Details

analyze84.0ms (1.2%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
18.7%	43.7%	37.6%	6
28.1%	34.3%	37.6%	7
32.8%	23.4%	43.8%	8
36.7%	18.3%	45%	9
39.4%	12.3%	48.3%	10
41.6%	9.5%	49%	11
43%	6.3%	50.7%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.6s (23.4%)

Results

1.5s	8253×	body	256	valid
57.0ms	441×	body	256	invalid
0.0ms	2×	body	1024	valid
0.0ms	1×	body	512	valid

preprocess55.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

258×	`fma-neg_binary64`
254×	`fma-def_binary64`
74×	`cancel-sign-sub-inv_binary64`
60×	`sub-neg_binary64`
40×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	26	20
2	65	20
3	130	20
4	285	20
5	592	20
6	983	20
7	1146	20
8	1206	20
9	1218	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(+.f64 (-.f64 1 y) (*.f64 x (sqrt.f64 y)))

Outputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(+.f64 (-.f64 1 y) (*.f64 x (sqrt.f64 y)))
(fma.f64 x (sqrt.f64 y) (-.f64 1 y))
(-.f64 (fma.f64 x (sqrt.f64 y) 1) y)

Compiler

Compiled 12 to 9 computations (25% saved)

simplify24.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

151×	`fma-def_binary64`
131×	`fma-neg_binary64`
46×	`cancel-sign-sub-inv_binary64`
37×	`sub-neg_binary64`
30×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	72	10
4	150	10
5	312	10
6	511	10
7	635	10
8	717	10
9	731	10

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Outputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)

eval1.0ms (0%)

Compiler: Compiled 17 to 10 computations (41.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 10 to 7 computations (30% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	0.2b	(*.f64 y (sqrt.f64 x))

Compiler

Compiled 22 to 10 computations (54.5% saved)

series8.0ms (0.1%)

Counts

2 → 15

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(*.f64 y (sqrt.f64 x))
1.0ms	x	@	0	(*.f64 y (sqrt.f64 x))
1.0ms	x	@	-inf	(*.f64 y (sqrt.f64 x))
1.0ms	y	@	0	(*.f64 y (sqrt.f64 x))
1.0ms	y	@	inf	(*.f64 y (sqrt.f64 x))

rewrite56.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

969×	`pow1_binary64`
903×	`add-log-exp_binary64`
903×	`log1p-expm1-u_binary64`
903×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	174	16
2	2425	16

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

Inputs
(*.f64 y (sqrt.f64 x))
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

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

Outputs

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

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

simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

190×	`fma-def_binary64`
155×	`fma-neg_binary64`
55×	`cancel-sign-sub-inv_binary64`
34×	`distribute-rgt-in_binary64`
33×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	113
1	21	113
2	32	113
3	54	113
4	88	113
5	147	113
6	283	113
7	436	113
8	595	113
9	733	113
10	825	113
11	831	113

Stop Event

1×

saturated

Counts

67 → 57

Calls

Call 1

Inputs
1
(*.f64 -1 x)
(*.f64 -1 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)

Outputs
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

eval15.0ms (0.2%)

Compiler: Compiled 799 to 397 computations (50.3% saved)

prune21.0ms (0.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	44	13	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	14	58

Error

0.0b

Counts

58 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	30.6b	(.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (/.f64 1 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x))))))
	22.1b	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
	0.9b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	0.5b	(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
▶	42.4b	(neg.f64 x)
▶	0.1b	(fma.f64 (sqrt.f64 x) y (-.f64 1 x))
▶	30.6b	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (*.f64 y y)))))
	31.4b	(+.f64 (-.f64 1 x) (pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) 2))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
▶	39.8b	(*.f64 y (sqrt.f64 x))
	25.6b	(/.f64 (-.f64 1 (.f64 (-.f64 x (.f64 y (sqrt.f64 x))) (-.f64 x (.f64 y (sqrt.f64 x))))) (+.f64 1 (-.f64 x (.f64 y (sqrt.f64 x)))))
	24.3b	(-.f64 1 x)
▶	30.6b	(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
	44.9b	1

Compiler

Compiled 371 to 248 computations (33.2% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sqrt.f64 x) y (-.f64 1 x))

Compiler

Compiled 17 to 9 computations (47.1% saved)

series3.0ms (0%)

Counts

1 → 15

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(fma.f64 (sqrt.f64 x) y (-.f64 1 x))
1.0ms	x	@	-inf	(fma.f64 (sqrt.f64 x) y (-.f64 1 x))
0.0ms	x	@	0	(fma.f64 (sqrt.f64 x) y (-.f64 1 x))
0.0ms	y	@	0	(fma.f64 (sqrt.f64 x) y (-.f64 1 x))
0.0ms	y	@	inf	(fma.f64 (sqrt.f64 x) y (-.f64 1 x))

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`pow1_binary64`
649×	`add-log-exp_binary64`
649×	`log1p-expm1-u_binary64`
649×	`expm1-log1p-u_binary64`
634×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	143	10
2	1729	10

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 x) y (-.f64 1 x))

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

Outputs

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

simplify27.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

190×	`fma-def_binary64`
155×	`fma-neg_binary64`
55×	`cancel-sign-sub-inv_binary64`
34×	`distribute-rgt-in_binary64`
33×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	113
1	21	113
2	32	113
3	54	113
4	88	113
5	147	113
6	283	113
7	436	113
8	595	113
9	733	113
10	825	113
11	831	113

Stop Event

1×

saturated

Counts

38 → 30

Calls

Call 1

Inputs
1
(*.f64 -1 x)
(*.f64 -1 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)

Outputs
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

localize3.0ms (0%)

Compiler: Compiled 5 to 3 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 x))

Compiler

Compiled 10 to 4 computations (60% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 x))
✓	4.7b	(-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y)))
✓	10.7b	(.f64 x (.f64 y y))
✓	23.8b	(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))

Compiler

Compiled 73 to 30 computations (58.9% saved)

series13.0ms (0.2%)

Counts

3 → 63

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
2.0ms	y	@	-inf	(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
2.0ms	x	@	0	(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
1.0ms	x	@	inf	(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
1.0ms	y	@	0	(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))

rewrite95.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

874×	`fma-def_binary64`
395×	`fma-neg_binary64`
293×	`expm1-udef_binary64`
291×	`log1p-udef_binary64`
240×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	53
1	348	51
2	5185	51

Stop Event

1×	node limit

Counts

3 → 176

Calls

Call 1

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

Outputs

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

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

496×	`unsub-neg_binary64`
409×	`fma-def_binary64`
296×	`difference-of-squares_binary64`
283×	`sub-neg_binary64`
256×	`distribute-rgt-out--_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	664
1	86	592
2	218	528
3	628	528
4	2522	528
5	5604	528

Stop Event

1×	node limit

Counts

239 → 199

Calls

Call 1

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

Outputs
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
(*.f64 (pow.f64 y 2) x)
(.f64 x (.f64 y y))
1
(+.f64 1 (.f64 -1 (.f64 x (+.f64 2 (pow.f64 y 2)))))
(+.f64 1 (.f64 (neg.f64 x) (+.f64 2 (.f64 y y))))
(-.f64 1 (*.f64 x (fma.f64 y y 2)))
(+.f64 1 (+.f64 (.f64 -1 (.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 1 (+.f64 (.f64 -1 (.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 -1 (.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2))
(fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x))
(*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2))))
(*.f64 x (-.f64 x (fma.f64 y y 2)))
(+.f64 1 (+.f64 (.f64 -1 (.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 1 (+.f64 (.f64 -1 (.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 (-.f64 2 (*.f64 -1 (pow.f64 y 2))) x)))
(fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x))
(*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2))))
(*.f64 x (-.f64 x (fma.f64 y y 2)))
(+.f64 1 (+.f64 (pow.f64 x 2) (.f64 -1 (.f64 (-.f64 2 (*.f64 -1 (pow.f64 y 2))) x))))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 1 (+.f64 (pow.f64 x 2) (.f64 -1 (.f64 (-.f64 2 (*.f64 -1 (pow.f64 y 2))) x))))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(pow.f64 (-.f64 1 x) 2)
(+.f64 (pow.f64 (-.f64 1 x) 2) (.f64 -1 (.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (.f64 -1 (.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (.f64 -1 (.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 (neg.f64 (.f64 y y)) x)
(.f64 x (.f64 y (neg.f64 y)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (.f64 -1 (.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (.f64 -1 (.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (.f64 -1 (.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 (neg.f64 (.f64 y y)) x)
(.f64 x (.f64 y (neg.f64 y)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (.f64 -1 (.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (.f64 -1 (.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (.f64 -1 (.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (.f64 x (+.f64 2 (.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 x))
	4.7b	(-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y)))
	10.7b	(.f64 x (.f64 y y))
✓	23.8b	(/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (*.f64 y y))))

Compiler

Compiled 95 to 40 computations (57.9% saved)

series6.0ms (0.1%)

Counts

1 → 15

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (*.f64 y y))))
1.0ms	x	@	0	(/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (*.f64 y y))))
1.0ms	x	@	inf	(/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (*.f64 y y))))
1.0ms	y	@	0	(/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (*.f64 y y))))
1.0ms	y	@	inf	(/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (*.f64 y y))))

rewrite73.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

865×	`fma-def_binary64`
388×	`fma-neg_binary64`
291×	`expm1-udef_binary64`
289×	`log1p-udef_binary64`
239×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	30
1	347	28
2	5102	28

Stop Event

1×	node limit

Counts

1 → 43

Calls

Call 1

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

Outputs

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

simplify42.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

570×	`cancel-sign-sub-inv_binary64`
547×	`associate-/l/_binary64`
536×	`fma-neg_binary64`
464×	`associate-/r/_binary64`
318×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	486
1	148	451
2	515	441
3	2842	429

Stop Event

1×	node limit

Counts

58 → 60

Calls

Call 1

Inputs
1
(/.f64 -1 x)
(/.f64 -1 x)
(/.f64 1 (-.f64 1 x))
(+.f64 (/.f64 1 (-.f64 1 x)) (.f64 -1 (.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))
(+.f64 (/.f64 (.f64 (pow.f64 y 2) x) (pow.f64 (-.f64 1 x) 3)) (+.f64 (/.f64 1 (-.f64 1 x)) (.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))))
(+.f64 (.f64 -1 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 3)))) (+.f64 (/.f64 (.f64 (pow.f64 y 2) x) (pow.f64 (-.f64 1 x) 3)) (+.f64 (/.f64 1 (-.f64 1 x)) (.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 (pow.f64 y 4) (pow.f64 x 2)))) (.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 (pow.f64 y 4) (pow.f64 x 2)))) (.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))

