Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.3s (54.2%)

Results

1.2s	2204×	body	2048	valid
488.0ms	4248×	body	128	valid
434.0ms	1034×	body	1024	valid
152.0ms	500×	body	512	valid
52.0ms	270×	body	256	valid

preprocess20.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	29	15
3	37	15
4	44	15
5	54	15
6	65	15
7	77	15
8	80	15
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	29	15
3	37	15
4	44	15
5	54	15
6	65	15
7	77	15
8	80	15

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

16.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	2.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series6.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms	x	@	inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms	x	@	-inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0ms	x	@	-inf	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0ms	x	@	inf	(/.f64 1/2 (hypot.f64 1 x))

rewrite63.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

406×	`log-prod_binary64`
387×	`prod-diff_binary64`
205×	`fma-def_binary64`
170×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	44
1	201	44
2	2591	44

Stop Event

1×	node limit

Counts

4 → 139

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 1/2 (hypot.f64 1 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) (neg.f64 (+.f64 (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)) (+.f64 1 (-.f64 (.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))) (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))) (sqrt.f64 (-.f64 (+.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (/.f64 1/4 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))
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simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-def_binary64`
310×	`times-frac_binary64`
274×	`fma-neg_binary64`
253×	`sub-neg_binary64`
233×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	910
1	388	838
2	1144	822
3	3504	822

Stop Event

1×	node limit

Counts

187 → 219

Calls

Call 1

Inputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (.f64 -11/128 (pow.f64 x 4)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
1
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 1 (.f64 11/128 (pow.f64 x 4))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 -69/1024 (pow.f64 x 6)) (+.f64 1 (*.f64 11/128 (pow.f64 x 4)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
1
(+.f64 1 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 1/2) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
(/.f64 1/2 x)
(-.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 5/32 (/.f64 1 (pow.f64 x 7)))))
(/.f64 -1/2 x)
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 5/32 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))))

Outputs
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (.f64 -11/128 (pow.f64 x 4))))
(fma.f64 1/8 (.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (.f64 69/1024 (pow.f64 x 6))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -1843/32768 (pow.f64 x 8) (.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (.f64 -1843/32768 (pow.f64 x 8)))))
(fma.f64 1/8 (.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (.f64 -1843/32768 (pow.f64 x 8)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x) (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) 1) (sqrt.f64 1/2)) (/.f64 -1/4 (.f64 x (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (/.f64 1/16 (.f64 x (.f64 x (sqrt.f64 1/2)))) (-.f64 (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (+.f64 (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 (.f64 -1/2 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4)) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(+.f64 1 (+.f64 (/.f64 3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (.f64 x (*.f64 x (sqrt.f64 1/2)))) (-.f64 (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x) (sqrt.f64 1/2)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))) (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 1/16 (.f64 x (.f64 x (sqrt.f64 1/2)))) (-.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (sqrt.f64 1/2))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(-.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))) (sqrt.f64 1/2))
(+.f64 (+.f64 1 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))) (-.f64 (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 1/16 (.f64 x (.f64 x (sqrt.f64 1/2))))) (-.f64 (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (-.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x))) (-.f64 (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2))))
1
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 1)
(fma.f64 -1/8 (*.f64 x x) 1)
(fma.f64 (*.f64 x x) -1/8 1)
(fma.f64 x (*.f64 x -1/8) 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 1 (.f64 11/128 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/8 (.f64 x x) 1) (.f64 (pow.f64 x 4) 11/128))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 4) 11/128 1))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 1))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 -69/1024 (pow.f64 x 6)) (+.f64 1 (*.f64 11/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 -69/1024 (pow.f64 x 6) (+.f64 1 (.f64 (pow.f64 x 4) 11/128))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 6) -69/1024 (fma.f64 (pow.f64 x 4) 11/128 1)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 (fma.f64 (pow.f64 x 6) -69/1024 1)))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (.f64 x (sqrt.f64 1/2)))) (/.f64 1/32 (.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (.f64 (/.f64 2 (sqrt.f64 1/2)) 1/32) (.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (.f64 x (sqrt.f64 1/2))))) (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)) (-.f64 (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 (.f64 (/.f64 2 (sqrt.f64 1/2)) 1/32) (*.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x))) (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(-.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (-.f64 (sqrt.f64 1/2) (/.f64 1/4 (.f64 x (sqrt.f64 1/2)))) (/.f64 1/32 (.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 (.f64 -1/2 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4)) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x))))
1
(+.f64 1 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 1)
(fma.f64 x (*.f64 x -1/4) 1)
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/4 (.f64 x x) (.f64 (pow.f64 x 4) 3/16)))
(+.f64 1 (fma.f64 (.f64 x x) -1/4 (.f64 (pow.f64 x 4) 3/16)))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) 3/16 1))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/4 (.f64 x x) (fma.f64 -5/32 (pow.f64 x 6) (.f64 (pow.f64 x 4) 3/16))))
(+.f64 (fma.f64 (.f64 x x) -1/4 1) (fma.f64 (pow.f64 x 4) 3/16 (.f64 (pow.f64 x 6) -5/32)))
(+.f64 (fma.f64 x (.f64 x -1/4) 1) (fma.f64 (pow.f64 x 4) 3/16 (.f64 (pow.f64 x 6) -5/32)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 1/2 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 1/2) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 1/2 (/.f64 1/2 x)) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (+.f64 1/2 (/.f64 1/2 x)) (/.f64 -1/4 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (+.f64 1/2 (/.f64 1/2 x)) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (+.f64 (+.f64 1/2 (/.f64 3/16 (pow.f64 x 5))) (/.f64 -1/4 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (/.f64 1/2 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (/.f64 1/2 x))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 1/2 (/.f64 -1/2 x)))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 x)))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(+.f64 1/2 (+.f64 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5))) (/.f64 -1/2 x)))
(+.f64 1/2 (+.f64 (/.f64 -1/2 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -3/16 (pow.f64 x 5)))))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (.f64 (.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 1/2)
(fma.f64 x (*.f64 x -1/4) 1/2)
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (.f64 (pow.f64 x 4) 3/16)))
(+.f64 1/2 (fma.f64 (.f64 x x) -1/4 (.f64 (pow.f64 x 4) 3/16)))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) 3/16 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (fma.f64 -5/32 (pow.f64 x 6) (.f64 (pow.f64 x 4) 3/16))))
(+.f64 1/2 (fma.f64 (.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) 3/16 (.f64 (pow.f64 x 6) -5/32))))
(+.f64 1/2 (fma.f64 x (.f64 x -1/4) (fma.f64 (pow.f64 x 4) 3/16 (.f64 (pow.f64 x 6) -5/32))))
(/.f64 1/2 x)
(-.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 5/32 (/.f64 1 (pow.f64 x 7)))))
(-.f64 (-.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3))) (/.f64 5/32 (pow.f64 x 7)))
(+.f64 (/.f64 3/16 (pow.f64 x 5)) (-.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 5/32 (pow.f64 x 7)))))
(-.f64 (+.f64 (/.f64 1/2 x) (/.f64 -5/32 (pow.f64 x 7))) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -3/16 (pow.f64 x 5))))
(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (+.f64 (/.f64 -1/4 (pow.f64 x 3)) (/.f64 -5/32 (pow.f64 x 7))))
(/.f64 -1/2 x)
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 x))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))))
(+.f64 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5))) (/.f64 -1/2 x))
(+.f64 (/.f64 -1/2 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -3/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 5/32 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 5/32 (pow.f64 x 7)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(+.f64 (/.f64 5/32 (pow.f64 x 7)) (+.f64 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5))) (/.f64 -1/2 x)))
(+.f64 (/.f64 5/32 (pow.f64 x 7)) (+.f64 (/.f64 -1/2 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -3/16 (pow.f64 x 5)))))
(+.f64 (/.f64 5/32 (pow.f64 x 7)) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5)))))

