
15	4456	168
16	5297	168
17	5691	168
18	5979	168
19	6255	168
20	6329	168
21	6363	168
22	7304	168

Stop Event

1×	node limit

Counts

57 → 38

Calls

Call 1

Inputs
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))

Outputs
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 x x (*.f64 2 y))

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	0.0b	(+.f64 (*.f64 x x) y)

Compiler

Compiled 19 to 5 computations (73.7% saved)

series4.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

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

rewrite67.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

850×	`pow1_binary64`
796×	`add-log-exp_binary64`
796×	`log1p-expm1-u_binary64`
796×	`expm1-log1p-u_binary64`
778×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	141	13
2	2161	13

Stop Event

1×	node limit

Counts

2 → 71

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x 4) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 y (fma.f64 x x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (fma.f64 x x y) y)) (/.f64 (.f64 y y) (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2) (cbrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) (sqrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y)) (/.f64 1 (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y)))) (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 x x y) y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y)) (-.f64 (fma.f64 x x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 y y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (.f64 x x) (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (.f64 x x) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x x y) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (-.f64 (*.f64 x x) y)) (/.f64 (*.f64 y y) (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (/.f64 1 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 x x) y) (-.f64 (pow.f64 x 4) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (*.f64 y y) (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (-.f64 (*.f64 x x) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (neg.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 y y) (pow.f64 x 4)) (-.f64 y (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 y (fma.f64 x x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (fma.f64 x x y) y)) (/.f64 (*.f64 y y) (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2) (cbrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) (sqrt.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (/.f64 1 (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))) (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 x x y) y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (*.f64 y y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 y y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (+.f64 y y) (+.f64 y y)) (*.f64 (*.f64 x x) (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (*.f64 x x) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 y (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 y (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x x y) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))))))

simplify180.0ms (8.7%)

Algorithm

1×	egg-herbie

Rules

1366×	`sqr-pow_binary64`
695×	`pow-sqr_binary64`
617×	`cube-prod_binary64`
604×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	309
1	17	273
2	29	273
3	40	273
4	72	273
5	170	273
6	607	273
7	1492	273
8	1696	273
9	1880	273
10	2088	273
11	2385	273
12	2780	273
13	3263	273
14	3829	273
15	4517	273
16	5352	273
17	5744	273
18	6030	273
19	6302	273
20	6372	273
21	6408	273
22	7349	273

Stop Event

1×	node limit

Counts

119 → 79

Calls

Call 1

Inputs
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))

Outputs
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(*.f64 2 y)
(*.f64 y 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(*.f64 2 y)
(*.f64 y 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(*.f64 2 y)
(*.f64 y 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 2 y (*.f64 x x))
(fma.f64 y 2 (*.f64 x x))

eval23.0ms (1.1%)

Compiler: Compiled 1500 to 495 computations (67% saved)

prune18.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	114	5	119

Error

Counts

119 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
▶	0b	(fma.f64 y 2 (*.f64 x x))
▶	33.5b	(+.f64 (*.f64 x x) y)
▶	23.5b	(+.f64 y y)
▶	39.6b	(*.f64 x x)

Compiler

Compiled 34 to 20 computations (41.2% saved)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (*.f64 x x) y)

Compiler

Compiled 12 to 4 computations (66.7% saved)

localize5.0ms (0.3%)

Compiler: Compiled 14 to 6 computations (57.1% saved)

eval7.0ms (0.3%)

Compiler: Compiled 371 to 155 computations (58.2% saved)

prune8.0ms (0.4%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	36	6	42

Error

Counts

42 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	0b	(fma.f64 y 2 (*.f64 x x))
	55.7b	y
✓	33.5b	(+.f64 (*.f64 x x) y)
✓	23.5b	(+.f64 y y)
✓	39.6b	(*.f64 x x)

Compiler

Compiled 37 to 22 computations (40.5% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	5	5
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	0b	(fma.f64 y 2 (*.f64 x x))
	55.7b	y
✓	33.5b	(+.f64 (*.f64 x x) y)
✓	23.5b	(+.f64 y y)
✓	39.6b	(*.f64 x x)

Compiler

Compiled 37 to 22 computations (40.5% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	5	5
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	0b	(fma.f64 y 2 (*.f64 x x))
	55.7b	y
✓	33.5b	(+.f64 (*.f64 x x) y)
✓	23.5b	(+.f64 y y)
✓	39.6b	(*.f64 x x)

Compiler

Compiled 37 to 22 computations (40.5% saved)

regimes22.0ms (1.1%)

Counts

7 → 1

Calls

Call 1

Inputs
y
(+.f64 y y)
(*.f64 x x)
(+.f64 (*.f64 x x) y)
(+.f64 (+.f64 (*.f64 x x) y) y)
(fma.f64 y 2 (*.f64 x x))
(+.f64 y (fma.f64 x x y))

Outputs
(fma.f64 y 2 (*.f64 x x))

Calls

4 calls:

6.0ms	y
5.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
5.0ms	x
5.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`y`
0b	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
0b	1	`(*.f64 x x)`