Outputs
1
(/.f64 -1 x)
(/.f64 -1 x)
(/.f64 1 (-.f64 1 x))
(+.f64 (/.f64 1 (-.f64 1 x)) (.f64 -1 (.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))
(+.f64 (/.f64 1 (-.f64 1 x)) (neg.f64 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))
(-.f64 (/.f64 1 (-.f64 1 x)) (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))
(fma.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (neg.f64 (sqrt.f64 x)) (/.f64 1 (-.f64 1 x)))
(+.f64 (/.f64 (.f64 (pow.f64 y 2) x) (pow.f64 (-.f64 1 x) 3)) (+.f64 (/.f64 1 (-.f64 1 x)) (.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))))
(+.f64 (+.f64 (/.f64 (.f64 y y) (/.f64 (pow.f64 (-.f64 1 x) 3) x)) (/.f64 1 (-.f64 1 x))) (neg.f64 (.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))
(+.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))) (/.f64 x (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 y y))))
(-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 1 x) 3) y)) x (/.f64 1 (-.f64 1 x))) (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))
(-.f64 (/.f64 1 (-.f64 1 x)) (.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (-.f64 (sqrt.f64 x) (/.f64 (.f64 x y) (-.f64 1 x)))))
(+.f64 (.f64 -1 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 3)))) (+.f64 (/.f64 (.f64 (pow.f64 y 2) x) (pow.f64 (-.f64 1 x) 3)) (+.f64 (/.f64 1 (-.f64 1 x)) (.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))))
(fma.f64 -1 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 3))) (+.f64 (+.f64 (/.f64 (.f64 y y) (/.f64 (pow.f64 (-.f64 1 x) 3) x)) (/.f64 1 (-.f64 1 x))) (neg.f64 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))))
(+.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))) (fma.f64 (neg.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4))) (sqrt.f64 (pow.f64 x 3)) (/.f64 x (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 y y)))))
(-.f64 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4)) (neg.f64 (pow.f64 x 3/2)) (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 1 x) 3) y)) x (/.f64 1 (-.f64 1 x)))) (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))
(-.f64 (/.f64 1 (-.f64 1 x)) (+.f64 (.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (-.f64 (sqrt.f64 x) (/.f64 (.f64 x y) (-.f64 1 x)))) (/.f64 (pow.f64 y 3) (/.f64 (pow.f64 (-.f64 1 x) 4) (pow.f64 x 3/2)))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 x (.f64 y y))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (sqrt.f64 (/.f64 1 x)) y)) (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (.f64 (/.f64 (-.f64 1 x) (.f64 y y)) (+.f64 (/.f64 -1 x) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (-.f64 1 x) y)))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 (pow.f64 y 4) (pow.f64 x 2)))) (.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)) (fma.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 (pow.f64 y 4) (.f64 x x))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 x (.f64 y y)))) (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (neg.f64 (pow.f64 (-.f64 1 x) 3)) (.f64 x (.f64 x (pow.f64 y 4))))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 x (.f64 x (pow.f64 y 4)))))) (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 (pow.f64 y 4) (.f64 x x)))) (.f64 (/.f64 (-.f64 1 x) (.f64 y y)) (+.f64 (/.f64 -1 x) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (-.f64 1 x) y)))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 x (.f64 y y))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (sqrt.f64 (/.f64 1 x)) y)) (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (.f64 (/.f64 (-.f64 1 x) (.f64 y y)) (+.f64 (/.f64 -1 x) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (-.f64 1 x) y)))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 (pow.f64 y 4) (pow.f64 x 2)))) (.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)) (fma.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 (pow.f64 y 4) (.f64 x x))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 x (.f64 y y)))) (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (neg.f64 (pow.f64 (-.f64 1 x) 3)) (.f64 x (.f64 x (pow.f64 y 4))))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 x (.f64 x (pow.f64 y 4)))))) (/.f64 (-.f64 1 x) (.f64 x (.f64 y y))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 (pow.f64 y 4) (.f64 x x)))) (.f64 (/.f64 (-.f64 1 x) (.f64 y y)) (+.f64 (/.f64 -1 x) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (-.f64 1 x) y)))))

eval310.0ms (4.5%)

Compiler: Compiled 13290 to 6218 computations (53.2% saved)

prune263.0ms (3.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	457	9	466
Fresh	6	2	8
Picked	1	0	1
Done	2	3	5
Total	466	14	480

Error

0.0b

Counts

480 → 14

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.9b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))
	44.9b	1
	30.6b	(.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (/.f64 1 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x))))))
▶	22.1b	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
	58.2b	(/.f64 (.f64 x (.f64 y (neg.f64 y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	42.4b	(neg.f64 x)
	42.4b	(/.f64 1 (/.f64 -1 x))
▶	59.4b	(sqrt.f64 (.f64 x (.f64 y y)))
▶	58.2b	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))
	39.8b	(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
▶	24.3b	(-.f64 1 x)
✓	39.8b	(*.f64 y (sqrt.f64 x))
	40.1b	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)

Compiler

Compiled 287 to 203 computations (29.3% saved)

localize45.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (sqrt.f64 x) y (-.f64 1 x))
✓	0.2b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))
✓	0.4b	(pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2)
✓	0.4b	(cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))

Compiler

Compiled 55 to 31 computations (43.6% saved)

series38.0ms (0.6%)

Counts

3 → 25

Calls

18 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2)
4.0ms	x	@	inf	(pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2)
4.0ms	x	@	-inf	(cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))
4.0ms	y	@	0	(pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2)
3.0ms	x	@	inf	(cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))

rewrite132.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

893×	`pow1_binary64`
833×	`add-log-exp_binary64`
832×	`log1p-expm1-u_binary64`
832×	`expm1-log1p-u_binary64`
812×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	228	37
2	2360	37

Stop Event

1×	node limit

Counts

3 → 55

Calls

Call 1

Inputs

(cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))

(pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2)

(*.f64 (pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))

Outputs

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

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

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

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-l_binary64`
536×	`associate-r_binary64`
459×	`distribute-rgt-in_binary64`
449×	`distribute-lft-in_binary64`
429×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	696
1	250	641
2	812	630
3	3837	629

Stop Event

1×	node limit

Counts

80 → 78

Calls

Call 1

Inputs
1
(pow.f64 (-.f64 1 x) 1/3)
(+.f64 (pow.f64 (-.f64 1 x) 1/3) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/9) (*.f64 y (sqrt.f64 x)))))
(+.f64 (pow.f64 (-.f64 1 x) 1/3) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/9) (.f64 (pow.f64 y 2) x))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/9) (.f64 y (sqrt.f64 x))))))
(+.f64 (pow.f64 (-.f64 1 x) 1/3) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/9) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/9) (.f64 y (sqrt.f64 x)))) (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (.f64 (+.f64 (.f64 -2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (sqrt.f64 (pow.f64 x 3))))) (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (sqrt.f64 (pow.f64 x 3))))) (pow.f64 y 3)))))))
1
(pow.f64 (pow.f64 (-.f64 1 x) 2) 1/3)
(+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (.f64 y (sqrt.f64 x)))) (pow.f64 (pow.f64 (-.f64 1 x) 2) 1/3))
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/9) x)) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/9) x)))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (*.f64 y (sqrt.f64 x)))) (pow.f64 (pow.f64 (-.f64 1 x) 2) 1/3)))
(+.f64 (.f64 (+.f64 (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (-.f64 1 x)) 1/3) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (sqrt.f64 (pow.f64 x 3))))) (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (sqrt.f64 (pow.f64 x 3))))))) (.f64 -2/27 (.f64 (pow.f64 1 1/9) (.f64 (sqrt.f64 (pow.f64 x 3)) (/.f64 1 (-.f64 1 x)))))) (pow.f64 y 3)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/9) x)) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/9) x)))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (.f64 y (sqrt.f64 x)))) (pow.f64 (pow.f64 (-.f64 1 x) 2) 1/3))))
1
(*.f64 -1 x)
(*.f64 -1 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)