prune211.0ms (5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	2	220

Error

0.0b

Counts

220 → 2

Alt Table

Status

Error

Program

31.3b

(fma.f64 1/8 (*.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 -1843/32768 (pow.f64 x 8)))))

▶

15.7b

(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

Compiler

Compiled 4014 to 3567 computations (11.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	1.7b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0ms	x	@	0	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0ms	x	@	-inf	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0ms	x	@	-inf	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0ms	x	@	inf	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite49.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

474×	`prod-diff_binary64`
311×	`fma-def_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
149×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	225	25
2	2996	25

Stop Event

1×	node limit

Counts

2 → 88

Calls

Call 1

Inputs
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

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

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

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

307×	`times-frac_binary64`
277×	`fma-def_binary64`
241×	`associate-/l*_binary64`
193×	`associate-/r*_binary64`
176×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	454
1	265	420
2	815	412
3	2648	412

Stop Event

1×	node limit

Counts

112 → 129

Calls

Call 1

Inputs
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -3/16 (pow.f64 x 4)))
(+.f64 (.f64 5/32 (pow.f64 x 6)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(+.f64 (.f64 5/32 (pow.f64 x 6)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/16 (pow.f64 x 4)) (.f64 -35/256 (pow.f64 x 8)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 1/2) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
2
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 2 (.f64 11/128 (pow.f64 x 4))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 -69/1024 (pow.f64 x 6)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4)))))
(+.f64 1 (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))

Outputs
(*.f64 1/4 (pow.f64 x 2))
(.f64 1/4 (.f64 x x))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -3/16 (pow.f64 x 4)))
(fma.f64 1/4 (.f64 x x) (.f64 -3/16 (pow.f64 x 4)))
(fma.f64 -3/16 (pow.f64 x 4) (.f64 1/4 (.f64 x x)))
(+.f64 (.f64 5/32 (pow.f64 x 6)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (.f64 x x) (.f64 -3/16 (pow.f64 x 4))))
(fma.f64 -3/16 (pow.f64 x 4) (fma.f64 5/32 (pow.f64 x 6) (.f64 1/4 (.f64 x x))))
(fma.f64 1/4 (.f64 x x) (fma.f64 -3/16 (pow.f64 x 4) (.f64 5/32 (pow.f64 x 6))))
(+.f64 (.f64 5/32 (pow.f64 x 6)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/16 (pow.f64 x 4)) (.f64 -35/256 (pow.f64 x 8)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (.f64 x x) (fma.f64 -3/16 (pow.f64 x 4) (.f64 -35/256 (pow.f64 x 8)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (.f64 x x) (fma.f64 -35/256 (pow.f64 x 8) (.f64 -3/16 (pow.f64 x 4)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 -3/16 (pow.f64 x 4) (fma.f64 1/4 (.f64 x x) (.f64 -35/256 (pow.f64 x 8)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (/.f64 -1/2 x))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(-.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))))
(+.f64 (+.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (/.f64 -1/2 x)) (/.f64 -3/16 (pow.f64 x 5)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 1/2 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 1/2) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 1/2 (/.f64 1/4 (pow.f64 x 3))))
(+.f64 1/2 (-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 1/2 (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 1/2 (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 1/2 (-.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3)))))
(+.f64 1/2 (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (/.f64 -1/4 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (+.f64 1/2 (/.f64 -1/4 (pow.f64 x 3))))
2
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 2)
(fma.f64 -1/8 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) -1/8 2)
(fma.f64 x (*.f64 x -1/8) 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 2 (.f64 11/128 (pow.f64 x 4))))
(fma.f64 -1/8 (.f64 x x) (+.f64 2 (.f64 (pow.f64 x 4) 11/128)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 4) 11/128 2))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 -69/1024 (pow.f64 x 6)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 -69/1024 (pow.f64 x 6) (+.f64 2 (.f64 (pow.f64 x 4) 11/128))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 6) -69/1024 (fma.f64 (pow.f64 x 4) 11/128 2)))
(fma.f64 (pow.f64 x 6) -69/1024 (fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 2)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 (fma.f64 (pow.f64 x 6) -69/1024 2)))
(+.f64 1 (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(+.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (.f64 x (sqrt.f64 1/2)))) (/.f64 1/32 (.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(-.f64 (+.f64 1 (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (sqrt.f64 1/2))) (.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x))))
(+.f64 1 (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)))))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (.f64 (pow.f64 x 3) (sqrt.f64 1/2))) (+.f64 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (.f64 x (sqrt.f64 1/2))))) (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(+.f64 (+.f64 1 (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (sqrt.f64 1/2))) (-.f64 (/.f64 (/.f64 -3/32 (sqrt.f64 1/2)) (pow.f64 x 3)) (.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)))))
(+.f64 (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 -3/32 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2)))))
(+.f64 (+.f64 1 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)) (+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -3/32 (.f64 (pow.f64 x 3) (sqrt.f64 1/2)))) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x))))
(+.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (sqrt.f64 1/2) (-.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (-.f64 1 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 1/2) (-.f64 1 (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))))
(+.f64 (sqrt.f64 1/2) (-.f64 1 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 -1/4 (.f64 x (sqrt.f64 1/2))))))
(+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)) (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (.f64 x (sqrt.f64 1/2))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 -1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))) (.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 1 (.f64 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (.f64 (pow.f64 x 3) (sqrt.f64 1/2))) -1/2)) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 1 (/.f64 (/.f64 3/32 (pow.f64 x 3)) (sqrt.f64 1/2))) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))))
(+.f64 1 (+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 3/32 (pow.f64 x 3)) (sqrt.f64 1/2))) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 -1/4 (.f64 x (sqrt.f64 1/2))))))
(+.f64 (/.f64 3/32 (.f64 (pow.f64 x 3) (sqrt.f64 1/2))) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)) (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))))))

