Details

analyze136.0ms (6.8%)

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
51.6%	6.1%	42.2%	13
52.7%	4.2%	43%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (53.3%)

Results

983.0ms	8256×	body	128	valid
73.0ms	96×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess21.0ms (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)

simplify7.0ms (0.3%)

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 (0.1%)

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

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)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	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	y	@	inf	(fma.f64 x (+.f64 x 2) (*.f64 y y))
1.0ms	x	@	inf	(fma.f64 x (+.f64 x 2) (*.f64 y y))

rewrite35.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

742×	`pow1_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_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 → 23

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 (exp.f64 (log1p.f64 (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 log.f64 (+.f64 1 (expm1.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 exp.f64 (.f64 (log.f64 (fma.f64 x (+.f64 x 2) (.f64 y y))) 1))))) (#(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 (exp.f64 (log1p.f64 (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 log.f64 (+.f64 1 (expm1.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 exp.f64 (*.f64 (log.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))) 1))))) (#(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))))))))

simplify62.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
502×	`fma-def_binary64`
422×	`associate-l_binary64`
288×	`cube-prod_binary64`
285×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	300
1	24	214
2	54	214
3	89	214
4	190	214
5	472	214
6	1645	214
7	2318	214
8	2638	214
9	2898	214
10	3237	214
11	3719	214
12	4378	214

Stop Event

1×	node limit

Counts

47 → 33

Calls

Call 1

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

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

prune27.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

Counts

35 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
	40.6b	(cbrt.f64 (pow.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y)) 3))
	17.9b	(fma.f64 y y (*.f64 2 x))

Compiler

Compiled 442 to 250 computations (43.4% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series3.0ms (0.2%)

Counts

2 → 36

Calls

9 calls:

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

rewrite62.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`fma-def_binary64`
467×	`log-prod_binary64`
280×	`fma-neg_binary64`
177×	`expm1-udef_binary64`
177×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	203	18
2	2902	18

Stop Event

1×	node limit

Counts

2 → 157

Calls

Call 1

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

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

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

simplify64.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
502×	`fma-def_binary64`
413×	`associate-l_binary64`
298×	`associate-r_binary64`
288×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	402
1	24	289
2	54	289
3	89	289
4	189	289
5	480	289
6	1631	289
7	2307	289
8	2627	289
9	2887	289
10	3230	289
11	3714	289
12	4373	289

Stop Event

1×	node limit

Counts

193 → 168

Calls

Call 1

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

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

prune99.0ms (4.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	169	2	171

Error

Counts

171 → 2

Alt Table

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

Compiler

Compiled 2591 to 1170 computations (54.8% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.7%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	y	@	inf	(fma.f64 (hypot.f64 x y) (hypot.f64 x y) (+.f64 x x))
2.0ms	y	@	0	(fma.f64 (hypot.f64 x y) (hypot.f64 x y) (+.f64 x x))
2.0ms	x	@	inf	(fma.f64 (hypot.f64 x y) (hypot.f64 x y) (+.f64 x x))
2.0ms	x	@	0	(fma.f64 (hypot.f64 x y) (hypot.f64 x y) (+.f64 x x))
1.0ms	y	@	-inf	(fma.f64 (hypot.f64 x y) (hypot.f64 x y) (+.f64 x x))

rewrite63.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

607×	`pow1_binary64`
564×	`add-log-exp_binary64`
563×	`log1p-expm1-u_binary64`
563×	`expm1-log1p-u_binary64`
68×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	128	17
2	1723	17

Stop Event

1×	node limit

Counts

2 → 41

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (hypot.f64 x y) 2) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (hypot.f64 x y) 2) 1) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 (hypot.f64 x y) 2) x) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2))) (cbrt.f64 (pow.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)) 2)) (cbrt.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (hypot.f64 x y) (/.f64 0 0)) (hypot.f64 (hypot.f64 x y) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 x y) 2) 3) (/.f64 0 0)) (+.f64 (*.f64 (pow.f64 (hypot.f64 x y) 2) (pow.f64 (hypot.f64 x y) 2)) (-.f64 (/.f64 0 0) (*.f64 (pow.f64 (hypot.f64 x y) 2) (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 (hypot.f64 x y) 2) (pow.f64 (hypot.f64 x y) 2)) (/.f64 0 0)) (-.f64 (pow.f64 (hypot.f64 x y) 2) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (hypot.f64 x y) (/.f64 0 0)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 0 0) (pow.f64 (hypot.f64 x y) 2))))))))

