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)

sample1.8s (24%)

Results

916.0ms	2195×	body	2048	valid
489.0ms	4522×	body	256	valid
309.0ms	1052×	body	1024	valid
103.0ms	487×	body	512	valid

preprocess18.0ms (0.2%)

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 14 to 13 computations (7.1% saved)

simplify8.0ms (0.1%)

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)))))

eval1.0ms (0%)

Compiler: Compiled 23 to 21 computations (8.7% saved)

prune1.0ms (0%)

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

16.3b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	16.3b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 11 to 10 computations (9.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.0b	(hypot.f64 1 x)
✓	1.6b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 37 to 31 computations (16.2% saved)

series7.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite79.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

595×	`unpow-prod-down_binary64`
406×	`log-prod_binary64`
387×	`prod-diff_binary64`
249×	`pow2_binary64`
228×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	201	38
2	2602	38

Stop Event

1×	node limit

Counts

4 → 178

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(hypot.f64 1 x)
(sqrt.f64 (+.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 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2)) (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 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (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)) (pow.f64 (/.f64 1 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) 1))))) (#(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 1/2 (/.f64 1/2 (hypot.f64 1 x))) (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)) 1/3) (pow.f64 (sqrt.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 .f64 (pow.f64 (pow.f64 (.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))))))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (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 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2) 3) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 3) (pow.f64 (sqrt.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 /.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (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 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (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 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (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 (.f64 -1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) (neg.f64 (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))))) 2)) (-.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))))) 2) 1/2)))) (#(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 pow.f64 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (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))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.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)))) -1)))) (#(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 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 log1p.f64 (expm1.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 (neg.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 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/3 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (/.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (/.f64 1 (neg.f64 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (pow.f64 (/.f64 1 (neg.f64 (hypot.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (hypot.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (/.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 1/2) 3) (/.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) 2) 3) (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 1/2) 2) (/.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1/8 1/3) (/.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (/.f64 1/4 (fma.f64 x x 1)) 1/2) 1/3) (cbrt.f64 (/.f64 1 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (/.f64 1/4 (fma.f64 x x 1)) (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1)))) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (hypot.f64 1 x) 2)) 2) -1) (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (fma.f64 x x 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/8 (pow.f64 (hypot.f64 1 x) -3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (hypot.f64 1 x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (hypot.f64 1 x) 2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 1/8 (pow.f64 (hypot.f64 1 x) -3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 1/2 (hypot.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/8 (pow.f64 (hypot.f64 1 x) -3))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (hypot.f64 1 x) 2)) -1))))))

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary64`
347×	`associate-*l/_binary64`
338×	`times-frac_binary64`
330×	`associate-*r/_binary64`
323×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	918
1	424	841
2	1268	824
3	3912	824

Stop Event

1×	node limit

Counts

226 → 261

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

eval191.0ms (2.5%)

Compiler: Compiled 4713 to 4212 computations (10.6% saved)

prune108.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	252	9	261
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	253	9	262

Error

0.0b

Counts

262 → 9

Alt Table

Click to see full alt table

Status	Error	Program
	33.8b	(-.f64 1 (sqrt.f64 1/2))
▶	29.0b	(.f64 1/8 (.f64 x x))
	34.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
▶	29.7b	(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))
▶	33.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))
	15.9b	(/.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))))))
▶	34.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
▶	15.9b	(/.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)))))
	33.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))

Compiler

Compiled 212 to 182 computations (14.2% saved)

localize68.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 x)
✓	0.0b	(/.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)))))
✓	0.0b	(/.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))))
✓	1.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 82 to 71 computations (13.4% saved)

series13.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(/.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)))))
2.0ms	x	@	inf	(/.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))))
2.0ms	x	@	-inf	(/.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)))))
1.0ms	x	@	0	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
1.0ms	x	@	-inf	(/.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))))

rewrite142.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

630×	`log-prod_binary64`
504×	`prod-diff_binary64`
323×	`fma-def_binary64`
243×	`log-div_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	67
1	279	43
2	3973	43

Stop Event

1×	node limit

Counts

3 → 146

Calls

Call 1

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

Inputs

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

(/.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 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)))))

Outputs
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Outputs

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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1/2 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 -1/2 (hypot.f64 1 x))))))))

simplify139.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

727×	`times-frac_binary64`
601×	`associate-l_binary64`
387×	`associate-/l*_binary64`
231×	`fma-def_binary64`
228×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	1903
1	801	1644
2	2888	1593