prune304.0ms (7.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	239	4	243

Error

0.0b

Counts

243 → 4

Alt Table

Status	Error	Program
	31.3b	(fma.f64 1/8 (.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (.f64 -1843/32768 (pow.f64 x 8)))))
▶	15.7b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	15.7b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	16.2b	(/.f64 (*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

Compiler

Compiled 6435 to 5681 computations (11.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	0.0b	(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
✓	1.7b	(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))
0.0ms	x	@	-inf	(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))
0.0ms	x	@	inf	(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))
0.0ms	x	@	inf	(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
0.0ms	x	@	-inf	(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)

rewrite58.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`prod-diff_binary64`
208×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`
120×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	256	39
2	3320	39

Stop Event

1×	node limit

Counts

3 → 98

Calls

Call 1

Inputs
(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

Outputs

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

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) (/.f64 1 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)) 2) (cbrt.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)) (sqrt.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) 2) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (cbrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 6)) (*.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (+.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (+.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4)) (*.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2) 1) (-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) (neg.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3))) (neg.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 27/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))) (+.f64 9/4 (-.f64 (/.f64 1/4 (+.f64 1 (*.f64 x x))) (*.f64 3/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 9/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (-.f64 3/2 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2)))))))

simplify40.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-neg_binary64`
376×	`fma-def_binary64`
311×	`times-frac_binary64`
240×	`*-commutative_binary64`
195×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	468
1	263	464
2	702	460
3	2003	460
4	4196	460