Outputs
1
(pow.f64 (-.f64 1 x) 1/3)
(cbrt.f64 (-.f64 1 x))
(+.f64 (pow.f64 (-.f64 1 x) 1/3) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/9) (*.f64 y (sqrt.f64 x)))))
(+.f64 (cbrt.f64 (-.f64 1 x)) (.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)) (.f64 y (sqrt.f64 x)))))
(fma.f64 (.f64 (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)) (*.f64 y (sqrt.f64 x)) (cbrt.f64 (-.f64 1 x)))
(fma.f64 (.f64 y (sqrt.f64 x)) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (*.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18))) (cbrt.f64 (-.f64 1 x)))
(fma.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (.f64 (sqrt.f64 x) (*.f64 y (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)))) (cbrt.f64 (-.f64 1 x)))
(+.f64 (pow.f64 (-.f64 1 x) 1/3) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/9) (.f64 (pow.f64 y 2) x))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/9) (.f64 y (sqrt.f64 x))))))
(+.f64 (cbrt.f64 (-.f64 1 x)) (fma.f64 -1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18)) (.f64 x (.f64 y y))) (.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)) (.f64 y (sqrt.f64 x))))))
(+.f64 (cbrt.f64 (-.f64 1 x)) (fma.f64 (.f64 (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)) (.f64 y (sqrt.f64 x)) (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18)) (.f64 (.f64 x (.f64 y y)) -1/9))))
(fma.f64 (.f64 y (sqrt.f64 x)) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18))) (fma.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18)) (.f64 x (.f64 -1/9 (*.f64 y y))) (cbrt.f64 (-.f64 1 x))))
(fma.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (.f64 (sqrt.f64 x) (.f64 y (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)))) (fma.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18) (.f64 y (.f64 (*.f64 x y) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18)))) (cbrt.f64 (-.f64 1 x))))
(+.f64 (pow.f64 (-.f64 1 x) 1/3) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/9) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/9) (.f64 y (sqrt.f64 x)))) (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (.f64 (+.f64 (.f64 -2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (sqrt.f64 (pow.f64 x 3))))) (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (sqrt.f64 (pow.f64 x 3))))) (pow.f64 y 3)))))))
(+.f64 (cbrt.f64 (-.f64 1 x)) (fma.f64 -1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18)) (.f64 x (.f64 y y))) (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)) (.f64 y (sqrt.f64 x))) (.f64 (.f64 -1/3 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)))) (.f64 (+.f64 (.f64 -2/9 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (sqrt.f64 (pow.f64 x 3)))) (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (sqrt.f64 (pow.f64 x 3))) 1/27)) (pow.f64 y 3))))))
(+.f64 (cbrt.f64 (-.f64 1 x)) (fma.f64 -1/9 (.f64 x (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18)) (.f64 y y))) (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)) (.f64 y (sqrt.f64 x))) (.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (sqrt.f64 (pow.f64 x 3))) -5/27) (pow.f64 y 3)))))))
(+.f64 (cbrt.f64 (-.f64 1 x)) (fma.f64 -1/9 (.f64 x (.f64 y (.f64 y (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18))))) (fma.f64 (.f64 y (sqrt.f64 x)) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18))) (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (.f64 (pow.f64 x 3/2) -5/27)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (.f64 -1/3 (pow.f64 y 3)))))))
(+.f64 (fma.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18) (.f64 (sqrt.f64 x) (.f64 y (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/18)))) (cbrt.f64 (-.f64 1 x))) (.f64 (.f64 y y) (+.f64 (.f64 -1/9 (.f64 x (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/18)))) (.f64 (.f64 -1/3 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)))) (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (pow.f64 x 3/2)) (*.f64 -5/27 y))))))
1
(pow.f64 (pow.f64 (-.f64 1 x) 2) 1/3)
(cbrt.f64 (pow.f64 (-.f64 1 x) 2))
(+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (.f64 y (sqrt.f64 x)))) (pow.f64 (pow.f64 (-.f64 1 x) 2) 1/3))
(fma.f64 2/3 (.f64 (.f64 y (sqrt.f64 x)) (*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2)))
(fma.f64 2/3 (.f64 y (.f64 (sqrt.f64 x) (*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2)))
(fma.f64 (.f64 y (sqrt.f64 x)) (.f64 2/3 (*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2)))
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/9) x)) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/9) x)))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (*.f64 y (sqrt.f64 x)))) (pow.f64 (pow.f64 (-.f64 1 x) 2) 1/3)))
(fma.f64 (.f64 y y) (.f64 (.f64 x (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18))) -1/9) (fma.f64 2/3 (.f64 (.f64 y (sqrt.f64 x)) (*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2))))
(fma.f64 (.f64 y y) (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18)) (.f64 x -1/9)) (fma.f64 2/3 (.f64 y (.f64 (sqrt.f64 x) (*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2))))
(fma.f64 (.f64 y (sqrt.f64 x)) (.f64 2/3 (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))) (fma.f64 y (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18)) (.f64 (*.f64 x -1/9) y)) (cbrt.f64 (pow.f64 (-.f64 1 x) 2))))
(fma.f64 y (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18)) (.f64 (.f64 x -1/9) y)) (fma.f64 (.f64 y (sqrt.f64 x)) (.f64 2/3 (*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2))))
(+.f64 (.f64 (+.f64 (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (-.f64 1 x)) 1/3) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (sqrt.f64 (pow.f64 x 3))))) (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/3) (sqrt.f64 (pow.f64 x 3))))))) (.f64 -2/27 (.f64 (pow.f64 1 1/9) (.f64 (sqrt.f64 (pow.f64 x 3)) (/.f64 1 (-.f64 1 x)))))) (pow.f64 y 3)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/9) x)) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/9) x)))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (.f64 y (sqrt.f64 x)))) (pow.f64 (pow.f64 (-.f64 1 x) 2) 1/3))))
(fma.f64 (fma.f64 -2/3 (.f64 (+.f64 (.f64 -2/9 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (sqrt.f64 (pow.f64 x 3)))) (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (sqrt.f64 (pow.f64 x 3))) 1/27)) (cbrt.f64 (/.f64 1 (-.f64 1 x)))) (.f64 -2/27 (.f64 (sqrt.f64 (pow.f64 x 3)) (/.f64 1 (-.f64 1 x))))) (pow.f64 y 3) (fma.f64 (.f64 y y) (.f64 (.f64 x (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18))) -1/9) (fma.f64 2/3 (.f64 (.f64 y (sqrt.f64 x)) (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2)))))
(fma.f64 (pow.f64 y 3) (fma.f64 -2/3 (.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (sqrt.f64 (pow.f64 x 3))) -5/27) (cbrt.f64 (/.f64 1 (-.f64 1 x)))) (.f64 -2/27 (/.f64 (sqrt.f64 (pow.f64 x 3)) (-.f64 1 x)))) (fma.f64 (.f64 y y) (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18)) (.f64 x -1/9)) (fma.f64 2/3 (.f64 y (.f64 (sqrt.f64 x) (*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2)))))
(fma.f64 y (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18)) (.f64 (.f64 x -1/9) y)) (fma.f64 (pow.f64 y 3) (fma.f64 (cbrt.f64 (/.f64 1 (-.f64 1 x))) (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (pow.f64 x 3/2)) 10/81) (.f64 (pow.f64 x 3/2) (/.f64 -2/27 (-.f64 1 x)))) (fma.f64 (.f64 y (sqrt.f64 x)) (.f64 2/3 (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2)))))
(fma.f64 y (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 4)) 1/18)) (.f64 (.f64 x -1/9) y)) (fma.f64 (pow.f64 y 3) (fma.f64 (pow.f64 x 3/2) (/.f64 -2/27 (-.f64 1 x)) (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 2))) (.f64 (pow.f64 x 3/2) (cbrt.f64 (/.f64 1 (-.f64 1 x))))) 10/81)) (fma.f64 (.f64 y (sqrt.f64 x)) (.f64 2/3 (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))) (cbrt.f64 (pow.f64 (-.f64 1 x) 2)))))
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

localize3.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	10.7b	(.f64 x (.f64 y y))
✓	25.3b	(sqrt.f64 (.f64 x (.f64 y y)))

Compiler

Compiled 18 to 5 computations (72.2% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

6 calls:

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

rewrite52.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`pow1_binary64`
511×	`add-sqr-sqrt_binary64`
496×	`add-log-exp_binary64`
496×	`log1p-expm1-u_binary64`
496×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	121	6
2	1448	6

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

Outputs

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

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

36 → 26

Calls

Call 1

Inputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(.f64 -1 (.f64 y (sqrt.f64 x)))
(.f64 -1 (.f64 y (sqrt.f64 x)))
(.f64 -1 (.f64 y (sqrt.f64 x)))
(.f64 -1 (.f64 y (sqrt.f64 x)))

Outputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(.f64 -1 (.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(.f64 -1 (.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(.f64 -1 (.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(.f64 -1 (.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 y (neg.f64 (sqrt.f64 x)))

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
	10.7b	(.f64 x (.f64 y y))
	25.3b	(sqrt.f64 (.f64 x (.f64 y y)))

Compiler

Compiled 32 to 11 computations (65.6% saved)

series2.0ms (0%)

Counts

1 → 15

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
0.0ms	x	@	-inf	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
0.0ms	x	@	inf	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
0.0ms	y	@	-inf	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
0.0ms	y	@	0	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))

rewrite101.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`fma-def_binary64`
464×	`log-prod_binary64`
348×	`pow-prod-down_binary64`
337×	`exp-prod_binary64`
252×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	197	10
2	2803	10

Stop Event

1×	node limit

Counts

1 → 64

Calls

Call 1

Inputs
(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))

Outputs

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

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

224×	`fma-neg_binary64`
110×	`fma-def_binary64`
73×	`cancel-sign-sub-inv_binary64`
44×	`sub-neg_binary64`
34×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	124
1	32	121
2	67	121
3	140	115
4	264	115
5	423	115
6	702	115
7	848	115
8	893	115
9	897	115

Stop Event

1×

saturated

Counts

79 → 74

Calls

Call 1

Inputs
1
(*.f64 -1 x)
(*.f64 -1 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(.f64 -1 (.f64 y (sqrt.f64 x)))
(-.f64 (+.f64 (.f64 -1 (.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (+.f64 (.f64 -1 (.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (+.f64 (.f64 -1 (.f64 y (sqrt.f64 x))) 1) x)

Outputs
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(.f64 -1 (.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (neg.f64 y))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(-.f64 (+.f64 (.f64 -1 (.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (fma.f64 -1 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) 1) x)
(-.f64 1 (+.f64 (*.f64 y (sqrt.f64 x)) x))
(-.f64 1 (fma.f64 y (sqrt.f64 x) x))
(-.f64 (+.f64 (.f64 -1 (.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (fma.f64 -1 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) 1) x)
(-.f64 1 (+.f64 (*.f64 y (sqrt.f64 x)) x))
(-.f64 1 (fma.f64 y (sqrt.f64 x) x))
(-.f64 (+.f64 (.f64 -1 (.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (fma.f64 -1 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) 1) x)
(-.f64 1 (+.f64 (*.f64 y (sqrt.f64 x)) x))
(-.f64 1 (fma.f64 y (sqrt.f64 x) x))

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 x))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))
✓	10.7b	(.f64 x (.f64 y (neg.f64 y)))
✓	14.3b	(/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y))))

Compiler

Compiled 69 to 19 computations (72.5% saved)

series14.0ms (0.2%)

Counts

3 → 54

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))
1.0ms	x	@	inf	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))
1.0ms	x	@	0	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))
1.0ms	y	@	0	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))
1.0ms	y	@	inf	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))

rewrite86.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`log-prod_binary64`
550×	`fma-def_binary64`
302×	`fma-neg_binary64`
224×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	296	45
2	4701	45

Stop Event

1×	node limit

Counts

3 → 143

Calls

Call 1

Inputs

(/.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))) (*.f64 x (*.f64 y (neg.f64 y))))

(*.f64 x (*.f64 y (neg.f64 y)))

(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))) (*.f64 x (*.f64 y (neg.f64 y)))))

Outputs

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

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

515×	`times-frac_binary64`
401×	`div-sub_binary64`
350×	`distribute-neg-frac_binary64`
275×	`associate-/l*_binary64`
260×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	978
1	237	890
2	849	860
3	4919	856

Stop Event

1×	node limit

Counts

197 → 173

Calls

Call 1

Inputs
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 1 (pow.f64 y 2))
(/.f64 1 (pow.f64 y 2))
(.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(pow.f64 y 2)
(pow.f64 y 2)
(.f64 -1 (/.f64 (.f64 (pow.f64 y 2) x) (-.f64 1 x)))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) x) (-.f64 1 x))) (.f64 -1 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 (pow.f64 x 3)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) x) (-.f64 1 x))) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 4) (pow.f64 x 2)) (pow.f64 (-.f64 1 x) 3))) (.f64 -1 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 (pow.f64 x 3))))))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) x) (-.f64 1 x))) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 4) (pow.f64 x 2)) (pow.f64 (-.f64 1 x) 3))) (+.f64 (.f64 -1 (.f64 (/.f64 (pow.f64 y 5) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 5)))) (.f64 -1 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 (pow.f64 x 3)))))))
(*.f64 y (sqrt.f64 x))
(+.f64 (.f64 y (sqrt.f64 x)) (.f64 -1 (-.f64 x 1)))
(+.f64 (.f64 y (sqrt.f64 x)) (+.f64 (.f64 -1 (-.f64 x 1)) (.f64 -1 (.f64 (/.f64 (*.f64 (-.f64 x 1) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x))))))
(+.f64 (.f64 y (sqrt.f64 x)) (+.f64 (.f64 -1 (-.f64 x 1)) (+.f64 (.f64 -1 (/.f64 (.f64 (-.f64 x 1) (pow.f64 (-.f64 1 x) 2)) (.f64 (pow.f64 y 2) x))) (.f64 -1 (.f64 (/.f64 (.f64 (-.f64 x 1) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))))))
(*.f64 y (sqrt.f64 x))
(+.f64 (.f64 y (sqrt.f64 x)) (.f64 -1 (-.f64 x 1)))
(+.f64 (.f64 y (sqrt.f64 x)) (+.f64 (.f64 -1 (-.f64 x 1)) (.f64 -1 (.f64 (/.f64 (*.f64 (-.f64 x 1) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x))))))
(+.f64 (.f64 y (sqrt.f64 x)) (+.f64 (.f64 -1 (-.f64 x 1)) (+.f64 (.f64 -1 (/.f64 (.f64 (-.f64 x 1) (pow.f64 (-.f64 1 x) 2)) (.f64 (pow.f64 y 2) x))) (.f64 -1 (.f64 (/.f64 (.f64 (-.f64 x 1) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))))))