Stop Event

1×	node limit

Counts

182 → 211

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))))
(/.f64 8 (pow.f64 x 2))
(+.f64 11/2 (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(+.f64 11/2 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) (.f64 -17/32 (pow.f64 x 2))))
(+.f64 11/2 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 69/256 (pow.f64 x 4)) (*.f64 -17/32 (pow.f64 x 2)))))
(*.f64 2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/2 (.f64 (sqrt.f64 1/2) x))) (*.f64 -2 (/.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(-.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (*.f64 -2 (/.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(-.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2))) (+.f64 (.f64 1/64 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (.f64 -2 (/.f64 (+.f64 1 (sqrt.f64 1/2)) x)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 3)))) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))
(*.f64 2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)))
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)) (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (*.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2)))))
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2))) (.f64 -1 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 5))) (+.f64 (sqrt.f64 1/2) (+.f64 1 (+.f64 (.f64 1/4 (/.f64 1 (sqrt.f64 1/2))) (+.f64 (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2))))) (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))))))) (pow.f64 x 3))))))
(*.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 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(-.f64 (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)) (.f64 1/4 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 x 3))))))) (+.f64 (.f64 -1/4 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (+.f64 (.f64 1/32 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 3))))) (+.f64 (.f64 1/4 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (.f64 1/4 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (/.f64 1/8 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (+.f64 (/.f64 1/2 (.f64 (+.f64 (sqrt.f64 1/2) 1) x)) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (.f64 1/4 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2)))) (+.f64 (.f64 1/4 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/32 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 (sqrt.f64 1/2) 3))))))) (pow.f64 x 3))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (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 1/4 (.f64 x x) (.f64 (pow.f64 x 4) -3/16))
(fma.f64 (pow.f64 x 4) -3/16 (.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 5/32 (pow.f64 x 6) (fma.f64 1/4 (.f64 x x) (.f64 (pow.f64 x 4) -3/16)))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (.f64 1/4 (.f64 x x))))
(+.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 (pow.f64 x 4) -3/16 (.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 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (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 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 1/2 (/.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 1/2 (+.f64 (/.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 x) (+.f64 1/2 (/.f64 3/16 (pow.f64 x 5)))) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (+.f64 1/2 (/.f64 1/2 x)) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3))))
(+.f64 (+.f64 1/2 (/.f64 3/16 (pow.f64 x 5))) (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 (/.f64 8 x) x)
(+.f64 11/2 (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(+.f64 11/2 (/.f64 8 (*.f64 x x)))
(+.f64 11/2 (/.f64 (/.f64 8 x) x))
(+.f64 11/2 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) (.f64 -17/32 (pow.f64 x 2))))
(+.f64 11/2 (+.f64 (/.f64 8 (.f64 x x)) (.f64 (*.f64 x x) -17/32)))
(+.f64 11/2 (fma.f64 (*.f64 x x) -17/32 (/.f64 (/.f64 8 x) x)))
(+.f64 11/2 (fma.f64 (.f64 x x) -17/32 (/.f64 8 (.f64 x x))))
(+.f64 11/2 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 69/256 (pow.f64 x 4)) (*.f64 -17/32 (pow.f64 x 2)))))
(+.f64 11/2 (+.f64 (/.f64 8 (.f64 x x)) (fma.f64 69/256 (pow.f64 x 4) (.f64 (*.f64 x x) -17/32))))
(+.f64 11/2 (+.f64 (/.f64 (/.f64 8 x) x) (fma.f64 (pow.f64 x 4) 69/256 (.f64 x (.f64 x -17/32)))))
