Details

analyze85.0ms (4.6%)

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%	62.4%	12.6%	6
25%	43.7%	31.3%	7
31.2%	31.2%	37.6%	8
39%	23.4%	37.6%	9
42.9%	16.4%	40.7%	10
47.2%	12.1%	40.7%	11
49.4%	8.4%	42.2%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.0s (56.7%)

Results

995.0ms	8248×	body	64	valid
24.0ms	240×	body	64	invalid
1.0ms	8×	body	128	valid

preprocess18.0ms (1%)

Algorithm

2×	egg-herbie

Rules

26×	`fma-def_binary64`
10×	`+-commutative_binary64`
6×	`associate-+r+_binary64`
6×	`associate-+l+_binary64`
4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	28	22
2	62	22
3	76	22
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 2) (.f64 x x)) (*.f64 y y))
(+.f64 (+.f64 (.f64 y 2) (.f64 y y)) (*.f64 x x))

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

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
6×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	11
2	34	11
3	42	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune3.0ms (0.2%)

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

Status	Error	Program
▶	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))
	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

Compiler

Compiled 67 to 39 computations (41.8% saved)

localize7.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(fma.f64 x (+.f64 x 2) (*.f64 y y))
1.0ms	x	@	-inf	(fma.f64 x (+.f64 x 2) (*.f64 y y))
1.0ms	y	@	0	(fma.f64 x (+.f64 x 2) (*.f64 y y))
1.0ms	x	@	inf	(fma.f64 x (+.f64 x 2) (*.f64 y y))
0.0ms	y	@	inf	(fma.f64 x (+.f64 x 2) (*.f64 y y))

rewrite47.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

742×	`pow1_binary64`
690×	`add-log-exp_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
675×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	150	11
2	1857	11

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

Outputs

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

simplify134.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

1238×	`sqr-pow_binary64`
666×	`cube-prod_binary64`
662×	`fabs-mul_binary64`
532×	`pow-sqr_binary64`
505×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	262
1	34	214
2	59	214
3	87	214
4	194	214
5	499	214
6	1666	214
7	2322	214
8	2641	214
9	2901	214
10	3244	214
11	3730	214
12	4389	214
13	5179	214
14	6112	214
15	6635	214
16	7046	214
17	7439	214
18	7558	214
19	7604	214

Stop Event

1×	node limit

Counts

45 → 33

Calls

Call 1

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

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

prune44.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	32	3	35

Error

Counts

35 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))
▶	0.0b	(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
	14.7b	(fma.f64 y y (*.f64 2 x))

Compiler

Compiled 416 to 237 computations (43% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))

series3.0ms (0.2%)

Counts

1 → 9

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
1.0ms	y	@	-inf	(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
1.0ms	y	@	0	(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
1.0ms	y	@	inf	(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
0.0ms	x	@	-inf	(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))

rewrite61.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

505×	`fma-def_binary64`
453×	`log-prod_binary64`
369×	`pow-prod-down_binary64`
334×	`exp-prod_binary64`
260×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	208	11
2	2864	11