Stop Event

1×	node limit

Counts

134 → 159

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -7/16 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -7/16 (pow.f64 x 4)) (*.f64 13/32 (pow.f64 x 6))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -7/16 (pow.f64 x 4)) (+.f64 (.f64 -99/256 (pow.f64 x 8)) (.f64 13/32 (pow.f64 x 6)))))
3/4
(-.f64 3/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 3/4 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 3/4 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
3/4
(+.f64 3/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 3/4) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 3/4) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 7/16 (pow.f64 x 4)) (.f64 -1/2 (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 7/16 (pow.f64 x 4)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (*.f64 -13/32 (pow.f64 x 6)))))
1/4
(+.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/4 (.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/4 (.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
1/4
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/4 (.f64 1/4 (/.f64 1 (pow.f64 x 2)))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/4 (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 1/2 (/.f64 1 x)))
2
(+.f64 2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4))))
(+.f64 2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
3/2
(+.f64 3/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 3/2) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 3/2 (.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
3/2
(-.f64 3/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 3/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 3/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -7/16 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -7/16 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -7/16 (pow.f64 x 4)) (*.f64 13/32 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -7/16 (pow.f64 x 4) (.f64 13/32 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 13/32 (pow.f64 x 6) (.f64 -7/16 (pow.f64 x 4))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -7/16 (pow.f64 x 4)) (+.f64 (.f64 -99/256 (pow.f64 x 8)) (.f64 13/32 (pow.f64 x 6)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -7/16 (pow.f64 x 4) (fma.f64 -99/256 (pow.f64 x 8) (.f64 13/32 (pow.f64 x 6)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -7/16 (pow.f64 x 4) (fma.f64 13/32 (pow.f64 x 6) (.f64 -99/256 (pow.f64 x 8)))))
3/4
(-.f64 3/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 3/4 (/.f64 1/2 x))
(+.f64 3/4 (/.f64 -1/2 x))
(-.f64 3/4 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 3/4 (+.f64 (/.f64 1/2 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 3/4 (+.f64 (/.f64 -1/2 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (+.f64 3/4 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 3/4 (/.f64 1/4 (pow.f64 x 3))) (+.f64 (/.f64 1/2 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (+.f64 3/4 (/.f64 1/4 (pow.f64 x 3))) (+.f64 (/.f64 -1/2 x) (/.f64 -1/4 (*.f64 x x))))
(+.f64 3/4 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/4 (*.f64 x x)))))
3/4
(+.f64 3/4 (*.f64 1/2 (/.f64 1 x)))
(+.f64 3/4 (/.f64 1/2 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 3/4) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/2 x) (-.f64 3/4 (/.f64 1/4 (*.f64 x x))))
(+.f64 3/4 (-.f64 (/.f64 1/2 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (+.f64 3/4 (/.f64 1/2 x)) (/.f64 -1/4 (*.f64 x x)))
(+.f64 3/4 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 3/4) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 1/2 x) (-.f64 3/4 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 3)))))
(+.f64 (+.f64 3/4 (/.f64 1/2 x)) (-.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 -1/4 (*.f64 x x)) (+.f64 (+.f64 3/4 (/.f64 1/2 x)) (/.f64 -1/4 (pow.f64 x 3))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 x (*.f64 x -1/2) 1)
(+.f64 1 (+.f64 (.f64 7/16 (pow.f64 x 4)) (.f64 -1/2 (pow.f64 x 2))))
(+.f64 1 (fma.f64 7/16 (pow.f64 x 4) (.f64 (.f64 x x) -1/2)))
(+.f64 1 (fma.f64 (pow.f64 x 4) 7/16 (.f64 x (.f64 x -1/2))))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 7/16 1))
(+.f64 1 (+.f64 (.f64 7/16 (pow.f64 x 4)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (*.f64 -13/32 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 7/16 (pow.f64 x 4) (fma.f64 -1/2 (.f64 x x) (.f64 (pow.f64 x 6) -13/32))))
(+.f64 1 (fma.f64 (pow.f64 x 4) 7/16 (fma.f64 (.f64 x x) -1/2 (.f64 (pow.f64 x 6) -13/32))))
(+.f64 1 (fma.f64 (pow.f64 x 6) -13/32 (fma.f64 (pow.f64 x 4) 7/16 (.f64 x (.f64 x -1/2)))))
(+.f64 1 (fma.f64 x (.f64 x -1/2) (fma.f64 (pow.f64 x 4) 7/16 (.f64 (pow.f64 x 6) -13/32))))
1/4
(+.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 x) 1/4)
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/4 (.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 1/2 x) (+.f64 1/4 (/.f64 1/4 (*.f64 x x))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 1/2 x) 1/4))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/4 (.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 1/4 (/.f64 1/4 (*.f64 x x))) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1/2 x) 1/4) (-.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (+.f64 1/4 (/.f64 1/4 (*.f64 x x))) (-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 -1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) 1/4)))
1/4
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))
(-.f64 (+.f64 1/4 (.f64 1/4 (/.f64 1 (pow.f64 x 2)))) (.f64 1/2 (/.f64 1 x)))
(+.f64 1/4 (-.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/2 x)))
(+.f64 1/4 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 -1/2 x)))
(+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 1/4 (/.f64 1/2 x)))
(-.f64 (+.f64 1/4 (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/4 (-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 3))) (/.f64 1/2 x)))
(+.f64 (+.f64 1/4 (/.f64 1/4 (pow.f64 x 3))) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 -1/2 x)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 1/4 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 -1/2 x))))
(+.f64 1/4 (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 x))))
2
(+.f64 2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 2 (.f64 (.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 2)
(fma.f64 x (*.f64 x -1/4) 2)
(+.f64 2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/4 (.f64 x x) (.f64 (pow.f64 x 4) 3/16)))
(+.f64 2 (fma.f64 (.f64 x x) -1/4 (.f64 (pow.f64 x 4) 3/16)))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) 3/16 2))
(+.f64 2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -1/4 (.f64 x x) (fma.f64 -5/32 (pow.f64 x 6) (.f64 (pow.f64 x 4) 3/16))))
(+.f64 (fma.f64 (.f64 x x) -1/4 2) (fma.f64 (pow.f64 x 6) -5/32 (.f64 (pow.f64 x 4) 3/16)))
(+.f64 (fma.f64 x (.f64 x -1/4) 2) (fma.f64 (pow.f64 x 6) -5/32 (.f64 (pow.f64 x 4) 3/16)))
(+.f64 (fma.f64 x (.f64 x -1/4) 2) (fma.f64 (pow.f64 x 4) 3/16 (.f64 (pow.f64 x 6) -5/32)))
3/2
(+.f64 3/2 (*.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 x) 3/2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) 3/2) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1/2 x) 3/2) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (-.f64 3/2 (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1/2 x) 3/2) (/.f64 -1/4 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 3/2 (.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (+.f64 (/.f64 1/2 x) 3/2) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3)))
(-.f64 (+.f64 3/2 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 3/2 (-.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 3/2 (/.f64 -1/4 (pow.f64 x 3)))))
3/2
(-.f64 3/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 3/2 (/.f64 1/2 x))
(+.f64 3/2 (/.f64 -1/2 x))
(-.f64 (+.f64 3/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 x)))
(+.f64 3/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 3/2 (/.f64 -1/2 x)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 3/2 (/.f64 1/2 x)))
(-.f64 (+.f64 3/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 3/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 3/2 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 3/2 (-.f64 (/.f64 -1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -3/16 (pow.f64 x 5)) (-.f64 3/2 (/.f64 1/2 x))))

prune327.0ms (7.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	215	5	220

Error

0.0b

Counts

220 → 5

Alt Table

Status	Error	Program
▶	15.7b	(/.f64 (/.f64 (pow.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3) 1/3) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	31.3b	(fma.f64 1/8 (.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (.f64 -1843/32768 (pow.f64 x 8)))))
	31.5b	(/.f64 (/.f64 (fma.f64 1/2 (.f64 x x) (.f64 -7/16 (pow.f64 x 4))) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	15.7b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	16.2b	(/.f64 (*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