(+.f64 11/2 (+.f64 (/.f64 8 (.f64 x x)) (fma.f64 (pow.f64 x 4) 69/256 (.f64 x (*.f64 x -17/32)))))
(*.f64 2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 2 (sqrt.f64 1/2)) 2)
(fma.f64 2 (sqrt.f64 1/2) 2)
(-.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/2 (.f64 (sqrt.f64 1/2) x))) (*.f64 -2 (/.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (+.f64 (.f64 2 (sqrt.f64 1/2)) 2) (/.f64 (+.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (.f64 2 (sqrt.f64 1/2)) 2)) x))
(+.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (/.f64 (+.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (/.f64 1/2 (sqrt.f64 1/2))) x))
(+.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (/.f64 (-.f64 (/.f64 1/2 (sqrt.f64 1/2)) (fma.f64 (sqrt.f64 1/2) -2 -2)) x))
(-.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (*.f64 -2 (/.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (fma.f64 -1 (/.f64 (fma.f64 -1 (+.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (.f64 2 (sqrt.f64 1/2)) 2)) (/.f64 1/16 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 x x)) (/.f64 1/2 (.f64 x (sqrt.f64 1/2))))) (.f64 2 (/.f64 (+.f64 1 (sqrt.f64 1/2)) x)))
(+.f64 (-.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (/.f64 (-.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (/.f64 1/2 (sqrt.f64 1/2)))) (*.f64 x x))) (/.f64 (+.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (/.f64 1/2 (sqrt.f64 1/2))) x))
(+.f64 (-.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (/.f64 (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2)))) (*.f64 x x))) (/.f64 (-.f64 (/.f64 1/2 (sqrt.f64 1/2)) (fma.f64 (sqrt.f64 1/2) -2 -2)) x))
(-.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2))) (+.f64 (.f64 1/64 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (.f64 -2 (/.f64 (+.f64 1 (sqrt.f64 1/2)) x)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 3)))) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))
(-.f64 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (fma.f64 -1 (/.f64 (fma.f64 -1 (+.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (.f64 2 (sqrt.f64 1/2)) 2)) (/.f64 1/16 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 x x)) (+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 1/2))) (/.f64 1/64 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5)))))) (+.f64 (/.f64 1/4 (.f64 (pow.f64 x 3) (sqrt.f64 1/2))) (+.f64 (/.f64 1 (pow.f64 x 3)) (fma.f64 -2 (/.f64 (+.f64 1 (sqrt.f64 1/2)) x) (fma.f64 -1 (/.f64 (+.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (.f64 2 (sqrt.f64 1/2)) 2)) (pow.f64 x 3)) (+.f64 (/.f64 1/16 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))
(+.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (-.f64 (-.f64 (+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 1/2))) (/.f64 1/64 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5)))) (/.f64 (-.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (/.f64 1/2 (sqrt.f64 1/2)))) (.f64 x x))) (+.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) x) (-.f64 (+.f64 (/.f64 (/.f64 1/8 (sqrt.f64 1/2)) (pow.f64 x 3)) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 (+.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (/.f64 1/2 (sqrt.f64 1/2))) (pow.f64 x 3)))) (/.f64 1/4 (.f64 (pow.f64 x 3) (sqrt.f64 1/2)))))))
(+.f64 (fma.f64 2 (sqrt.f64 1/2) 2) (+.f64 (-.f64 (/.f64 1/64 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))) (/.f64 (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2)))) (.f64 x x))) (-.f64 (/.f64 (/.f64 1/2 (sqrt.f64 1/2)) x) (+.f64 (+.f64 (/.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))) (pow.f64 x 3)) (+.f64 (+.f64 (/.f64 (/.f64 1/8 (sqrt.f64 1/2)) (pow.f64 x 3)) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) x))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1/4 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2))))))))
(*.f64 2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 2 (sqrt.f64 1/2)) 2)
(fma.f64 2 (sqrt.f64 1/2) 2)
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)))
(fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 (neg.f64 (+.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (*.f64 2 (sqrt.f64 1/2)) 2))) x))