Outputs
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 (/.f64 -1 (*.f64 y y)) x)
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 1 (pow.f64 y 2))
(/.f64 1 (*.f64 y y))
(/.f64 1 (pow.f64 y 2))
(/.f64 1 (*.f64 y y))
(.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x)))
(neg.f64 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)))
(/.f64 (neg.f64 (-.f64 1 x)) (.f64 y (.f64 y x)))
(/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x))
(/.f64 (+.f64 -1 x) (.f64 y (.f64 y x)))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 y (.f64 y x))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 y (.f64 y x))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 y (.f64 y x))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 y (.f64 y x))))
(+.f64 (.f64 -1 (/.f64 (-.f64 1 x) (.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 y (.f64 y x))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 y (.f64 y x))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 y (.f64 y x))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 y (.f64 y x))))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 y (.f64 y x))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 y (.f64 y x))))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 y (.f64 y x))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 y (.f64 y x))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 y (.f64 y x))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 y (.f64 y x))))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 y (.f64 y x))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 y (.f64 y x))))
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (.f64 -1 (/.f64 (-.f64 (/.f64 1 x) 1) (pow.f64 y 2))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (.f64 (.f64 y y) x)) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (.f64 y (.f64 y x))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (/.f64 (+.f64 -1 x) y) (*.f64 y x)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (.f64 y (.f64 y x))))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 y (neg.f64 (.f64 y x)))
(.f64 y (.f64 x (neg.f64 y)))
(pow.f64 y 2)
(*.f64 y y)
(pow.f64 y 2)
(*.f64 y y)
(.f64 -1 (/.f64 (.f64 (pow.f64 y 2) x) (-.f64 1 x)))
(/.f64 (neg.f64 (.f64 (.f64 y y) x)) (-.f64 1 x))
(/.f64 (.f64 (.f64 y y) (neg.f64 x)) (-.f64 1 x))
(.f64 (/.f64 (.f64 y (neg.f64 y)) (-.f64 1 x)) x)
(/.f64 y (/.f64 (+.f64 -1 x) (*.f64 y x)))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) x) (-.f64 1 x))) (.f64 -1 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 (pow.f64 x 3)))))
(.f64 -1 (+.f64 (/.f64 (.f64 y y) (/.f64 (-.f64 1 x) x)) (/.f64 (*.f64 (pow.f64 y 3) (sqrt.f64 (pow.f64 x 3))) (pow.f64 (-.f64 1 x) 2))))
(-.f64 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (neg.f64 (fabs.f64 (pow.f64 x 3/2)))) (.f64 (/.f64 (*.f64 y y) (-.f64 1 x)) x))
(neg.f64 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (pow.f64 x 3/2) (/.f64 (*.f64 y x) (/.f64 (-.f64 1 x) y))))
(-.f64 (/.f64 y (/.f64 (+.f64 -1 x) (*.f64 y x))) (/.f64 (pow.f64 x 3/2) (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3))))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) x) (-.f64 1 x))) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 4) (pow.f64 x 2)) (pow.f64 (-.f64 1 x) 3))) (.f64 -1 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 (pow.f64 x 3))))))
(fma.f64 -1 (/.f64 (.f64 y y) (/.f64 (-.f64 1 x) x)) (fma.f64 -1 (/.f64 (pow.f64 y 4) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 x x))) (neg.f64 (/.f64 (*.f64 (pow.f64 y 3) (sqrt.f64 (pow.f64 x 3))) (pow.f64 (-.f64 1 x) 2)))))
(-.f64 (-.f64 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (neg.f64 (fabs.f64 (pow.f64 x 3/2)))) (/.f64 (pow.f64 y 4) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 x x)))) (.f64 (/.f64 (.f64 y y) (-.f64 1 x)) x))
(neg.f64 (fma.f64 (/.f64 y (/.f64 (-.f64 1 x) y)) x (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (pow.f64 x 3/2) (.f64 (.f64 x x) (/.f64 (pow.f64 y 4) (pow.f64 (-.f64 1 x) 3))))))
(-.f64 (/.f64 y (/.f64 (+.f64 -1 x) (.f64 y x))) (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (pow.f64 x 3/2) (.f64 (*.f64 x x) (/.f64 (pow.f64 y 4) (pow.f64 (-.f64 1 x) 3)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) x) (-.f64 1 x))) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 4) (pow.f64 x 2)) (pow.f64 (-.f64 1 x) 3))) (+.f64 (.f64 -1 (.f64 (/.f64 (pow.f64 y 5) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 5)))) (.f64 -1 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 (pow.f64 x 3)))))))
(fma.f64 -1 (/.f64 (.f64 y y) (/.f64 (-.f64 1 x) x)) (fma.f64 -1 (/.f64 (pow.f64 y 4) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 x x))) (fma.f64 -1 (.f64 (/.f64 (pow.f64 y 5) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 5))) (neg.f64 (/.f64 (.f64 (pow.f64 y 3) (sqrt.f64 (pow.f64 x 3))) (pow.f64 (-.f64 1 x) 2))))))
(-.f64 (-.f64 (neg.f64 (fma.f64 (/.f64 (pow.f64 y 5) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 5)) (.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (fabs.f64 (pow.f64 x 3/2))))) (/.f64 (pow.f64 y 4) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 x x)))) (.f64 (/.f64 (.f64 y y) (-.f64 1 x)) x))
(-.f64 (neg.f64 (fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 (-.f64 1 x) 3)) (.f64 x x) (fma.f64 (/.f64 (pow.f64 y 5) (pow.f64 (-.f64 1 x) 4)) (pow.f64 x 5/2) (/.f64 (.f64 (pow.f64 y 3) (pow.f64 x 3/2)) (pow.f64 (-.f64 1 x) 2))))) (/.f64 (*.f64 y x) (/.f64 (-.f64 1 x) y)))
(-.f64 (/.f64 y (/.f64 (+.f64 -1 x) (.f64 y x))) (fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 (-.f64 1 x) 3)) (.f64 x x) (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 2)) (pow.f64 x 3/2) (/.f64 (pow.f64 y 5) (/.f64 (pow.f64 (-.f64 1 x) 4) (pow.f64 x 5/2))))))
(*.f64 y (sqrt.f64 x))
(+.f64 (.f64 y (sqrt.f64 x)) (.f64 -1 (-.f64 x 1)))
(fma.f64 y (sqrt.f64 x) (neg.f64 (+.f64 x -1)))
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(+.f64 (.f64 y (sqrt.f64 x)) (+.f64 (.f64 -1 (-.f64 x 1)) (.f64 -1 (.f64 (/.f64 (*.f64 (-.f64 x 1) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x))))))
(fma.f64 y (sqrt.f64 x) (.f64 -1 (+.f64 (+.f64 x -1) (/.f64 (.f64 (*.f64 (-.f64 1 x) (+.f64 x -1)) (sqrt.f64 (/.f64 1 x))) y))))
(fma.f64 y (sqrt.f64 x) (fma.f64 (/.f64 (-.f64 1 x) (/.f64 y (-.f64 1 x))) (sqrt.f64 (/.f64 1 x)) (-.f64 1 x)))
(fma.f64 y (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (pow.f64 (-.f64 1 x) 2) y) (-.f64 1 x)))
(+.f64 (.f64 y (sqrt.f64 x)) (+.f64 (.f64 -1 (-.f64 x 1)) (+.f64 (.f64 -1 (/.f64 (.f64 (-.f64 x 1) (pow.f64 (-.f64 1 x) 2)) (.f64 (pow.f64 y 2) x))) (.f64 -1 (.f64 (/.f64 (.f64 (-.f64 x 1) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))))))
(fma.f64 y (sqrt.f64 x) (fma.f64 -1 (+.f64 x -1) (fma.f64 -1 (/.f64 (.f64 (pow.f64 (-.f64 1 x) 2) (+.f64 x -1)) (.f64 (.f64 y y) x)) (neg.f64 (/.f64 (.f64 (*.f64 (-.f64 1 x) (+.f64 x -1)) (sqrt.f64 (/.f64 1 x))) y)))))
(+.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) (fma.f64 (/.f64 (-.f64 1 x) (/.f64 y (-.f64 1 x))) (sqrt.f64 (/.f64 1 x)) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 y (.f64 y x)))))
(+.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) (fma.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (pow.f64 (-.f64 1 x) 2) y) (/.f64 (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 y x)) y)))
(+.f64 (-.f64 1 x) (fma.f64 y (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (pow.f64 (-.f64 1 x) 2) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 y (.f64 y x))))))
(*.f64 y (sqrt.f64 x))
(+.f64 (.f64 y (sqrt.f64 x)) (.f64 -1 (-.f64 x 1)))
(fma.f64 y (sqrt.f64 x) (neg.f64 (+.f64 x -1)))
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(+.f64 (.f64 y (sqrt.f64 x)) (+.f64 (.f64 -1 (-.f64 x 1)) (.f64 -1 (.f64 (/.f64 (*.f64 (-.f64 x 1) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x))))))
(fma.f64 y (sqrt.f64 x) (.f64 -1 (+.f64 (+.f64 x -1) (/.f64 (.f64 (*.f64 (-.f64 1 x) (+.f64 x -1)) (sqrt.f64 (/.f64 1 x))) y))))
(fma.f64 y (sqrt.f64 x) (fma.f64 (/.f64 (-.f64 1 x) (/.f64 y (-.f64 1 x))) (sqrt.f64 (/.f64 1 x)) (-.f64 1 x)))
(fma.f64 y (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (pow.f64 (-.f64 1 x) 2) y) (-.f64 1 x)))
(+.f64 (.f64 y (sqrt.f64 x)) (+.f64 (.f64 -1 (-.f64 x 1)) (+.f64 (.f64 -1 (/.f64 (.f64 (-.f64 x 1) (pow.f64 (-.f64 1 x) 2)) (.f64 (pow.f64 y 2) x))) (.f64 -1 (.f64 (/.f64 (.f64 (-.f64 x 1) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))))))
(fma.f64 y (sqrt.f64 x) (fma.f64 -1 (+.f64 x -1) (fma.f64 -1 (/.f64 (.f64 (pow.f64 (-.f64 1 x) 2) (+.f64 x -1)) (.f64 (.f64 y y) x)) (neg.f64 (/.f64 (.f64 (*.f64 (-.f64 1 x) (+.f64 x -1)) (sqrt.f64 (/.f64 1 x))) y)))))
(+.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) (fma.f64 (/.f64 (-.f64 1 x) (/.f64 y (-.f64 1 x))) (sqrt.f64 (/.f64 1 x)) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 y (.f64 y x)))))
(+.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) (fma.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (pow.f64 (-.f64 1 x) 2) y) (/.f64 (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 y x)) y)))
(+.f64 (-.f64 1 x) (fma.f64 y (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (pow.f64 (-.f64 1 x) 2) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (.f64 y (.f64 y x))))))

eval218.0ms (3.2%)