Compiler

Compiled 53 to 22 computations (58.5% saved)

regimes19.0ms (0.9%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
5.0ms	x
5.0ms	y
3.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
0.0b	1	`(*.f64 x x)`

Compiler

Compiled 41 to 18 computations (56.1% saved)

regimes45.0ms (2.2%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

3 calls:

21.0ms	y
14.0ms	x
8.0ms	(*.f64 x x)

Results

Error	Segments	Branch
11.0b	3	`x`
14.3b	5	`y`
11.2b	2	`(*.f64 x x)`

Compiler

Compiled 25 to 12 computations (52% saved)

bsearch32.0ms (1.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
15.0ms	2.2505131163667035e-30	4.9001476779569944e-29
17.0ms	-2076697641788539400.0	-1280429986531258600.0

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes119.0ms (5.7%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

3 calls:

95.0ms	x
16.0ms	y
7.0ms	(*.f64 x x)

Results

Error	Segments	Branch
11.8b	3	`x`
15.5b	5	`y`
12.5b	2	`(*.f64 x x)`

Compiler

Compiled 20 to 11 computations (45% saved)

bsearch127.0ms (6.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
16.0ms	2.2505131163667035e-30	4.9001476779569944e-29
111.0ms	-2076697641788539400.0	-1280429986531258600.0

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes9.0ms (0.4%)

Accuracy

Total -32.1b remaining (-136.5%)

Threshold costs -32.1b (-136.5%)

Counts

2 → 1

Calls

Call 1

Inputs
y
(+.f64 y y)

Outputs
(+.f64 y y)

Calls

2 calls:

5.0ms	y
3.0ms	x

Results

Error	Segments	Branch
23.5b	1	`x`
23.5b	1	`y`

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	77
1	20	77

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 y 2 (*.f64 x x))
(+.f64 (+.f64 (*.f64 x x) y) y)
(if (<=.f64 x -2076697641788539392) (+.f64 (.f64 x x) y) (if (<=.f64 x 3289128604404610048/1461501637330902918203684832716283019655932542976) (+.f64 y y) (+.f64 (.f64 x x) y)))
(if (<=.f64 x -2076697641788539392) (.f64 x x) (if (<=.f64 x 3289128604404610048/1461501637330902918203684832716283019655932542976) (+.f64 y y) (.f64 x x)))
(+.f64 y y)
y

Outputs
(fma.f64 y 2 (*.f64 x x))
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 y (+.f64 y (*.f64 x x)))
(if (<=.f64 x -2076697641788539392) (+.f64 (.f64 x x) y) (if (<=.f64 x 3289128604404610048/1461501637330902918203684832716283019655932542976) (+.f64 y y) (+.f64 (.f64 x x) y)))
(if (<=.f64 x -2076697641788539392) (+.f64 y (.f64 x x)) (if (<=.f64 x 3212039652738877/1427247692705959881058285969449495136382746624) (+.f64 y y) (+.f64 y (.f64 x x))))
(if (<=.f64 x -2076697641788539392) (.f64 x x) (if (<=.f64 x 3289128604404610048/1461501637330902918203684832716283019655932542976) (+.f64 y y) (.f64 x x)))
(if (<=.f64 x -2076697641788539392) (.f64 x x) (if (<=.f64 x 3212039652738877/1427247692705959881058285969449495136382746624) (+.f64 y y) (.f64 x x)))
(+.f64 y y)
y

Compiler

Compiled 67 to 36 computations (46.3% saved)

soundness203.0ms (9.8%)

Algorithm

1×	egg-herbie

Rules

1366×	`sqr-pow_binary64`
695×	`pow-sqr_binary64`
617×	`cube-prod_binary64`
604×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	309
1	17	273
2	29	273
3	40	273
4	72	273
5	170	273
6	607	273
7	1492	273
8	1696	273
9	1880	273
10	2088	273
11	2385	273
12	2780	273
13	3263	273
14	3829	273
15	4517	273
16	5352	273
17	5744	273
18	6030	273
19	6302	273
20	6372	273
21	6408	273
22	7349	273

Stop Event

1×	node limit

Compiler

Compiled 34 to 25 computations (26.5% saved)

end37.0ms (1.8%)

Compiler: Compiled 57 to 20 computations (64.9% saved)

Details

analyze84.0ms (4%)

sample780.0ms (37.6%)

preprocess18.0ms (0.9%)

simplify8.0ms (0.4%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series3.0ms (0.2%)

rewrite53.0ms (2.6%)

simplify166.0ms (8%)

localize6.0ms (0.3%)

series4.0ms (0.2%)

rewrite67.0ms (3.2%)

simplify180.0ms (8.7%)

eval23.0ms (1.1%)

prune18.0ms (0.8%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize5.0ms (0.3%)

localize5.0ms (0.3%)

eval7.0ms (0.3%)

prune8.0ms (0.4%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes22.0ms (1.1%)

regimes19.0ms (0.9%)

regimes45.0ms (2.2%)

bsearch32.0ms (1.5%)

regimes119.0ms (5.7%)

bsearch127.0ms (6.1%)

regimes9.0ms (0.4%)

simplify6.0ms (0.3%)

soundness203.0ms (9.8%)

end37.0ms (1.8%)

Profiling