Stop Event

1×	node limit

Counts

1 → 87

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (.f64 x x) 4) (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2))) (/.f64 (pow.f64 (hypot.f64 x y) 4) (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) (pow.f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 2) (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 (hypot.f64 x y) (sqrt.f64 (+.f64 x x))) (hypot.f64 (hypot.f64 x y) (sqrt.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6)) (/.f64 1 (fma.f64 (pow.f64 (hypot.f64 x y) 2) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)) (.f64 (.f64 x x) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 (hypot.f64 x y) 4)) (/.f64 1 (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 (hypot.f64 x y) 2) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)) (.f64 (.f64 x x) 4)) (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2)) (-.f64 (.f64 (.f64 x x) 4) (pow.f64 (hypot.f64 x y) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6)) (fma.f64 (pow.f64 (hypot.f64 x y) 2) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)) (.f64 (.f64 x x) 4)))))) (#(struct:change #<rule 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(2) ((x /.f64 (-.f64 (pow.f64 (hypot.f64 x y) 4) (.f64 (.f64 x x) 4)) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 2 x (.f64 y y)) 2) (pow.f64 x 4)) (-.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (hypot.f64 x y) (sqrt.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (pow.f64 (hypot.f64 x y) 2) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)) (.f64 (.f64 x x) 4)) (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2)) (-.f64 (.f64 (.f64 x x) 4) (pow.f64 (hypot.f64 x y) 4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))) 2)) (cbrt.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))) (sqrt.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (+.f64 x x))) (exp.f64 (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (+.f64 x x))) (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x x))) (exp.f64 (fma.f64 2 x (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x y) 2))) (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (pow.f64 (hypot.f64 x y) 2)) (+.f64 1 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x y) 2))) (+.f64 1 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (fma.f64 2 x (.f64 y y))) (+.f64 1 (expm1.f64 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 (hypot.f64 x y) (sqrt.f64 (+.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (fma.f64 2 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x x) 1 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 y y) 1 (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) 1 (fma.f64 2 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (hypot.f64 x y) 2) 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 y y) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (fma.f64 2 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 2 x (.f64 y y)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) 2)) (cbrt.f64 (pow.f64 (hypot.f64 x y) 4)) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) 4)) (cbrt.f64 (pow.f64 (hypot.f64 x y) 2)) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) y) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 y) y) (pow.f64 (cbrt.f64 y) 2) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 (pow.f64 x 4)) (fma.f64 2 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (.f64 x x)) (fma.f64 2 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (cbrt.f64 (+.f64 x x)) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x y) (hypot.f64 x y) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (pow.f64 y 3/2) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (fma.f64 2 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (+.f64 x x)) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 y 6) (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)))) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 y 4) (pow.f64 x 4)) (/.f64 1 (fma.f64 y y (.f64 (neg.f64 x) x))) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 2 x (.f64 y y)) 1 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 y 3/2) (sqrt.f64 y) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x (.f64 y y))) 2) (cbrt.f64 (fma.f64 2 x (.f64 y y))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 y (sqrt.f64 (+.f64 x x))) (hypot.f64 y (sqrt.f64 (+.f64 x x))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (fma.f64 2 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 5) (cbrt.f64 y) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (fma.f64 2 x (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 2 (cbrt.f64 (.f64 x x))) (cbrt.f64 x) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 x) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (*.f64 x x) 4) (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2))) (/.f64 (pow.f64 (hypot.f64 x y) 4) (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) (pow.f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 2) (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (hypot.f64 x y) (sqrt.f64 (+.f64 x x))) (hypot.f64 (hypot.f64 x y) (sqrt.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6)) (/.f64 1 (fma.f64 (pow.f64 (hypot.f64 x y) 2) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)) (*.f64 (*.f64 x x) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 (hypot.f64 x y) 4)) (/.f64 1 (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 (hypot.f64 x y) 2) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)) (*.f64 (*.f64 x x) 4)) (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2)) (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 (hypot.f64 x y) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6)) (fma.f64 (pow.f64 (hypot.f64 x y) 2) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)) (*.f64 (*.f64 x x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6)) (+.f64 (pow.f64 (hypot.f64 x y) 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 2 (*.f64 x (pow.f64 (hypot.f64 x y) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 (hypot.f64 x y) 4)) (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6))) (neg.f64 (fma.f64 (pow.f64 (hypot.f64 x y) 2) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)) (*.f64 (*.f64 x x) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 (hypot.f64 x y) 4))) (neg.f64 (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 3) (pow.f64 x 6)) (+.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 2) (-.f64 (pow.f64 x 4) (*.f64 (fma.f64 2 x (*.f64 y y)) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (hypot.f64 x y) 4) (*.f64 (*.f64 x x) 4)) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 2) (pow.f64 x 4)) (-.f64 (fma.f64 2 x (*.f64 y y)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (hypot.f64 x y) (sqrt.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (pow.f64 (hypot.f64 x y) 2) (-.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x)) (*.f64 (*.f64 x x) 4)) (fma.f64 8 (pow.f64 x 3) (pow.f64 (hypot.f64 x y) 6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2)) (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 (hypot.f64 x y) 4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))) 2)) (cbrt.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))) (sqrt.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x x))) (exp.f64 (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x x))) (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x x))) (exp.f64 (fma.f64 2 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x y) 2))) (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (pow.f64 (hypot.f64 x y) 2)) (+.f64 1 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 x y) 2))) (+.f64 1 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 2 x (*.f64 y y))) (+.f64 1 (expm1.f64 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 (hypot.f64 x y) (sqrt.f64 (+.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x x) 1 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y y) 1 (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1 (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (hypot.f64 x y) 2) 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y y) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (hypot.f64 x y) 2) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 2 x (*.f64 y y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) 2)) (cbrt.f64 (pow.f64 (hypot.f64 x y) 4)) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 x y) 4)) (cbrt.f64 (pow.f64 (hypot.f64 x y) 2)) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) y) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 y) y) (pow.f64 (cbrt.f64 y) 2) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 (pow.f64 x 4)) (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (cbrt.f64 (+.f64 x x)) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x y) (hypot.f64 x y) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (pow.f64 y 3/2) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (+.f64 x x)) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 y 6) (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 y x) 2)))) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 y 4) (pow.f64 x 4)) (/.f64 1 (fma.f64 y y (*.f64 (neg.f64 x) x))) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 2 x (*.f64 y y)) 1 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 y 3/2) (sqrt.f64 y) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 2) (cbrt.f64 (fma.f64 2 x (*.f64 y y))) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 y (sqrt.f64 (+.f64 x x))) (hypot.f64 y (sqrt.f64 (+.f64 x x))) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 5) (cbrt.f64 y) (fma.f64 x x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (sqrt.f64 x)) (sqrt.f64 x) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))))))