Compiler: Compiled 10119 to 5470 computations (45.9% saved)

prune89.0ms (1.3%)

Pruning

18 alts after pruning (11 fresh and 7 done)

	Pruned	Kept	Total
New	501	7	508
Fresh	2	4	6
Picked	0	1	1
Done	1	6	7
Total	504	18	522

Error

0.0b

Counts

522 → 18

Alt Table

Click to see full alt table

Status	Error	Program
▶	39.8b	(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
▶	62.5b	(/.f64 1 (/.f64 -1 (.f64 y (.f64 y x))))
✓	24.3b	(-.f64 1 x)
	62.6b	(/.f64 y (/.f64 (+.f64 -1 x) (*.f64 y x)))
▶	52.6b	(.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 y))
▶	62.2b	(*.f64 y y)
	58.2b	(/.f64 (.f64 x (.f64 y (neg.f64 y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	42.4b	(neg.f64 x)
	42.4b	(/.f64 1 (/.f64 -1 x))
✓	59.4b	(sqrt.f64 (.f64 x (.f64 y y)))
✓	58.2b	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))
	39.7b	(.f64 (pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2) (cbrt.f64 (.f64 y (sqrt.f64 x))))
	58.2b	(.f64 (/.f64 1 (neg.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))) (.f64 x (*.f64 y y)))
	44.9b	1
✓	22.1b	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
✓	39.8b	(*.f64 y (sqrt.f64 x))
▶	1.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))

Compiler

Compiled 361 to 245 computations (32.1% saved)

localize69.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))
	0.4b	(cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))
✓	0.4b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 2)
✓	0.4b	(cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))

Compiler

Compiled 133 to 77 computations (42.1% saved)

series67.0ms (1%)

Counts

3 → 45

Calls

18 calls:

Time	Variable		Point	Expression
9.0ms	x	@	inf	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 2)
9.0ms	y	@	-inf	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))
5.0ms	x	@	inf	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))
5.0ms	y	@	inf	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))
4.0ms	x	@	-inf	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))

rewrite113.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

465×	`log-prod_binary64`
345×	`exp-prod_binary64`
321×	`pow-prod-down_binary64`
267×	`pow2_binary64`
230×	`prod-diff_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	57
1	244	48
2	2782	46

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

Inputs

(cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))

(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 2)

(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))

Outputs

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(#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/9 (log.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2/3 (log.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (*.f64 4/3 (log.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 4/3 (log.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 1/3) 4/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 1) 4/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 1/3) 4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/9 (log.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 1) 4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 2/3 (log.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 4/3 (log.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) 1) 1))))))

simplify113.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

396×	`associate-r_binary64`
381×	`fma-def_binary64`
364×	`associate-/r/_binary64`
314×	`associate-l_binary64`
308×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	5364
1	1326	4544
2	5775	3944

Stop Event

1×	node limit

Counts

161 → 199

Calls

Call 1

Inputs
1
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1))))
(pow.f64 (*.f64 -1 x) 1/9)
(pow.f64 (-.f64 1 x) 1/9)
(+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/9) (*.f64 y (sqrt.f64 x)))) (pow.f64 (-.f64 1 x) 1/9))
(+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/9) (.f64 y (sqrt.f64 x)))) (+.f64 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (.f64 (pow.f64 y 2) (+.f64 (.f64 1/162 (/.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 -1/18 (/.f64 x (pow.f64 (-.f64 1 x) 2)))))) (pow.f64 (-.f64 1 x) 1/9)))
(+.f64 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (.f64 (pow.f64 y 3) (+.f64 (.f64 1/27 (.f64 (sqrt.f64 (pow.f64 x 3)) (/.f64 1 (pow.f64 (-.f64 1 x) 3)))) (+.f64 (.f64 -1/162 (.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 3)) (sqrt.f64 (pow.f64 x 3)))) (.f64 1/4374 (.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 3)) (sqrt.f64 (pow.f64 x 3)))))))) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/9) (.f64 y (sqrt.f64 x)))) (+.f64 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (.f64 (pow.f64 y 2) (+.f64 (.f64 1/162 (/.f64 x (pow.f64 (-.f64 1 x) 2))) (*.f64 -1/18 (/.f64 x (pow.f64 (-.f64 1 x) 2)))))) (pow.f64 (-.f64 1 x) 1/9))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x)))))
(+.f64 (.f64 1/9 (.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))) (exp.f64 (.f64 1/9 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))))
(+.f64 (.f64 1/9 (.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x)))))) (pow.f64 y 2)) (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x)))))))
(+.f64 (.f64 1/9 (.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x)))))) (pow.f64 y 2)) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) (+.f64 (.f64 1/4374 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 (-.f64 1 x) 3))) (+.f64 (.f64 1/27 (.f64 (pow.f64 (-.f64 1 x) 3) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 -1/162 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 (-.f64 1 x) 3)))))) (pow.f64 y 3)) (exp.f64 (.f64 1/9 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))))))
(exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (*.f64 -1 (log.f64 (/.f64 -1 y))))))
(+.f64 (.f64 1/9 (.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))) (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (*.f64 -1 (log.f64 (/.f64 -1 y)))))))
(+.f64 (.f64 1/9 (.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))) (+.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) (/.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (*.f64 -1 (log.f64 (/.f64 -1 y))))))) (pow.f64 y 2))))
(+.f64 (.f64 1/9 (.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))) (+.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y))))))) (pow.f64 y 2)) (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) (+.f64 (.f64 1/162 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 (-.f64 1 x) 3))) (+.f64 (.f64 -1/4374 (.f64 (pow.f64 (-.f64 1 x) 3) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 -1/27 (.f64 (pow.f64 (-.f64 1 x) 3) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))) (pow.f64 y 3))))))
1
(pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1)))) 2)
(pow.f64 (pow.f64 x 2) 1/9)
(pow.f64 (pow.f64 (-.f64 1 x) 2) 1/9)
(+.f64 (pow.f64 (pow.f64 (-.f64 1 x) 2) 1/9) (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/9) (*.f64 y (sqrt.f64 x)))))
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 2 (.f64 (pow.f64 (.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/9) (+.f64 (.f64 1/162 (/.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 -1/18 (/.f64 x (pow.f64 (-.f64 1 x) 2)))))) (.f64 1/81 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 16)) 1/9) x)))) (+.f64 (pow.f64 (pow.f64 (-.f64 1 x) 2) 1/9) (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/9) (*.f64 y (sqrt.f64 x))))))
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 2 (.f64 (pow.f64 (.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/9) (+.f64 (.f64 1/162 (/.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 -1/18 (/.f64 x (pow.f64 (-.f64 1 x) 2)))))) (.f64 1/81 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 16)) 1/9) x)))) (+.f64 (pow.f64 (pow.f64 (-.f64 1 x) 2) 1/9) (+.f64 (.f64 (+.f64 (.f64 2 (.f64 (pow.f64 (.f64 1 (pow.f64 (-.f64 1 x) 2)) 1/9) (+.f64 (.f64 1/27 (.f64 (sqrt.f64 (pow.f64 x 3)) (/.f64 1 (pow.f64 (-.f64 1 x) 3)))) (+.f64 (.f64 -1/162 (.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 3)) (sqrt.f64 (pow.f64 x 3)))) (.f64 1/4374 (.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 3)) (sqrt.f64 (pow.f64 x 3)))))))) (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/9) (.f64 (+.f64 (.f64 1/162 (/.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 -1/18 (/.f64 x (pow.f64 (-.f64 1 x) 2)))) (sqrt.f64 x))))) (pow.f64 y 3)) (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 7)) 1/9) (.f64 y (sqrt.f64 x)))))))
(pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (.f64 2/9 (.f64 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))))
(+.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (+.f64 (.f64 2/9 (.f64 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 1/81 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (pow.f64 (-.f64 1 x) 2)) (.f64 (pow.f64 y 2) x))) (.f64 2 (/.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2)) (pow.f64 y 2))))))
(+.f64 (.f64 2/9 (.f64 (/.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (-.f64 1 x))) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 x)))) (+.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (+.f64 (.f64 2/9 (.f64 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (+.f64 (.f64 1/4374 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 (-.f64 1 x) 3))) (+.f64 (.f64 1/27 (.f64 (pow.f64 (-.f64 1 x) 3) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 -1/162 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 (-.f64 1 x) 3)))))) (pow.f64 y 3))) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2)) (pow.f64 y 2))) (.f64 1/81 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x))))) 2) (pow.f64 (-.f64 1 x) 2)) (.f64 (pow.f64 y 2) x))))))))
(pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (*.f64 -1 (log.f64 (/.f64 -1 y)))))) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (.f64 2/9 (.f64 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (*.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))))
(+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2)) (pow.f64 y 2))) (+.f64 (.f64 1/81 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (pow.f64 (-.f64 1 x) 2)) (.f64 (pow.f64 y 2) x))) (+.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (.f64 2/9 (.f64 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x)))))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 2 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (+.f64 (.f64 1/162 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 (-.f64 1 x) 3))) (+.f64 (.f64 -1/4374 (.f64 (pow.f64 (-.f64 1 x) 3) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 -1/27 (.f64 (pow.f64 (-.f64 1 x) 3) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))) (.f64 -2/9 (.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (-.f64 1 x))) (sqrt.f64 (/.f64 1 x))))) (pow.f64 y 3))) (+.f64 (.f64 1/81 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (pow.f64 (-.f64 1 x) 2)) (.f64 (pow.f64 y 2) x))) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 1/162 (/.f64 (pow.f64 (-.f64 1 x) 2) x)) (.f64 -1/18 (/.f64 (pow.f64 (-.f64 1 x) 2) x))) (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2)) (pow.f64 y 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (.f64 2/9 (.f64 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 x))) (*.f64 -1 (log.f64 (/.f64 -1 y)))))) 2) (-.f64 1 x)) y) (sqrt.f64 (/.f64 1 x))))))))
1
(pow.f64 (pow.f64 x 4) 1/9)
(pow.f64 (pow.f64 x 4) 1/9)
(pow.f64 (pow.f64 (-.f64 1 x) 4) 1/9)
(+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 14)) 1/9) (.f64 y (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (*.f64 (-.f64 1 x) (sqrt.f64 x)))))) (pow.f64 (pow.f64 (-.f64 1 x) 4) 1/9))
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(exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2)))))
(+.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2))))) (.f64 2/9 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2))))) (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x)))) (*.f64 y x))))
(+.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2))))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2))))) (+.f64 (.f64 2/81 (/.f64 (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 2) (pow.f64 x 2))) (.f64 1/18 (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 (pow.f64 (-.f64 1 x) 2) x) (+.f64 (.f64 x (pow.f64 (-.f64 1 x) 2)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 2))) (pow.f64 x 2))) (.f64 -4 (/.f64 (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 2) (pow.f64 x 2))))))) (pow.f64 y 2)) (.f64 2/9 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2))))) (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x)))) (.f64 y x)))))
(+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2))))) (+.f64 (.f64 1/81 (/.f64 (.f64 (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 (pow.f64 (-.f64 1 x) 2) x) (+.f64 (.f64 x (pow.f64 (-.f64 1 x) 2)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 2))) (pow.f64 x 2))) (.f64 -4 (/.f64 (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 2) (pow.f64 x 2)))) (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x)))) x)) (+.f64 (.f64 4/2187 (/.f64 (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 3) (pow.f64 x 3))) (.f64 1/54 (+.f64 (.f64 16 (/.f64 (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 3) (pow.f64 x 3))) (+.f64 (.f64 12 (/.f64 (.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) (pow.f64 (-.f64 1 x) 2)) (pow.f64 x 2))) (.f64 -12 (/.f64 (.f64 (+.f64 (.f64 (pow.f64 (-.f64 1 x) 2) x) (+.f64 (.f64 x (pow.f64 (-.f64 1 x) 2)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 2))) (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x)))) (pow.f64 x 3))))))))) (pow.f64 y 3)) (+.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2))))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2))))) (+.f64 (.f64 2/81 (/.f64 (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 2) (pow.f64 x 2))) (.f64 1/18 (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 (pow.f64 (-.f64 1 x) 2) x) (+.f64 (.f64 x (pow.f64 (-.f64 1 x) 2)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 2))) (pow.f64 x 2))) (.f64 -4 (/.f64 (pow.f64 (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x))) 2) (pow.f64 x 2))))))) (pow.f64 y 2)) (.f64 2/9 (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (.f64 -4 (log.f64 (/.f64 1 y))) (log.f64 (pow.f64 x 2))))) (+.f64 (.f64 (sqrt.f64 x) (-.f64 1 x)) (.f64 (-.f64 1 x) (sqrt.f64 x)))) (.f64 y x))))))
(exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y))))))
(+.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y)))))) (.f64 -2/9 (/.f64 (.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) (exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y))))))) (*.f64 y x))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 2/81 (/.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 2) (pow.f64 x 2))) (.f64 1/18 (+.f64 (.f64 -4 (/.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 2) (pow.f64 x 2))) (.f64 2 (/.f64 (+.f64 (.f64 (pow.f64 (-.f64 1 x) 2) x) (+.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 2) (.f64 x (pow.f64 (-.f64 1 x) 2)))) (pow.f64 x 2)))))) (exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y))))))) (pow.f64 y 2)) (+.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y)))))) (.f64 -2/9 (/.f64 (.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) (exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y))))))) (.f64 y x)))))
(+.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y)))))) (+.f64 (.f64 -2/9 (/.f64 (.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) (exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y))))))) (.f64 y x))) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 (.f64 4/2187 (/.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 3) (pow.f64 x 3))) (+.f64 (.f64 1/54 (+.f64 (.f64 16 (/.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 3) (pow.f64 x 3))) (+.f64 (.f64 12 (/.f64 (.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) (pow.f64 (-.f64 1 x) 2)) (pow.f64 x 2))) (.f64 -12 (/.f64 (.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) (+.f64 (.f64 (pow.f64 (-.f64 1 x) 2) x) (+.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 2) (.f64 x (pow.f64 (-.f64 1 x) 2))))) (pow.f64 x 3)))))) (.f64 1/81 (/.f64 (.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) (+.f64 (.f64 -4 (/.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 2) (pow.f64 x 2))) (.f64 2 (/.f64 (+.f64 (.f64 (pow.f64 (-.f64 1 x) 2) x) (+.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 2) (.f64 x (pow.f64 (-.f64 1 x) 2)))) (pow.f64 x 2))))) x)))) (exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y))))))) (pow.f64 y 3))) (/.f64 (.f64 (exp.f64 (.f64 1/9 (+.f64 (log.f64 (pow.f64 x 2)) (.f64 -4 (log.f64 (/.f64 -1 y)))))) (+.f64 (.f64 2/81 (/.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 2) (pow.f64 x 2))) (.f64 1/18 (+.f64 (.f64 -4 (/.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 2) (pow.f64 x 2))) (.f64 2 (/.f64 (+.f64 (.f64 (pow.f64 (-.f64 1 x) 2) x) (+.f64 (pow.f64 (+.f64 (.f64 -1 (.f64 (-.f64 1 x) (sqrt.f64 x))) (.f64 -1 (.f64 (sqrt.f64 x) (-.f64 1 x)))) 2) (*.f64 x (pow.f64 (-.f64 1 x) 2)))) (pow.f64 x 2))))))) (pow.f64 y 2)))))