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(+.f64 (/.f64 1/2 (.f64 x (+.f64 1 (sqrt.f64 1/2)))) (-.f64 (+.f64 (/.f64 1/64 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (.f64 x x) (+.f64 1 (sqrt.f64 1/2)))))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (.f64 x (+.f64 1 (sqrt.f64 1/2)))))))) (.f64 -1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (.f64 x x) (sqrt.f64 1/2)))))))
(+.f64 (/.f64 1/2 (.f64 x (+.f64 1 (sqrt.f64 1/2)))) (+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (.f64 x (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (sqrt.f64 1/2))))) (-.f64 (/.f64 1/64 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (.f64 x x) (+.f64 1/4 (.f64 1/2 (sqrt.f64 1/2)))))) (.f64 -1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (.f64 (*.f64 x x) (+.f64 1/2 (sqrt.f64 1/2))))))))
(+.f64 (/.f64 (/.f64 1/2 x) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 1/64 (.f64 (.f64 x x) (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/4 (.f64 1/2 (sqrt.f64 1/2)))))) (-.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 x (.f64 x (sqrt.f64 1/2))))) (/.f64 (/.f64 (+.f64 (/.f64 -1/8 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/32 (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (sqrt.f64 1/2))) (*.f64 x x)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (.f64 1/4 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2)))) (+.f64 (.f64 1/4 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/32 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 (sqrt.f64 1/2) 3))))))) (pow.f64 x 3))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 (/.f64 1/2 (.f64 x (+.f64 1 (sqrt.f64 1/2)))) (-.f64 (+.f64 (/.f64 1/64 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (.f64 x x) (+.f64 1 (sqrt.f64 1/2)))))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 -1 (/.f64 (-.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 1/4 (/.f64 (+.f64 (/.f64 1/64 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3)))) (.f64 1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))) (fma.f64 1/4 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) (.f64 1/32 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3))))))) (pow.f64 x 3)) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (.f64 x (+.f64 1 (sqrt.f64 1/2))))))))) (.f64 -1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (*.f64 x x) (sqrt.f64 1/2)))))))
(+.f64 (/.f64 1/2 (.f64 x (+.f64 1 (sqrt.f64 1/2)))) (+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/64 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (.f64 x x) (+.f64 1/4 (.f64 1/2 (sqrt.f64 1/2))))))) (-.f64 (-.f64 (/.f64 1/8 (.f64 (.f64 x (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (sqrt.f64 1/2)))) (/.f64 (-.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 1/4 (/.f64 (-.f64 (/.f64 (/.f64 1/64 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/4 (.f64 1/2 (sqrt.f64 1/2)))) (.f64 -1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (sqrt.f64 1/2))) (fma.f64 1/32 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/4 (.f64 1/2 (sqrt.f64 1/2)))) (/.f64 (/.f64 -3/64 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (sqrt.f64 1/2)))))) (pow.f64 x 3))) (.f64 -1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (.f64 (.f64 x x) (+.f64 1/2 (sqrt.f64 1/2))))))))
(+.f64 (/.f64 (/.f64 1/2 x) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/64 (.f64 (.f64 x x) (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/4 (.f64 1/2 (sqrt.f64 1/2))))))) (-.f64 (-.f64 (/.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 x (.f64 x (sqrt.f64 1/2)))) (/.f64 (-.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 (+.f64 (/.f64 1/64 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/256 (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/4 (.f64 1/2 (sqrt.f64 1/2)))) (.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (-.f64 (/.f64 (/.f64 1/64 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/4 (.f64 1/4 (sqrt.f64 1/2)))) (/.f64 (+.f64 (/.f64 -1/8 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/32 (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (.f64 1/2 (sqrt.f64 1/2))))) (/.f64 -3/16 (+.f64 1/2 (sqrt.f64 1/2))))))) (pow.f64 x 3))) (/.f64 (/.f64 (+.f64 (/.f64 -1/8 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/32 (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (sqrt.f64 1/2))) (*.f64 x x)))))