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

simplify35.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-neg_binary64`
537×	`cancel-sign-sub-inv_binary64`
312×	`distribute-rgt-neg-in_binary64`
310×	`distribute-lft-neg-in_binary64`
266×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	788
1	172	684
2	554	668
3	2442	668

Stop Event

1×	node limit

Counts

89 → 81

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 2 x))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 2 x))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 2 x))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 x 2) (*.f64 2 x))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
y
(+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))
(-.f64 (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y)))) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
x
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)) (*.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)))
x
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)) (*.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
y
(+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))
(-.f64 (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y)))) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(*.f64 -1 y)
(neg.f64 (+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))) (+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))))

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 2 x))
(+.f64 (.f64 y y) (.f64 2 x))
(fma.f64 y y (*.f64 2 x))
(fma.f64 2 x (*.f64 y y))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x))
(+.f64 (.f64 2 x) (.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x))
(+.f64 (.f64 2 x) (.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.f64 x x)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 x 2) (*.f64 2 x))
(+.f64 (.f64 2 x) (.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.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 (pow.f64 x 2) (*.f64 2 x)))
(+.f64 (.f64 y y) (+.f64 (.f64 2 x) (*.f64 x x)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
y
(+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))
(+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y)))
(fma.f64 1/2 (/.f64 (*.f64 x x) y) y)
(fma.f64 1/2 (*.f64 (/.f64 x y) x) y)
(-.f64 (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(+.f64 (+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 x x) y) y) (/.f64 (.f64 -1/8 (pow.f64 x 4)) (pow.f64 y 3)))
(fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 x y) x) y))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y)))) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) (+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y)))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) (fma.f64 1/2 (/.f64 (.f64 x x) y) y)) (/.f64 (.f64 -1/8 (pow.f64 x 4)) (pow.f64 y 3)))
(fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 x y) x) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) y)))
x
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)
(fma.f64 1/2 (/.f64 (*.f64 y y) x) x)
(fma.f64 1/2 (/.f64 y (/.f64 x y)) x)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 y y) x) x) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(+.f64 (fma.f64 1/2 (/.f64 y (/.f64 x y)) x) (/.f64 (*.f64 -1/8 (pow.f64 y 4)) (pow.f64 x 3)))
(fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) -1/8 (fma.f64 1/2 (/.f64 y (/.f64 x y)) x))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)) (*.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y (/.f64 x y)) x)) (/.f64 (*.f64 -1/8 (pow.f64 y 4)) (pow.f64 x 3)))
(fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) -1/8 (fma.f64 1/2 (/.f64 y (/.f64 x y)) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) -1/8 (fma.f64 1/2 (/.f64 y (/.f64 x y)) x)))
(*.f64 -1 x)
(neg.f64 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x))
(neg.f64 (fma.f64 1/2 (/.f64 (*.f64 y y) x) x))
(neg.f64 (fma.f64 1/2 (/.f64 y (/.f64 x y)) x))
(fma.f64 (/.f64 y (/.f64 x y)) -1/2 (neg.f64 x))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (fma.f64 1/2 (/.f64 (.f64 y y) x) x))
(-.f64 (/.f64 (*.f64 1/8 (pow.f64 y 4)) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 y (/.f64 x y)) x))
(-.f64 (*.f64 (/.f64 1/8 (pow.f64 x 3)) (pow.f64 y 4)) (fma.f64 1/2 (/.f64 y (/.f64 x y)) x))
(fma.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) (fma.f64 (/.f64 y (/.f64 x y)) -1/2 (neg.f64 x)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))
(-.f64 (/.f64 (*.f64 1/8 (pow.f64 y 4)) (pow.f64 x 3)) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y (/.f64 x y)) x)))
(-.f64 (*.f64 (/.f64 1/8 (pow.f64 x 3)) (pow.f64 y 4)) (fma.f64 1/2 (/.f64 y (/.f64 x y)) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) x)))
(-.f64 (*.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (fma.f64 1/2 (/.f64 y (/.f64 x y)) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) x)))
x
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)
(fma.f64 1/2 (/.f64 (*.f64 y y) x) x)
(fma.f64 1/2 (/.f64 y (/.f64 x y)) x)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 y y) x) x) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(+.f64 (fma.f64 1/2 (/.f64 y (/.f64 x y)) x) (/.f64 (*.f64 -1/8 (pow.f64 y 4)) (pow.f64 x 3)))
(fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) -1/8 (fma.f64 1/2 (/.f64 y (/.f64 x y)) x))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)) (*.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y (/.f64 x y)) x)) (/.f64 (*.f64 -1/8 (pow.f64 y 4)) (pow.f64 x 3)))
(fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) -1/8 (fma.f64 1/2 (/.f64 y (/.f64 x y)) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) -1/8 (fma.f64 1/2 (/.f64 y (/.f64 x y)) x)))
y
(+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))
(+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y)))
(fma.f64 1/2 (/.f64 (*.f64 x x) y) y)
(fma.f64 1/2 (*.f64 (/.f64 x y) x) y)
(-.f64 (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(+.f64 (+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 x x) y) y) (/.f64 (.f64 -1/8 (pow.f64 x 4)) (pow.f64 y 3)))
(fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 x y) x) y))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y)))) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) (+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y)))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) (fma.f64 1/2 (/.f64 (.f64 x x) y) y)) (/.f64 (.f64 -1/8 (pow.f64 x 4)) (pow.f64 y 3)))
(fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 x y) x) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) y)))
(*.f64 -1 y)
(neg.f64 y)
(neg.f64 (+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y))))
(neg.f64 (+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y))))
(-.f64 (.f64 (/.f64 (.f64 x x) y) -1/2) y)
(-.f64 (.f64 (.f64 (/.f64 x y) x) -1/2) y)
(-.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (.f64 1/2 (/.f64 (*.f64 x x) y))))
(-.f64 (/.f64 (.f64 1/8 (pow.f64 x 4)) (pow.f64 y 3)) (fma.f64 1/2 (/.f64 (.f64 x x) y) y))
(-.f64 (/.f64 (pow.f64 x 4) (/.f64 (pow.f64 y 3) 1/8)) (fma.f64 1/2 (*.f64 (/.f64 x y) x) y))
(-.f64 (.f64 (/.f64 1/8 (pow.f64 y 3)) (pow.f64 x 4)) (fma.f64 1/2 (.f64 (/.f64 x y) x) y))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))) (+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) (+.f64 y (.f64 1/2 (/.f64 (*.f64 x x) y)))))
(-.f64 (/.f64 (.f64 1/8 (pow.f64 x 4)) (pow.f64 y 3)) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) (fma.f64 1/2 (/.f64 (.f64 x x) y) y)))
(-.f64 (/.f64 (pow.f64 x 4) (/.f64 (pow.f64 y 3) 1/8)) (fma.f64 1/2 (*.f64 (/.f64 x y) x) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) y)))
(-.f64 (.f64 (/.f64 1/8 (pow.f64 y 3)) (pow.f64 x 4)) (fma.f64 1/2 (.f64 (/.f64 x y) x) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) y)))