Outputs
1
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 1/9) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1)))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 -1) (log.f64 x)))
(pow.f64 (*.f64 -1 x) 1/9)
(*.f64 (pow.f64 (neg.f64 x) 1/18) (pow.f64 (neg.f64 x) 1/18))
(pow.f64 (-.f64 1 x) 1/9)
(*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))
(+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/9) (*.f64 y (sqrt.f64 x)))) (pow.f64 (-.f64 1 x) 1/9))
(fma.f64 1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18)) (.f64 y (sqrt.f64 x))) (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)))
(fma.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18) (.f64 y (sqrt.f64 x)))) (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)))
(+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/9) (.f64 y (sqrt.f64 x)))) (+.f64 (.f64 (pow.f64 (.f64 1 (-.f64 1 x)) 1/9) (.f64 (pow.f64 y 2) (+.f64 (.f64 1/162 (/.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 -1/18 (/.f64 x (pow.f64 (-.f64 1 x) 2)))))) (pow.f64 (-.f64 1 x) 1/9)))
(fma.f64 1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18)) (.f64 y (sqrt.f64 x))) (fma.f64 (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)) (.f64 (.f64 y y) (.f64 (/.f64 x (pow.f64 (-.f64 1 x) 2)) -4/81)) (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18))))
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(fma.f64 (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)) (.f64 (pow.f64 y 3) (fma.f64 1/27 (.f64 (sqrt.f64 (pow.f64 x 3)) (/.f64 1 (pow.f64 (-.f64 1 x) 3))) (.f64 (.f64 (sqrt.f64 (pow.f64 x 3)) (/.f64 1 (pow.f64 (-.f64 1 x) 3))) -13/2187))) (fma.f64 1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18)) (.f64 y (sqrt.f64 x))) (fma.f64 (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)) (.f64 (.f64 y y) (.f64 (/.f64 x (pow.f64 (-.f64 1 x) 2)) -4/81)) (*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)))))
(fma.f64 (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)) (.f64 (pow.f64 y 3) (.f64 (/.f64 (sqrt.f64 (pow.f64 x 3)) (pow.f64 (-.f64 1 x) 3)) 68/2187)) (fma.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18) (.f64 y (sqrt.f64 x)))) (.f64 (+.f64 (.f64 y (.f64 y (/.f64 (.f64 x -4/81) (pow.f64 (-.f64 1 x) 2)))) 1) (*.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)))))
(+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18) (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 x) 8)) 1/18) (.f64 y (sqrt.f64 x))))) (.f64 (.f64 (pow.f64 (-.f64 1 x) 1/18) (pow.f64 (-.f64 1 x) 1/18)) (+.f64 (+.f64 (.f64 y (.f64 y (/.f64 (.f64 x -4/81) (pow.f64 (-.f64 1 x) 2)))) 1) (.f64 (pow.f64 y 3) (*.f64 (/.f64 (pow.f64 x 3/2) (pow.f64 (-.f64 1 x) 3)) 68/2187)))))
(exp.f64 (.f64 1/9 (+.f64 (.f64 -1 (log.f64 (/.f64 1 y))) (log.f64 (sqrt.f64 x)))))
(pow.f64 (exp.f64 1/9) (fma.f64 -1 (neg.f64 (log.f64 y)) (log.f64 (sqrt.f64 x))))
(pow.f64 (exp.f64 1/9) (+.f64 (log.f64 y) (log.f64 (sqrt.f64 x))))
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(+.f64 (pow.f64 (exp.f64 1/9) (+.f64 (.f64 2 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4))) (fma.f64 -2/9 (/.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) (/.f64 (.f64 x y) (pow.f64 (exp.f64 1/9) (+.f64 (.f64 2 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4))))) (fma.f64 -1 (/.f64 (fma.f64 4/2187 (/.f64 (pow.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) 3) (pow.f64 x 3)) (fma.f64 1/54 (fma.f64 16 (/.f64 (pow.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) 3) (pow.f64 x 3)) (fma.f64 12 (/.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) (/.f64 (.f64 x x) (pow.f64 (-.f64 1 x) 2))) (.f64 -12 (/.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) (/.f64 (pow.f64 x 3) (fma.f64 (pow.f64 (-.f64 1 x) 2) x (+.f64 (.f64 x (pow.f64 (-.f64 1 x) 2)) (pow.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) 2)))))))) (.f64 1/81 (/.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) (/.f64 x (fma.f64 -4 (/.f64 (pow.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) 2) (.f64 x x)) (.f64 2 (/.f64 (fma.f64 (pow.f64 (-.f64 1 x) 2) x (+.f64 (.f64 x (pow.f64 (-.f64 1 x) 2)) (pow.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) 2))) (.f64 x x))))))))) (/.f64 (pow.f64 y 3) (pow.f64 (exp.f64 1/9) (+.f64 (.f64 2 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4))))) (/.f64 (pow.f64 (exp.f64 1/9) (+.f64 (.f64 2 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4))) (/.f64 (.f64 y y) (fma.f64 2/81 (/.f64 (pow.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) 2) (.f64 x x)) (.f64 1/18 (fma.f64 -4 (/.f64 (pow.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) 2) (.f64 x x)) (.f64 2 (/.f64 (fma.f64 (pow.f64 (-.f64 1 x) 2) x (+.f64 (.f64 x (pow.f64 (-.f64 1 x) 2)) (pow.f64 (.f64 -1 (fma.f64 (sqrt.f64 x) (-.f64 1 x) (.f64 (-.f64 1 x) (sqrt.f64 x)))) 2))) (.f64 x x)))))))))))
(+.f64 (fma.f64 -2/9 (.f64 (/.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) x) (/.f64 (exp.f64 (+.f64 (.f64 2/9 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4/9))) y)) (exp.f64 (+.f64 (.f64 2/9 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4/9)))) (-.f64 (.f64 (/.f64 (exp.f64 (+.f64 (.f64 2/9 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4/9))) (.f64 y y)) (fma.f64 2/81 (/.f64 (pow.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) 2) (.f64 x x)) (+.f64 (.f64 -2/9 (/.f64 (pow.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) 2) (.f64 x x))) (.f64 1/9 (/.f64 (+.f64 (pow.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) 2) (.f64 (pow.f64 (-.f64 1 x) 2) (+.f64 x x))) (.f64 x x)))))) (/.f64 (fma.f64 4/2187 (/.f64 (pow.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) 3) (pow.f64 x 3)) (fma.f64 1/81 (.f64 (/.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) x) (fma.f64 2 (/.f64 (+.f64 (pow.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) 2) (.f64 (pow.f64 (-.f64 1 x) 2) (+.f64 x x))) (.f64 x x)) (.f64 -4 (/.f64 (pow.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) 2) (.f64 x x))))) (.f64 1/54 (fma.f64 16 (/.f64 (pow.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) 3) (pow.f64 x 3)) (fma.f64 -12 (.f64 (/.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) (pow.f64 x 3)) (+.f64 (pow.f64 (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2) 2) (.f64 (pow.f64 (-.f64 1 x) 2) (+.f64 x x)))) (/.f64 12 (/.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 1 x) 2) (.f64 (.f64 (-.f64 1 x) (sqrt.f64 x)) -2))))))))) (/.f64 (pow.f64 y 3) (exp.f64 (+.f64 (.f64 2/9 (log.f64 x)) (*.f64 (log.f64 (/.f64 -1 y)) -4/9)))))))
(+.f64 (fma.f64 -2/9 (.f64 (/.f64 (.f64 (-.f64 1 x) (.f64 (sqrt.f64 x) -2)) x) (/.f64 (exp.f64 (+.f64 (.f64 2/9 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4/9))) y)) (exp.f64 (+.f64 (.f64 2/9 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4/9)))) (.f64 (/.f64 (exp.f64 (+.f64 (.f64 2/9 (log.f64 x)) (.f64 (log.f64 (/.f64 -1 y)) -4/9))) (.f64 y y)) (-.f64 (+.f64 (.f64 1/9 (/.f64 (+.f64 (.f64 4 (.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 x (.f64 2 (pow.f64 (-.f64 1 x) 2)))) (.f64 x x))) (.f64 (/.f64 (.f64 4 (.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 x x)) -16/81)) (/.f64 (+.f64 (/.f64 (neg.f64 (.f64 (.f64 (-.f64 1 x) (.f64 (sqrt.f64 x) (fma.f64 2 (/.f64 (+.f64 (.f64 4 (.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 x (.f64 2 (pow.f64 (-.f64 1 x) 2)))) (.f64 x x)) (.f64 -4 (/.f64 (.f64 4 (.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 x x)))))) 2/81)) x) (+.f64 (.f64 (pow.f64 (/.f64 (.f64 (-.f64 1 x) (.f64 (sqrt.f64 x) -2)) x) 3) 652/2187) (.f64 1/54 (fma.f64 12 (.f64 (/.f64 (.f64 (-.f64 1 x) (.f64 (sqrt.f64 x) -2)) (.f64 x x)) (pow.f64 (-.f64 1 x) 2)) (/.f64 (neg.f64 (.f64 (.f64 (-.f64 1 x) (.f64 (sqrt.f64 x) (+.f64 (.f64 4 (.f64 x (pow.f64 (-.f64 1 x) 2))) (.f64 x (.f64 2 (pow.f64 (-.f64 1 x) 2)))))) -24)) (pow.f64 x 3)))))) y))))