localize9.0ms (0.1%)

Compiler: Compiled 11 to 5 computations (54.5% saved)

localize24.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
✓	0.4b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))

Compiler

Compiled 27 to 22 computations (18.5% saved)

series13.0ms (0.2%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
2.0ms	x	@	0	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
1.0ms	x	@	-inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
1.0ms	x	@	0	(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
1.0ms	x	@	inf	(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))

rewrite104.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

974×	`pow1_binary64`
910×	`add-log-exp_binary64`
910×	`log1p-expm1-u_binary64`
910×	`expm1-log1p-u_binary64`
98×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	199	21
2	2496	21

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

Outputs

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

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

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Rules

852×	`distribute-neg-frac_binary64`
828×	`fma-neg_binary64`
724×	`cancel-sign-sub-inv_binary64`
637×	`associate-/r*_binary64`
381×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	408
1	112	392
2	334	384
3	1192	384
4	5315	384

Stop Event

1×	node limit

Counts

68 → 66

Calls

Call 1

Inputs
(-.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 1 (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (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))))))) (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 (+.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 1 (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (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))))))) (sqrt.f64 1/2))
(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 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (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)))))))
(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 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (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 (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 1/4 (*.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 1 (-.f64 (/.f64 1/4 (*.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 1 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x))))) (sqrt.f64 1/2))
(+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x)) (sqrt.f64 1/2))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (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))))))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (+.f64 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x)))) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (sqrt.f64 1/2)))
(+.f64 (+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x)) (-.f64 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (sqrt.f64 1/2))))
(+.f64 (-.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x))))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))
(-.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 1/4 (*.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 1 (-.f64 (/.f64 1/4 (*.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 1 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x))))) (sqrt.f64 1/2))
(+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x)) (sqrt.f64 1/2))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (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))))))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (+.f64 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x)))) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (sqrt.f64 1/2)))
(+.f64 (+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x)) (-.f64 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (sqrt.f64 1/2))))
(+.f64 (-.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x))))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (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 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.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 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x)))))
(-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (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 (-.f64 (sqrt.f64 1/2) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x)))))
(-.f64 (-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 -1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))))
(+.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)))) (/.f64 -1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (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 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.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 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x)))))
(-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (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 (-.f64 (sqrt.f64 1/2) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x)))))
(-.f64 (-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 -1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))))
(+.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)))) (/.f64 -1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))

localize37.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))))
✓	0.1b	(/.f64 1/2 (+.f64 x (/.f64 1/2 x)))
✓	1.0b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))

Compiler

Compiled 50 to 38 computations (24% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite96.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

987×	`prod-diff_binary64`
516×	`log-prod_binary64`
382×	`fma-def_binary64`
206×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	235	43
2	3363	43

Stop Event

1×	node limit

Counts

3 → 99

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 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 (+.f64 x (/.f64 1/2 x)))))))) (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 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 (+.f64 x (/.f64 1/2 x))))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))))))) 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(/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))) 1/4)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x)))) 1/4) 1)))))

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

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

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

700×	`times-frac_binary64`
631×	`associate-/l*_binary64`
549×	`associate-*l/_binary64`
442×	`associate-*r/_binary64`
350×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	848
1	332	748
2	1122	724
3	3407	708

Stop Event

1×	node limit

Counts

135 → 141

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 x (sqrt.f64 1/2)))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 1 (.f64 -1/2 (/.f64 x (sqrt.f64 1/2))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 1/8 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 2) (pow.f64 x 3)) (sqrt.f64 1/2))) (+.f64 1 (*.f64 -1/2 (/.f64 x (sqrt.f64 1/2)))))) (sqrt.f64 1/2))
(-.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 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 (.f64 1/2 (/.f64 (-.f64 1/4 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.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)))))
x
(+.f64 (*.f64 -2 (pow.f64 x 3)) x)
(+.f64 (.f64 4 (pow.f64 x 5)) (+.f64 (.f64 -2 (pow.f64 x 3)) x))
(+.f64 (.f64 4 (pow.f64 x 5)) (+.f64 (.f64 -2 (pow.f64 x 3)) (+.f64 (*.f64 -8 (pow.f64 x 7)) x)))
(/.f64 1/2 x)
(-.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))))
(/.f64 1/2 x)
(-.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 1/2 (/.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 1/8 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 2) (pow.f64 x 3)) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 1/2))))))
(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 (+.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 1/4 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 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)))))

Outputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 x (sqrt.f64 1/2)))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)))
(-.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 1/2)) 1) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 1 (.f64 -1/2 (/.f64 x (sqrt.f64 1/2))))) (sqrt.f64 1/2))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (+.f64 1 (.f64 -1/2 (/.f64 x (sqrt.f64 1/2))))) (sqrt.f64 1/2))
(+.f64 (-.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 1/2)) 1) (sqrt.f64 1/2)) (.f64 1/4 (/.f64 (.f64 x x) (sqrt.f64 1/2))))
(-.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 1/2)) (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) 1)) (sqrt.f64 1/2))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (/.f64 x (sqrt.f64 1/2)) (+.f64 (/.f64 x 4) -1/2)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 1/8 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 2) (pow.f64 x 3)) (sqrt.f64 1/2))) (+.f64 1 (*.f64 -1/2 (/.f64 x (sqrt.f64 1/2)))))) (sqrt.f64 1/2))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1/8 (pow.f64 (sqrt.f64 1/2) 4)) -2) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (.f64 -1/2 (/.f64 x (sqrt.f64 1/2)))))) (sqrt.f64 1/2))
(+.f64 (.f64 1/4 (/.f64 (.f64 x x) (sqrt.f64 1/2))) (+.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 1/2)) 1) (-.f64 (/.f64 (*.f64 3/4 (pow.f64 x 3)) (sqrt.f64 1/2)) (sqrt.f64 1/2))))
(+.f64 (fma.f64 -1/2 (/.f64 x (sqrt.f64 1/2)) 1) (-.f64 (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) (*.f64 (/.f64 3/4 (sqrt.f64 1/2)) (pow.f64 x 3))) (sqrt.f64 1/2)))
(+.f64 (+.f64 1 (*.f64 (/.f64 x (sqrt.f64 1/2)) (+.f64 (/.f64 x 4) -1/2))) (fma.f64 (/.f64 3/4 (sqrt.f64 1/2)) (pow.f64 x 3) (neg.f64 (sqrt.f64 1/2))))
(-.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 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 -1/4 (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 1 (-.f64 (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) 1) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(+.f64 1 (-.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(+.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x)))) (/.f64 (/.f64 -1/4 (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 (+.f64 (+.f64 1 (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))) (.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 (sqrt.f64 1/2) x))))
(+.f64 1 (-.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 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(+.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (-.f64 (+.f64 1 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(+.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (+.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))
(-.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 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 -1/4 (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 1 (-.f64 (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) 1) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(+.f64 1 (-.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(+.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x)))) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 1/4 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.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 (+.f64 1 (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))) (.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 (sqrt.f64 1/2) x))))
(+.f64 1 (-.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 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(+.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (-.f64 (+.f64 1 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(+.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (+.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))
x
(+.f64 (*.f64 -2 (pow.f64 x 3)) x)
(fma.f64 -2 (pow.f64 x 3) x)
(fma.f64 (pow.f64 x 3) -2 x)
(+.f64 (.f64 4 (pow.f64 x 5)) (+.f64 (.f64 -2 (pow.f64 x 3)) x))
(fma.f64 4 (pow.f64 x 5) (fma.f64 -2 (pow.f64 x 3) x))
(fma.f64 4 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -2 x))
(+.f64 (.f64 4 (pow.f64 x 5)) (+.f64 (.f64 -2 (pow.f64 x 3)) (+.f64 (*.f64 -8 (pow.f64 x 7)) x)))
(fma.f64 4 (pow.f64 x 5) (fma.f64 -2 (pow.f64 x 3) (fma.f64 -8 (pow.f64 x 7) x)))
(fma.f64 4 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -2 (fma.f64 -8 (pow.f64 x 7) x)))
(/.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 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 5)) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 7)))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 7))))
(+.f64 (/.f64 1/2 x) (-.f64 (-.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 7))))
(+.f64 (/.f64 1/2 x) (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3))) (/.f64 -1/16 (pow.f64 x 7))))
(/.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 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 5)) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 7)))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 7))))
(+.f64 (/.f64 1/2 x) (-.f64 (-.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 7))))
(+.f64 (/.f64 1/2 x) (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3))) (/.f64 -1/16 (pow.f64 x 7))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 1/2 (/.f64 x (sqrt.f64 1/2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) (.f64 -1/4 (/.f64 (.f64 x x) (sqrt.f64 1/2)))))
(fma.f64 -1/4 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) (fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (*.f64 (/.f64 x (sqrt.f64 1/2)) (+.f64 1/2 (/.f64 x -4))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 1/8 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 2) (pow.f64 x 3)) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 1/2))))))
(fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/8 (pow.f64 (sqrt.f64 1/2) 4)) -2) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 1/2))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) (.f64 -1/4 (/.f64 (.f64 x x) (sqrt.f64 1/2)))) (/.f64 (*.f64 -3/4 (pow.f64 x 3)) (sqrt.f64 1/2))))
(+.f64 (fma.f64 -1/4 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) (fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2))) (*.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (pow.f64 x 3)))
(+.f64 (.f64 (/.f64 x (sqrt.f64 1/2)) (+.f64 1/2 (/.f64 x -4))) (+.f64 (sqrt.f64 1/2) (.f64 (/.f64 -3/4 (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 (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 (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 (sqrt.f64 1/2) x))) (/.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 -1/32 (.f64 1/2 (.f64 (sqrt.f64 1/2) (*.f64 x x)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (.f64 x x)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 -1/16 (.f64 (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 (sqrt.f64 1/2) x)))) (/.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 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)))))
(+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (*.f64 x x)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))))))
(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 (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 (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 (sqrt.f64 1/2) x))) (/.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 -1/32 (.f64 1/2 (.f64 (sqrt.f64 1/2) (*.f64 x x)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (.f64 x x)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (*.f64 x x)))))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 (-.f64 1/4 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 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 (sqrt.f64 1/2) x)))) (/.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 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)))))
(+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (*.f64 x x)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))))))