prune72.0ms (3.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	129	2	131

Error

Counts

131 → 2

Alt Table

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

Compiler

Compiled 2217 to 1031 computations (53.5% saved)

regimes153.0ms (7.6%)

Accuracy

Total 0.0b remaining (79.2%)

Threshold costs 0.0b (79.2%)

Counts

43 → 1

Compiler

Compiled 403 to 165 computations (59.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14

Stop Event

1×

saturated

Calls

Call 1

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

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

end57.0ms (2.9%)

Stop Event

1×

done

Compiler

Compiled 49 to 23 computations (53.1% saved)

Details

analyze136.0ms (6.8%)

sample1.1s (53.3%)

preprocess21.0ms (1%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite35.0ms (1.7%)

simplify62.0ms (3.1%)

prune27.0ms (1.3%)

localize6.0ms (0.3%)

series3.0ms (0.2%)

rewrite62.0ms (3.1%)

simplify64.0ms (3.2%)

prune99.0ms (4.9%)

localize7.0ms (0.3%)

series15.0ms (0.7%)

rewrite63.0ms (3.2%)

simplify35.0ms (1.8%)

prune72.0ms (3.6%)

regimes153.0ms (7.6%)

simplify2.0ms (0.1%)

end57.0ms (2.9%)

Profiling