simplify125.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

1238×	`sqr-pow_binary64`
666×	`cube-prod_binary64`
660×	`fabs-mul_binary64`
532×	`pow-sqr_binary64`
421×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	52
1	22	49
2	41	49
3	70	49
4	154	49
5	435	49
6	1572	49
7	2150	49
8	2469	49
9	2729	49
10	3070	49
11	3554	49
12	4213	49
13	5005	49
14	5934	49
15	6451	49
16	6868	49
17	7257	49
18	7382	49
19	7428	49

Stop Event

1×	node limit

Counts

96 → 95

Calls

Call 1

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

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

prune193.0ms (10.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	97	1	98

Error

Counts

98 → 1

Alt Table

Status	Error	Program
▶	0b	(fma.f64 y y (fma.f64 x x (+.f64 x x)))

Compiler

Compiled 1437 to 700 computations (51.3% saved)

localize7.0ms (0.4%)

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Error

Counts

1 → 1

Alt Table

Status	Error	Program
✓	0b	(fma.f64 y y (fma.f64 x x (+.f64 x x)))

Compiler

Compiled 13 to 7 computations (46.2% saved)

regimes26.0ms (1.4%)

Accuracy

Total -14.7b remaining (-∞%)

Threshold costs -14.7b (-∞%)

Counts

5 → 1

Calls

Call 1

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

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

Results

4.0ms	0b	`x`
4.0ms	0b	`y`
4.0ms	0b	`(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))`
6.0ms	0b	`(+.f64 (.f64 x 2) (.f64 x x))`
3.0ms	0b	`(*.f64 y y)`
3.0ms	0b	`(*.f64 y y)`

Compiler

Compiled 85 to 49 computations (42.4% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12

Stop Event

1×

saturated

Calls

Call 1

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

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

end16.0ms (0.8%)

Stop Event

1×

done

Compiler

Compiled 22 to 10 computations (54.5% saved)

Details

analyze85.0ms (4.6%)

sample1.0s (56.7%)

preprocess18.0ms (1%)

simplify8.0ms (0.4%)

prune3.0ms (0.2%)

localize7.0ms (0.4%)

series3.0ms (0.2%)

rewrite47.0ms (2.6%)

simplify134.0ms (7.3%)

prune44.0ms (2.4%)

localize6.0ms (0.3%)

series3.0ms (0.2%)

rewrite61.0ms (3.4%)

simplify125.0ms (6.8%)

prune193.0ms (10.6%)

localize7.0ms (0.4%)

prune1.0ms (0%)

regimes26.0ms (1.4%)

simplify5.0ms (0.3%)

end16.0ms (0.8%)

Profiling