Compiler

Compiled 8865 to 7920 computations (10.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
✓	0.0b	(pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3)
✓	0.1b	(pow.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3) 1/3)
	1.7b	(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(pow.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3) 1/3)
1.0ms	x	@	0	(pow.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3) 1/3)
1.0ms	x	@	-inf	(pow.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3) 1/3)
0.0ms	x	@	0	(pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3)
0.0ms	x	@	-inf	(pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3)

rewrite56.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`prod-diff_binary64`
226×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
191×	`fma-def_binary64`
140×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	322	35
2	3459	35

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3) 1/3)
(pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3)

Outputs

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

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

simplify32.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

446×	`times-frac_binary64`
315×	`fma-def_binary64`
166×	`distribute-neg-frac_binary64`
151×	`distribute-lft-out_binary64`
148×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	463
1	272	459
2	763	436
3	2612	435

Stop Event

1×	node limit

Counts

103 → 121

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 -7/16 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(+.f64 (.f64 -7/16 (pow.f64 x 4)) (+.f64 (.f64 13/32 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(+.f64 (.f64 -99/256 (pow.f64 x 8)) (+.f64 (.f64 -7/16 (pow.f64 x 4)) (+.f64 (.f64 13/32 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
3/4
(-.f64 3/4 (.f64 9/32 (/.f64 1 (.f64 (cbrt.f64 9/16) x))))
(-.f64 (+.f64 3/4 (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (pow.f64 x 2)))) (.f64 9/32 (/.f64 1 (.f64 (cbrt.f64 9/16) x))))
(-.f64 (+.f64 3/4 (+.f64 (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 1841/2048 (.f64 -3/4 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (cbrt.f64 9/16)))) (pow.f64 x 3))) (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (pow.f64 x 2))))) (.f64 9/32 (/.f64 1 (*.f64 (cbrt.f64 9/16) x))))
3/4
(+.f64 3/4 (.f64 9/32 (/.f64 1 (.f64 (cbrt.f64 9/16) x))))
(+.f64 3/4 (+.f64 (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (pow.f64 x 2))) (.f64 9/32 (/.f64 1 (.f64 (cbrt.f64 9/16) x)))))
(+.f64 3/4 (+.f64 (.f64 -667199944795629/1125899906842624 (/.f64 (-.f64 1841/2048 (.f64 -3/4 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (cbrt.f64 9/16)))) (pow.f64 x 3))) (+.f64 (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (pow.f64 x 2))) (.f64 9/32 (/.f64 1 (*.f64 (cbrt.f64 9/16) x))))))
(*.f64 1/8 (pow.f64 x 6))
(+.f64 (.f64 -21/64 (pow.f64 x 8)) (.f64 1/8 (pow.f64 x 6)))
(+.f64 (.f64 303/512 (pow.f64 x 10)) (+.f64 (.f64 -21/64 (pow.f64 x 8)) (*.f64 1/8 (pow.f64 x 6))))
(+.f64 (.f64 303/512 (pow.f64 x 10)) (+.f64 (.f64 -3715/4096 (pow.f64 x 12)) (+.f64 (.f64 -21/64 (pow.f64 x 8)) (.f64 1/8 (pow.f64 x 6)))))
27/64
(-.f64 27/64 (*.f64 27/32 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 9/64 (/.f64 1 (pow.f64 x 2))) 27/64) (.f64 27/32 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 9/64 (/.f64 1 (pow.f64 x 2))) (+.f64 27/64 (.f64 55/64 (/.f64 1 (pow.f64 x 3))))) (*.f64 27/32 (/.f64 1 x)))
27/64
(+.f64 27/64 (*.f64 27/32 (/.f64 1 x)))
(+.f64 (.f64 9/64 (/.f64 1 (pow.f64 x 2))) (+.f64 27/64 (.f64 27/32 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 9/64 (/.f64 1 (pow.f64 x 2))) (+.f64 27/64 (.f64 27/32 (/.f64 1 x)))) (*.f64 55/64 (/.f64 1 (pow.f64 x 3))))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(+.f64 (.f64 -7/16 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(fma.f64 -7/16 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.f64 (.f64 -7/16 (pow.f64 x 4)) (+.f64 (.f64 13/32 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -7/16 (pow.f64 x 4) (fma.f64 13/32 (pow.f64 x 6) (.f64 1/2 (.f64 x x))))
(fma.f64 -7/16 (pow.f64 x 4) (fma.f64 1/2 (.f64 x x) (.f64 13/32 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 13/32 (pow.f64 x 6) (.f64 -7/16 (pow.f64 x 4))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -7/16 (pow.f64 x 4) (.f64 13/32 (pow.f64 x 6))))