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	14.2b	(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))

Compiler

Compiled 26 to 15 computations (42.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))
1.0ms	x	@	-inf	(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))
1.0ms	x	@	0	(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))

rewrite85.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

746×	`pow1_binary64`
698×	`add-log-exp_binary64`
698×	`log1p-expm1-u_binary64`
698×	`expm1-log1p-u_binary64`
684×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	188	14
2	1977	14

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -11/128 (pow.f64 x 4)) 1) (*.f64 x (*.f64 x 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) (pow.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 2) (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) (sqrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 -11/128 (pow.f64 x 4)) 3) (pow.f64 (*.f64 x (*.f64 x 1/8)) 3)) (+.f64 (*.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 -11/128 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 -11/128 (pow.f64 x 4))) (*.f64 (pow.f64 x 4) 1/64)) (-.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))))

simplify180.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1057×	`sqr-pow_binary64`
538×	`fma-def_binary64`
506×	`pow-sqr_binary64`
443×	`cube-prod_binary64`
419×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	147
1	22	147
2	45	147
3	114	147
4	354	147
5	1406	147
6	2652	147
7	3114	147
8	3283	147
9	3482	147
10	3753	147
11	4112	147
12	4563	147
13	5094	147
14	5720	147
15	6469	147
16	6783	147
17	7007	147
18	7201	147
19	7257	147
20	7279	147

Stop Event

1×	node limit

Counts

33 → 26

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 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 -11/128 (pow.f64 x 4)))

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 x (.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(.f64 x (fma.f64 1/8 x (.f64 -11/128 (pow.f64 x 3))))
(+.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 x (.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(.f64 x (fma.f64 1/8 x (.f64 -11/128 (pow.f64 x 3))))
(+.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 x (.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(.f64 x (fma.f64 1/8 x (.f64 -11/128 (pow.f64 x 3))))
(*.f64 -11/128 (pow.f64 x 4))
(+.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 x (.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(.f64 x (fma.f64 1/8 x (.f64 -11/128 (pow.f64 x 3))))
(+.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 x (.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(.f64 x (fma.f64 1/8 x (.f64 -11/128 (pow.f64 x 3))))
(+.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 x (.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(.f64 x (fma.f64 1/8 x (.f64 -11/128 (pow.f64 x 3))))
(*.f64 -11/128 (pow.f64 x 4))
(+.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 x (.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(.f64 x (fma.f64 1/8 x (.f64 -11/128 (pow.f64 x 3))))
(+.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 x (.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(.f64 x (fma.f64 1/8 x (.f64 -11/128 (pow.f64 x 3))))
(+.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 x (.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(.f64 x (fma.f64 1/8 x (.f64 -11/128 (pow.f64 x 3))))

eval546.0ms (7.2%)

Compiler: Compiled 14033 to 12480 computations (11.1% saved)

prune148.0ms (1.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	554	6	560
Fresh	3	1	4
Picked	1	0	1
Done	1	3	4
Total	559	10	569

Error

Counts

569 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	34.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
▶	33.8b	(-.f64 1 (sqrt.f64 1/2))
▶	24.4b	(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
✓	34.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
	34.1b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x))))
✓	29.0b	(.f64 1/8 (.f64 x x))
✓	33.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))
▶	33.4b	(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
▶	29.4b	(/.f64 1 (/.f64 (/.f64 8 x) x))
	33.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))

Compiler

Compiled 166 to 143 computations (13.9% saved)

localize35.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 8 x) x)
✓	0.4b	(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))