localize3.0ms (0%)

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

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 y (.f64 y x))
✓	0.4b	(/.f64 -1 (.f64 y (.f64 y x)))
✓	0.4b	(/.f64 1 (/.f64 -1 (.f64 y (.f64 y x))))

Compiler

Compiled 30 to 12 computations (60% saved)

series7.0ms (0.1%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 -1 (.f64 y (.f64 y x)))
1.0ms	y	@	inf	(/.f64 -1 (.f64 y (.f64 y x)))
1.0ms	x	@	0	(/.f64 -1 (.f64 y (.f64 y x)))
0.0ms	y	@	0	(/.f64 -1 (.f64 y (.f64 y x)))
0.0ms	y	@	0	(/.f64 1 (/.f64 -1 (.f64 y (.f64 y x))))

rewrite120.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

703×	`pow1_binary64`
648×	`add-log-exp_binary64`
647×	`log1p-expm1-u_binary64`
647×	`expm1-log1p-u_binary64`
635×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	182	24
2	2273	24

Stop Event

1×	node limit

Counts

3 → 109

Calls

Call 1

Inputs
(/.f64 1 (/.f64 -1 (.f64 y (.f64 y x))))
(/.f64 -1 (.f64 y (.f64 y x)))
(.f64 y (.f64 y x))

Outputs

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

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

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

simplify278.0ms (4%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
566×	`distribute-lft-neg-in_binary64`
557×	`distribute-rgt-neg-in_binary64`
507×	`fma-def_binary64`
315×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	624
1	21	624
2	50	624
3	117	624
4	315	624
5	1066	624
6	2166	624
7	3331	624
8	4425	624
9	5270	624
10	5877	624
11	6655	624
12	7799	624

Stop Event

1×	node limit

Counts

181 → 98

Calls

Call 1

Inputs
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)

Outputs
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(.f64 -1 (.f64 (pow.f64 y 2) x))
(neg.f64 (.f64 (.f64 y y) x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (neg.f64 y) (.f64 y x))
(.f64 x (.f64 y (neg.f64 y)))
(.f64 y (.f64 y (neg.f64 x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(/.f64 -1 (*.f64 (pow.f64 y 2) x))
(/.f64 -1 (.f64 (.f64 y y) x))
(/.f64 (/.f64 -1 x) (*.f64 y y))
(/.f64 -1 (.f64 y (.f64 y x)))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))
(*.f64 (pow.f64 y 2) x)
(.f64 (.f64 y y) x)
(.f64 y (.f64 y x))

localize20.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.2b	(/.f64 (sqrt.f64 (/.f64 1 x)) y)
✓	0.3b	(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))

Compiler

Compiled 26 to 18 computations (30.8% saved)

series16.0ms (0.2%)

Counts

3 → 24

Calls

15 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	(/.f64 (sqrt.f64 (/.f64 1 x)) y)
1.0ms	y	@	0	(/.f64 (sqrt.f64 (/.f64 1 x)) y)
1.0ms	x	@	-inf	(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
1.0ms	x	@	0	(/.f64 (sqrt.f64 (/.f64 1 x)) y)
1.0ms	y	@	-inf	(/.f64 (sqrt.f64 (/.f64 1 x)) y)

rewrite95.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

796×	`pow1_binary64`
737×	`add-log-exp_binary64`
737×	`log1p-expm1-u_binary64`
737×	`expm1-log1p-u_binary64`
717×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	170	17
2	2192	17

Stop Event

1×	node limit

Counts

3 → 94

Calls

Call 1

Inputs
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(sqrt.f64 (/.f64 1 x))

Outputs

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

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

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

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`associate-/l*_binary64`
3×	`*-commutative_binary64`
3×	`associate-*l/_binary64`
3×	`associate-/r*_binary64`
3×	`*-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	216
1	16	180
2	21	180
3	32	180
4	32	180
5	33	180
6	36	180
7	43	180
8	43	180

Stop Event

1×

saturated

Counts

118 → 96

Calls

Call 1

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

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

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 y))
✓	8.4b	(sqrt.f64 (*.f64 x y))

Compiler

Compiled 20 to 6 computations (70% saved)

series12.0ms (0.2%)

Counts

2 → 12

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 y))
2.0ms	y	@	-inf	(.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 y))
1.0ms	x	@	0	(sqrt.f64 (*.f64 x y))
1.0ms	y	@	0	(sqrt.f64 (*.f64 x y))
1.0ms	x	@	-inf	(sqrt.f64 (*.f64 x y))

rewrite81.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`pow1_binary64`
569×	`add-log-exp_binary64`
569×	`log1p-expm1-u_binary64`
569×	`expm1-log1p-u_binary64`
552×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	140	12
2	1641	12

Stop Event

1×	node limit

Counts

2 → 37

Calls

Call 1

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

Outputs

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

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

simplify108.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

899×	`fma-def_binary64`
445×	`cube-prod_binary64`
388×	`distribute-rgt-neg-in_binary64`
388×	`fma-neg_binary64`
330×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	72
1	25	72
2	74	72
3	179	72
4	706	72
5	1548	72
6	2571	72
7	3718	72
8	4857	72
9	6712	72

Stop Event

1×

unsound

Counts

49 → 39

Calls

Call 1

Inputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(.f64 -1 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(.f64 -1 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(.f64 -1 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(.f64 -1 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))

Outputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(.f64 -1 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(.f64 -1 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(.f64 -1 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(.f64 -1 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))

eval987.0ms (14.4%)

Compiler: Compiled 25887 to 16946 computations (34.5% saved)

prune101.0ms (1.5%)

Pruning

21 alts after pruning (12 fresh and 9 done)

	Pruned	Kept	Total
New	615	7	622
Fresh	1	5	6
Picked	0	1	1
Done	3	8	11
Total	619	21	640

Error

Counts

640 → 21

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.3b	(-.f64 1 x)
	62.6b	(/.f64 y (/.f64 (+.f64 -1 x) (*.f64 y x)))
✓	52.6b	(.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 y))
	40.1b	(.f64 (.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
✓	62.2b	(*.f64 y y)
	58.2b	(/.f64 (.f64 x (.f64 y (neg.f64 y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	1.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))
	56.7b	(sqrt.f64 (.f64 y (.f64 x y)))
	39.8b	(/.f64 1 (/.f64 (pow.f64 x -1/2) y))
✓	42.4b	(neg.f64 x)
	42.4b	(/.f64 1 (/.f64 -1 x))
	62.5b	(.f64 (/.f64 1 (/.f64 -1 y)) (.f64 y x))
	44.9b	1
✓	22.1b	(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
	62.7b	(.f64 (.f64 y y) (neg.f64 x))
	62.5b	(.f64 (.f64 y x) (neg.f64 y))
✓	39.8b	(*.f64 y (sqrt.f64 x))
	62.5b	(/.f64 1 (.f64 (/.f64 -1 y) (/.f64 1 (.f64 y x))))
✓	58.2b	(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))
	58.2b	(.f64 (/.f64 1 (neg.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))) (.f64 x (*.f64 y y)))