(+.f64 (.f64 -99/256 (pow.f64 x 8)) (+.f64 (.f64 -7/16 (pow.f64 x 4)) (+.f64 (.f64 13/32 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -99/256 (pow.f64 x 8) (fma.f64 -7/16 (pow.f64 x 4) (fma.f64 13/32 (pow.f64 x 6) (.f64 1/2 (.f64 x x)))))
(fma.f64 -99/256 (pow.f64 x 8) (fma.f64 -7/16 (pow.f64 x 4) (fma.f64 1/2 (.f64 x x) (.f64 13/32 (pow.f64 x 6)))))
(fma.f64 -7/16 (pow.f64 x 4) (fma.f64 -99/256 (pow.f64 x 8) (fma.f64 13/32 (pow.f64 x 6) (.f64 1/2 (.f64 x x)))))
(fma.f64 -7/16 (pow.f64 x 4) (fma.f64 -99/256 (pow.f64 x 8) (fma.f64 1/2 (.f64 x x) (.f64 13/32 (pow.f64 x 6)))))
3/4
(-.f64 3/4 (.f64 9/32 (/.f64 1 (.f64 (cbrt.f64 9/16) x))))
(-.f64 3/4 (/.f64 9/32 (*.f64 x (cbrt.f64 9/16))))
(+.f64 3/4 (/.f64 (/.f64 -9/32 (cbrt.f64 9/16)) x))
(-.f64 (+.f64 3/4 (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (pow.f64 x 2)))) (.f64 9/32 (/.f64 1 (.f64 (cbrt.f64 9/16) x))))
(+.f64 3/4 (-.f64 (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (/.f64 729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x))) (/.f64 9/32 (*.f64 x (cbrt.f64 9/16)))))
(+.f64 3/4 (fma.f64 667199944795629/1125899906842624 (/.f64 (+.f64 9/64 (/.f64 -729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x)) (/.f64 -9/32 (.f64 x (cbrt.f64 9/16)))))
(+.f64 3/4 (+.f64 (/.f64 (+.f64 6004799503160661/72057594037927936 (/.f64 -486388759756013541/4611686018427387904 (pow.f64 (cbrt.f64 9/16) 2))) (*.f64 x x)) (/.f64 (/.f64 -9/32 (cbrt.f64 9/16)) x)))
(-.f64 (+.f64 3/4 (+.f64 (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 1841/2048 (.f64 -3/4 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (cbrt.f64 9/16)))) (pow.f64 x 3))) (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (pow.f64 x 2))))) (.f64 9/32 (/.f64 1 (*.f64 (cbrt.f64 9/16) x))))
(+.f64 3/4 (-.f64 (.f64 667199944795629/1125899906842624 (+.f64 (/.f64 (+.f64 1841/2048 (.f64 3/4 (/.f64 (-.f64 9/64 (/.f64 729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (cbrt.f64 9/16)))) (pow.f64 x 3)) (/.f64 (-.f64 9/64 (/.f64 729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x)))) (/.f64 9/32 (.f64 x (cbrt.f64 9/16)))))
(+.f64 (fma.f64 667199944795629/1125899906842624 (+.f64 (/.f64 (+.f64 9/64 (/.f64 -729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x)) (/.f64 (+.f64 1841/2048 (.f64 3/4 (/.f64 (+.f64 9/64 (/.f64 -729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (cbrt.f64 9/16)))) (pow.f64 x 3))) 3/4) (/.f64 -9/32 (*.f64 x (cbrt.f64 9/16))))
(+.f64 3/4 (+.f64 (/.f64 (+.f64 6004799503160661/72057594037927936 (/.f64 -486388759756013541/4611686018427387904 (pow.f64 (cbrt.f64 9/16) 2))) (*.f64 x x)) (fma.f64 667199944795629/1125899906842624 (/.f64 (fma.f64 3/4 (+.f64 (/.f64 9/64 (cbrt.f64 9/16)) -81/256) 1841/2048) (pow.f64 x 3)) (/.f64 (/.f64 -9/32 (cbrt.f64 9/16)) x))))
(+.f64 (*.f64 (/.f64 (/.f64 667199944795629/1125899906842624 x) x) (+.f64 (/.f64 (fma.f64 3/4 (+.f64 (/.f64 9/64 (cbrt.f64 9/16)) -81/256) 1841/2048) x) (+.f64 9/64 (/.f64 -729/4096 (pow.f64 (cbrt.f64 9/16) 2))))) (+.f64 3/4 (/.f64 (/.f64 -9/32 (cbrt.f64 9/16)) x)))
3/4
(+.f64 3/4 (.f64 9/32 (/.f64 1 (.f64 (cbrt.f64 9/16) x))))
(+.f64 3/4 (/.f64 9/32 (*.f64 x (cbrt.f64 9/16))))
(+.f64 3/4 (+.f64 (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (pow.f64 x 2))) (.f64 9/32 (/.f64 1 (.f64 (cbrt.f64 9/16) x)))))
(+.f64 3/4 (fma.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (/.f64 729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x)) (/.f64 9/32 (.f64 x (cbrt.f64 9/16)))))
(+.f64 3/4 (fma.f64 667199944795629/1125899906842624 (/.f64 (+.f64 9/64 (/.f64 -729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x)) (/.f64 9/32 (.f64 x (cbrt.f64 9/16)))))
(+.f64 3/4 (+.f64 (/.f64 9/32 (.f64 x (cbrt.f64 9/16))) (/.f64 (+.f64 6004799503160661/72057594037927936 (/.f64 -486388759756013541/4611686018427387904 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x))))
(+.f64 3/4 (+.f64 (.f64 -667199944795629/1125899906842624 (/.f64 (-.f64 1841/2048 (.f64 -3/4 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (cbrt.f64 9/16)))) (pow.f64 x 3))) (+.f64 (.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (.f64 729/4096 (/.f64 1 (pow.f64 (cbrt.f64 9/16) 2)))) (pow.f64 x 2))) (.f64 9/32 (/.f64 1 (*.f64 (cbrt.f64 9/16) x))))))
(+.f64 3/4 (fma.f64 -667199944795629/1125899906842624 (/.f64 (+.f64 1841/2048 (.f64 3/4 (/.f64 (-.f64 9/64 (/.f64 729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (cbrt.f64 9/16)))) (pow.f64 x 3)) (fma.f64 667199944795629/1125899906842624 (/.f64 (-.f64 9/64 (/.f64 729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x)) (/.f64 9/32 (*.f64 x (cbrt.f64 9/16))))))
(+.f64 3/4 (fma.f64 (/.f64 (+.f64 1841/2048 (.f64 3/4 (/.f64 (+.f64 9/64 (/.f64 -729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (cbrt.f64 9/16)))) (pow.f64 x 3)) -667199944795629/1125899906842624 (fma.f64 667199944795629/1125899906842624 (/.f64 (+.f64 9/64 (/.f64 -729/4096 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x)) (/.f64 9/32 (*.f64 x (cbrt.f64 9/16))))))
(+.f64 (+.f64 (/.f64 9/32 (.f64 x (cbrt.f64 9/16))) (/.f64 (+.f64 6004799503160661/72057594037927936 (/.f64 -486388759756013541/4611686018427387904 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x))) (fma.f64 (/.f64 (fma.f64 3/4 (+.f64 (/.f64 9/64 (cbrt.f64 9/16)) -81/256) 1841/2048) (pow.f64 x 3)) -667199944795629/1125899906842624 3/4))
(+.f64 3/4 (fma.f64 (/.f64 (fma.f64 3/4 (+.f64 (/.f64 9/64 (cbrt.f64 9/16)) -81/256) 1841/2048) (pow.f64 x 3)) -667199944795629/1125899906842624 (+.f64 (/.f64 9/32 (.f64 x (cbrt.f64 9/16))) (/.f64 (+.f64 6004799503160661/72057594037927936 (/.f64 -486388759756013541/4611686018427387904 (pow.f64 (cbrt.f64 9/16) 2))) (.f64 x x)))))
(*.f64 1/8 (pow.f64 x 6))
(*.f64 (pow.f64 x 6) 1/8)
(+.f64 (.f64 -21/64 (pow.f64 x 8)) (.f64 1/8 (pow.f64 x 6)))
(fma.f64 -21/64 (pow.f64 x 8) (*.f64 (pow.f64 x 6) 1/8))
(fma.f64 (pow.f64 x 6) 1/8 (*.f64 (pow.f64 x 8) -21/64))
(+.f64 (.f64 303/512 (pow.f64 x 10)) (+.f64 (.f64 -21/64 (pow.f64 x 8)) (*.f64 1/8 (pow.f64 x 6))))
(fma.f64 303/512 (pow.f64 x 10) (fma.f64 -21/64 (pow.f64 x 8) (*.f64 (pow.f64 x 6) 1/8)))
(fma.f64 303/512 (pow.f64 x 10) (fma.f64 (pow.f64 x 6) 1/8 (*.f64 (pow.f64 x 8) -21/64)))
(fma.f64 (pow.f64 x 6) 1/8 (fma.f64 303/512 (pow.f64 x 10) (*.f64 (pow.f64 x 8) -21/64)))
(fma.f64 (pow.f64 x 8) -21/64 (fma.f64 (pow.f64 x 6) 1/8 (*.f64 303/512 (pow.f64 x 10))))
(+.f64 (.f64 303/512 (pow.f64 x 10)) (+.f64 (.f64 -3715/4096 (pow.f64 x 12)) (+.f64 (.f64 -21/64 (pow.f64 x 8)) (.f64 1/8 (pow.f64 x 6)))))
(fma.f64 303/512 (pow.f64 x 10) (fma.f64 -3715/4096 (pow.f64 x 12) (fma.f64 -21/64 (pow.f64 x 8) (*.f64 (pow.f64 x 6) 1/8))))
(fma.f64 303/512 (pow.f64 x 10) (fma.f64 -3715/4096 (pow.f64 x 12) (fma.f64 (pow.f64 x 6) 1/8 (*.f64 (pow.f64 x 8) -21/64))))
(fma.f64 303/512 (pow.f64 x 10) (fma.f64 (pow.f64 x 6) 1/8 (fma.f64 -3715/4096 (pow.f64 x 12) (*.f64 (pow.f64 x 8) -21/64))))
(fma.f64 -3715/4096 (pow.f64 x 12) (fma.f64 (pow.f64 x 8) -21/64 (fma.f64 (pow.f64 x 6) 1/8 (*.f64 303/512 (pow.f64 x 10)))))
27/64
(-.f64 27/64 (*.f64 27/32 (/.f64 1 x)))
(-.f64 27/64 (/.f64 27/32 x))
(+.f64 27/64 (/.f64 -27/32 x))
(-.f64 (+.f64 (.f64 9/64 (/.f64 1 (pow.f64 x 2))) 27/64) (.f64 27/32 (/.f64 1 x)))
(+.f64 (/.f64 9/64 (*.f64 x x)) (-.f64 27/64 (/.f64 27/32 x)))
(+.f64 27/64 (-.f64 (/.f64 (/.f64 9/64 x) x) (/.f64 27/32 x)))
(+.f64 (/.f64 9/64 (*.f64 x x)) (+.f64 27/64 (/.f64 -27/32 x)))
(+.f64 (/.f64 (/.f64 9/64 x) x) (+.f64 27/64 (/.f64 -27/32 x)))
(-.f64 (+.f64 (.f64 9/64 (/.f64 1 (pow.f64 x 2))) (+.f64 27/64 (.f64 55/64 (/.f64 1 (pow.f64 x 3))))) (*.f64 27/32 (/.f64 1 x)))
(+.f64 (/.f64 9/64 (*.f64 x x)) (-.f64 (+.f64 27/64 (/.f64 55/64 (pow.f64 x 3))) (/.f64 27/32 x)))
(+.f64 (/.f64 (/.f64 9/64 x) x) (+.f64 (/.f64 55/64 (pow.f64 x 3)) (+.f64 27/64 (/.f64 -27/32 x))))
(+.f64 (/.f64 9/64 (*.f64 x x)) (+.f64 27/64 (+.f64 (/.f64 55/64 (pow.f64 x 3)) (/.f64 -27/32 x))))
(+.f64 (+.f64 27/64 (/.f64 (/.f64 9/64 x) x)) (+.f64 (/.f64 55/64 (pow.f64 x 3)) (/.f64 -27/32 x)))
27/64
(+.f64 27/64 (*.f64 27/32 (/.f64 1 x)))
(+.f64 27/64 (/.f64 27/32 x))
(+.f64 (.f64 9/64 (/.f64 1 (pow.f64 x 2))) (+.f64 27/64 (.f64 27/32 (/.f64 1 x))))
(+.f64 (/.f64 9/64 (*.f64 x x)) (+.f64 27/64 (/.f64 27/32 x)))
(+.f64 27/64 (+.f64 (/.f64 (/.f64 9/64 x) x) (/.f64 27/32 x)))
(+.f64 27/64 (+.f64 (/.f64 27/32 x) (/.f64 (/.f64 9/64 x) x)))
(-.f64 (+.f64 (.f64 9/64 (/.f64 1 (pow.f64 x 2))) (+.f64 27/64 (.f64 27/32 (/.f64 1 x)))) (*.f64 55/64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 9/64 (*.f64 x x)) (-.f64 (+.f64 27/64 (/.f64 27/32 x)) (/.f64 55/64 (pow.f64 x 3))))
(+.f64 (/.f64 (/.f64 9/64 x) x) (+.f64 (/.f64 27/32 x) (-.f64 27/64 (/.f64 55/64 (pow.f64 x 3)))))
(+.f64 27/64 (-.f64 (+.f64 (/.f64 27/32 x) (/.f64 9/64 (*.f64 x x))) (/.f64 55/64 (pow.f64 x 3))))
(+.f64 27/64 (+.f64 (+.f64 (/.f64 27/32 x) (/.f64 (/.f64 9/64 x) x)) (/.f64 -55/64 (pow.f64 x 3))))