Compiler

Compiled 236 to 161 computations (31.8% saved)

regimes93.0ms (1.4%)

Counts

37 → 1

Calls

Call 1

Inputs
1
1
(neg.f64 x)
(*.f64 y y)
(-.f64 1 x)
(-.f64 1 x)
(/.f64 1 (/.f64 -1 x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (.f64 y x) (neg.f64 y))
(.f64 (/.f64 1 (/.f64 -1 y)) (.f64 y x))
(/.f64 1 (/.f64 -1 (.f64 y (.f64 y x))))
(/.f64 y (/.f64 (+.f64 -1 x) (*.f64 y x)))
(/.f64 1 (.f64 (/.f64 -1 y) (/.f64 1 (.f64 y x))))
(*.f64 y (sqrt.f64 x))
(sqrt.f64 (.f64 y (.f64 x y)))
(sqrt.f64 (.f64 x (.f64 y y)))
(/.f64 1 (/.f64 (pow.f64 x -1/2) y))
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(+.f64 (-.f64 1 x) (sqrt.f64 (.f64 x (.f64 y y))))
(/.f64 (.f64 x (.f64 y (neg.f64 y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (.f64 x (*.f64 y (neg.f64 y)))))
(.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 y))
(fma.f64 (sqrt.f64 x) y (-.f64 1 x))
(.f64 (/.f64 1 (neg.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))) (.f64 x (*.f64 y y)))
(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
(.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (/.f64 1 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x))))))
(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (*.f64 y y)))))
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
(+.f64 (-.f64 1 x) (pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) 2))
(/.f64 (-.f64 1 (.f64 (-.f64 x (.f64 y (sqrt.f64 x))) (-.f64 x (.f64 y (sqrt.f64 x))))) (+.f64 1 (-.f64 x (.f64 y (sqrt.f64 x)))))
(.f64 (.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2) (cbrt.f64 (.f64 y (sqrt.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))) 2) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) (cbrt.f64 (fma.f64 (sqrt.f64 x) y (-.f64 1 x))))

Outputs
(fma.f64 (sqrt.f64 x) y (-.f64 1 x))

Calls

4 calls:

31.0ms	x
18.0ms	y
17.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
15.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`
0.1b	1	`(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))`
0.1b	1	`(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 427 to 211 computations (50.6% saved)

regimes74.0ms (1.1%)

Counts

23 → 1

Calls

Call 1

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

Outputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Calls

3 calls:

22.0ms	x
22.0ms	y
20.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`
0.1b	1	`(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 174 to 88 computations (49.4% saved)

regimes192.0ms (2.8%)

Counts

18 → 3

Calls

Call 1

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

Outputs
(*.f64 y (sqrt.f64 x))
(-.f64 1 x)
(*.f64 y (sqrt.f64 x))

Calls

2 calls:

118.0ms	x
66.0ms	y

Results

Error	Segments	Branch
19.1b	7	`x`
3.7b	3	`y`

Compiler

Compiled 107 to 61 computations (43% saved)

bsearch67.0ms (1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
33.0ms	2.3880407861532236e+47	3.9935502897945506e+63
34.0ms	-1.6005103240451402e+111	-9.675443665038213e+104

Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes36.0ms (0.5%)

Counts

13 → 1

Calls

Call 1

Inputs
1
1
(neg.f64 x)
(*.f64 y y)
(-.f64 1 x)
(-.f64 1 x)
(/.f64 1 (/.f64 -1 x))
(.f64 (.f64 y y) (neg.f64 x))
(.f64 (.f64 y x) (neg.f64 y))
(.f64 (/.f64 1 (/.f64 -1 y)) (.f64 y x))
(/.f64 1 (/.f64 -1 (.f64 y (.f64 y x))))
(/.f64 y (/.f64 (+.f64 -1 x) (*.f64 y x)))
(/.f64 1 (.f64 (/.f64 -1 y) (/.f64 1 (.f64 y x))))

Outputs
(-.f64 1 x)

Calls

2 calls:

15.0ms	y
15.0ms	x

Results

Error	Segments	Branch
24.3b	1	`x`
24.3b	1	`y`

Compiler

Compiled 76 to 43 computations (43.4% saved)

regimes63.0ms (0.9%)

Counts

4 → 2

Calls

Call 1

Inputs
1
1
(neg.f64 x)
(*.f64 y y)

Outputs
1
(neg.f64 x)

Calls

2 calls:

45.0ms	y
16.0ms	x

Results

Error	Segments	Branch
24.6b	2	`x`
37.1b	5	`y`

Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch31.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
31.0ms	0.27153354619694675	8.563278674788002

Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes16.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
1
1

Outputs
1

Calls

2 calls:

8.0ms	x
7.0ms	y

Results

Error	Segments	Branch
44.9b	1	`x`
44.9b	1	`y`

Compiler

Compiled 10 to 8 computations (20% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	65
1	28	65
2	31	65
3	32	65

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 x) y (-.f64 1 x))
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(if (<=.f64 y -1600510324045140238051638598780226236789543674997992500049563756557902438430744913442909156210477788111526952960) (.f64 y (sqrt.f64 x)) (if (<=.f64 y 238804078615322359580670617693055249744463396864) (-.f64 1 x) (.f64 y (sqrt.f64 x))))
(-.f64 1 x)
(if (<=.f64 x 4891513509884635/18014398509481984) 1 (neg.f64 x))
1

Outputs
(fma.f64 (sqrt.f64 x) y (-.f64 1 x))
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(+.f64 (-.f64 1 x) (*.f64 (sqrt.f64 x) y))
(if (<=.f64 y -1600510324045140238051638598780226236789543674997992500049563756557902438430744913442909156210477788111526952960) (.f64 y (sqrt.f64 x)) (if (<=.f64 y 238804078615322359580670617693055249744463396864) (-.f64 1 x) (.f64 y (sqrt.f64 x))))
(if (<=.f64 y -1600510324045140238051638598780226236789543674997992500049563756557902438430744913442909156210477788111526952960) (.f64 (sqrt.f64 x) y) (if (<=.f64 y 238804078615322359580670617693055249744463396864) (-.f64 1 x) (.f64 (sqrt.f64 x) y)))
(-.f64 1 x)
(if (<=.f64 x 4891513509884635/18014398509481984) 1 (neg.f64 x))
1

Compiler

Compiled 57 to 39 computations (31.6% saved)

soundness0.0ms (0%)

end75.0ms (1.1%)

Compiler: Compiled 47 to 26 computations (44.7% saved)

Iter	Nodes	Cost
0	11	113
1	21	113
2	32	113
3	54	113
4	88	113
5	147	113
6	283	113
7	436	113
8	595	113
9	733	113
10	825	113
11	831	113

Iter	Nodes	Cost
0	11	113
1	21	113
2	32	113
3	54	113
4	88	113
5	147	113
6	283	113
7	436	113
8	595	113
9	733	113
10	825	113
11	831	113

Iter	Nodes	Cost
0	14	124
1	32	121
2	67	121
3	140	115
4	264	115
5	423	115
6	702	115
7	848	115
8	893	115
9	897	115

Iter	Nodes	Cost
0	11	113
1	21	113
2	32	113
3	54	113
4	88	113
5	147	113
6	283	113
7	436	113
8	595	113
9	733	113
10	825	113
11	831	113

Iter	Nodes	Cost
0	11	113
1	21	113
2	32	113
3	54	113
4	88	113
5	147	113
6	283	113
7	436	113
8	595	113
9	733	113
10	825	113
11	831	113

Iter	Nodes	Cost
0	14	124
1	32	121
2	67	121
3	140	115
4	264	115
5	423	115
6	702	115
7	848	115
8	893	115
9	897	115

Details

analyze84.0ms (1.2%)

sample1.6s (23.4%)

preprocess55.0ms (0.8%)

simplify24.0ms (0.4%)

eval1.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.1%)

series8.0ms (0.1%)

rewrite56.0ms (0.8%)

simplify30.0ms (0.4%)

eval15.0ms (0.2%)

prune21.0ms (0.3%)

localize8.0ms (0.1%)

series3.0ms (0%)

rewrite48.0ms (0.7%)

simplify27.0ms (0.4%)

localize3.0ms (0%)

localize5.0ms (0.1%)

localize25.0ms (0.4%)

series13.0ms (0.2%)

rewrite95.0ms (1.4%)

simplify74.0ms (1.1%)

localize30.0ms (0.4%)

series6.0ms (0.1%)

rewrite73.0ms (1.1%)

simplify42.0ms (0.6%)

eval310.0ms (4.5%)

prune263.0ms (3.8%)

localize45.0ms (0.7%)

series38.0ms (0.6%)

rewrite132.0ms (1.9%)

simplify64.0ms (0.9%)

localize3.0ms (0%)

localize6.0ms (0.1%)

series3.0ms (0%)

rewrite52.0ms (0.8%)

simplify12.0ms (0.2%)

localize17.0ms (0.2%)

series2.0ms (0%)

rewrite101.0ms (1.5%)

simplify34.0ms (0.5%)

localize21.0ms (0.3%)

series14.0ms (0.2%)

rewrite86.0ms (1.2%)

simplify96.0ms (1.4%)

eval218.0ms (3.2%)

prune89.0ms (1.3%)

localize69.0ms (1%)

series67.0ms (1%)

rewrite113.0ms (1.6%)

simplify113.0ms (1.7%)

localize3.0ms (0%)

localize9.0ms (0.1%)

series7.0ms (0.1%)

rewrite120.0ms (1.8%)

simplify278.0ms (4%)

localize20.0ms (0.3%)

series16.0ms (0.2%)

rewrite95.0ms (1.4%)

simplify28.0ms (0.4%)

localize14.0ms (0.2%)

series12.0ms (0.2%)

rewrite81.0ms (1.2%)

simplify108.0ms (1.6%)

eval987.0ms (14.4%)

prune101.0ms (1.5%)

regimes93.0ms (1.4%)

regimes74.0ms (1.1%)

regimes192.0ms (2.8%)

bsearch67.0ms (1%)

regimes36.0ms (0.5%)

regimes63.0ms (0.9%)

bsearch31.0ms (0.5%)

regimes16.0ms (0.2%)

simplify9.0ms (0.1%)

soundness0.0ms (0%)

end75.0ms (1.1%)

Profiling

Iter	Nodes	Cost
0	11	113
1	21	113
2	32	113
3	54	113
4	88	113
5	147	113
6	283	113
7	436	113
8	595	113
9	733	113
10	825	113
11	831	113

Iter	Nodes	Cost
0	11	113
1	21	113
2	32	113
3	54	113
4	88	113
5	147	113
6	283	113
7	436	113
8	595	113
9	733	113
10	825	113
11	831	113

Iter	Nodes	Cost
0	14	124
1	32	121
2	67	121
3	140	115
4	264	115
5	423	115
6	702	115
7	848	115
8	893	115
9	897	115