prune383.0ms (9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	222	5	227

Error

0.0b

Counts

227 → 5

Alt Table

Status	Error	Program
	15.7b	(/.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 6)) (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 2)) (+.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) 1/3) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	31.3b	(fma.f64 1/8 (.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (.f64 -1843/32768 (pow.f64 x 8)))))
	31.5b	(/.f64 (/.f64 (fma.f64 1/2 (.f64 x x) (.f64 -7/16 (pow.f64 x 4))) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	15.7b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	16.2b	(/.f64 (*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

Compiler

Compiled 10094 to 9096 computations (9.9% saved)

regimes221.0ms (5.2%)

Accuracy

Total -63.6b remaining (-174357.5%)

Threshold costs -63.6b (-174357.5%)

Counts

35 → 2

Calls

Call 1

Inputs
(/.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 6)) (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 2)) (+.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 4)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) 1/3) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (sqrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) 3) (pow.f64 (sqrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) 3)) 1/3) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (/.f64 (pow.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) 3) 1/3) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (/.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) (sqrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)))) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (/.f64 (fma.f64 1/2 (.f64 x x) (.f64 -7/16 (pow.f64 x 4))) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (/.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -7/16 (pow.f64 x 4))) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (*.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (/.f64 1 (+.f64 (+.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (/.f64 1/4 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 1/2)))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(/.f64 (+.f64 1/2 (/.f64 1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
(pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3)
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(*.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(*.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(*.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(*.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 1)
(-.f64 1 (sqrt.f64 1/2))
(fma.f64 1/8 (.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (.f64 -1843/32768 (pow.f64 x 8)))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 -1843/32768 (pow.f64 x 8)) (.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 1/8 (.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (.f64 69/1024 (pow.f64 x 6))))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Outputs

(fma.f64 1/8 (*.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 -1843/32768 (pow.f64 x 8)))))

(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

Results

43.0ms	0.0b	`x`
9.0ms	0.0b	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
6.0ms	0.0b	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
6.0ms	0.0b	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
8.0ms	0.0b	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
6.0ms	0.0b	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
6.0ms	0.0b	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
18.0ms	0.0b	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
6.0ms	0.0b	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
23.0ms	0.0b	`(/.f64 1 (hypot.f64 1 x))`
44.0ms	0.0b	`(/.f64 1 (hypot.f64 1 x))`
12.0ms	0.0b	`(hypot.f64 1 x)`
11.0ms	0.0b	`(hypot.f64 1 x)`

Compiler

Compiled 861 to 759 computations (11.8% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(hypot.f64 1 x)

Steps

Iters	Point		Range
1.0005	∈ [	1.000025719052235	,	1.0007186928175256	]

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	64
1	37	64
2	44	64
3	46	64
4	47	64

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (hypot.f64 1 x) 4505851427184181/4503599627370496) (fma.f64 1/8 (*.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 -1843/32768 (pow.f64 x 8))))) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Outputs

(if (<=.f64 (hypot.f64 1 x) 4505851427184181/4503599627370496) (fma.f64 1/8 (*.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 -1843/32768 (pow.f64 x 8))))) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

(if (<=.f64 (hypot.f64 1 x) 4505851427184181/4503599627370496) (fma.f64 1/8 (*.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 -1843/32768 (pow.f64 x 8))))) (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

end35.0ms (0.8%)

Stop Event

1×

fuel

Compiler

Compiled 90 to 74 computations (17.8% saved)

Details

analyze0.0ms (0%)

sample2.3s (54.2%)

preprocess20.0ms (0.5%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series6.0ms (0.2%)

rewrite63.0ms (1.5%)

simplify42.0ms (1%)

prune211.0ms (5%)

localize8.0ms (0.2%)

series3.0ms (0.1%)

rewrite49.0ms (1.2%)

simplify30.0ms (0.7%)

prune304.0ms (7.2%)

localize11.0ms (0.3%)

series4.0ms (0.1%)

rewrite58.0ms (1.4%)

simplify40.0ms (0.9%)

prune327.0ms (7.7%)

localize14.0ms (0.3%)

series5.0ms (0.1%)

rewrite56.0ms (1.3%)

simplify32.0ms (0.8%)

prune383.0ms (9%)

regimes221.0ms (5.2%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end35.0ms (0.8%)

Profiling