Compiler

Compiled 29 to 21 computations (27.6% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
1.0ms	x	@	0	(/.f64 (/.f64 8 x) x)
1.0ms	x	@	inf	(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
1.0ms	x	@	inf	(/.f64 (/.f64 8 x) x)
1.0ms	x	@	-inf	(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))

rewrite92.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

427×	`log-prod_binary64`
342×	`exp-prod_binary64`
252×	`prod-exp_binary64`
245×	`pow2_binary64`
219×	`pow-prod-down_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	203	20
2	2638	18

Stop Event

1×	node limit

Counts

2 → 99

Calls

Call 1

Inputs
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(/.f64 (/.f64 8 x) x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 8 (pow.f64 x -2) 11/2))) (cbrt.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -2)) (/.f64 1 (cbrt.f64 (fma.f64 8 (pow.f64 x -2) 11/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -1/2) (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (fma.f64 8 (pow.f64 x -2) 11/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1331/8 (/.f64 512 (pow.f64 x 6)))) (fma.f64 (*.f64 8 (pow.f64 x -2)) (fma.f64 8 (pow.f64 x -2) -11/2) 121/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 121/4 (/.f64 64 (pow.f64 x 4)))) (-.f64 11/2 (*.f64 8 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 8 (pow.f64 x -2) 11/2)) -2) (/.f64 1 (cbrt.f64 (fma.f64 8 (pow.f64 x -2) 11/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (neg.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 8 (pow.f64 x -2) 11/2)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 8 (pow.f64 x -2) 11/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 8 (pow.f64 x -2) 11/2)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 -1) (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (fma.f64 8 (pow.f64 x -2) 11/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2)))) 2)) (cbrt.f64 (neg.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2))))) (sqrt.f64 (neg.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -2) 11/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 8 (pow.f64 x -2) 11/2) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (cbrt.f64 (fma.f64 8 (pow.f64 x -2) 11/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (*.f64 (log.f64 (fma.f64 8 (pow.f64 x -2) 11/2)) 1)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 8 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 8) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 8) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 8 (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 8 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 8 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 8 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 8 x)) 2) (*.f64 (cbrt.f64 (/.f64 8 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 8 (pow.f64 x -2))) (cbrt.f64 (/.f64 64 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 64 (pow.f64 x 4))) (cbrt.f64 (*.f64 8 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 8 x)) (*.f64 (sqrt.f64 (/.f64 8 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 8) x) (/.f64 (sqrt.f64 8) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -8 x) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 8 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 8 x)) 2) 1) (/.f64 (cbrt.f64 (/.f64 8 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 8 x)) 1) (/.f64 (sqrt.f64 (/.f64 8 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (/.f64 8 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 8 (cbrt.f64 (*.f64 x x))) (/.f64 (/.f64 1 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 8 x)) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (*.f64 8 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 8 x)) (cbrt.f64 (*.f64 x x))) (/.f64 (sqrt.f64 (/.f64 8 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (/.f64 8 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 8 (sqrt.f64 x)) (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 8 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 8 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 8 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 64 (pow.f64 x 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 8 (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 8) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 512 (pow.f64 x 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 1/8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x (*.f64 x 1/8)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) 8) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 8 (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 8 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 8 (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 8 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 8 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 64 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 8) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 8 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 512 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 8 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 8 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 8 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 8 (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 8 (pow.f64 x -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 8) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 512 (pow.f64 x 6))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x 1/8))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 8 (pow.f64 x -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 8 (pow.f64 x -2))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 8 x)) 1) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (/.f64 8 x)) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 8 x)) 1) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 8 x)) 1) (neg.f64 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (neg.f64 (log.f64 x)) (*.f64 (log.f64 (/.f64 8 x)) 1)))))))

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary64`
478×	`distribute-lft-out_binary64`
413×	`unswap-sqr_binary64`
402×	`associate-/l/_binary64`
379×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	270
1	101	270
2	247	270
3	711	270
4	3105	270

Stop Event

1×	node limit

Counts

123 → 116

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 121/2048 (pow.f64 x 6)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (.f64 121/2048 (pow.f64 x 6)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 -1331/32768 (pow.f64 x 8)) (.f64 -11/128 (pow.f64 x 4)))))
2/11
(-.f64 2/11 (*.f64 32/121 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 2/11 (.f64 512/1331 (/.f64 1 (pow.f64 x 4)))) (.f64 32/121 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 2/11 (.f64 512/1331 (/.f64 1 (pow.f64 x 4)))) (+.f64 (.f64 8192/14641 (/.f64 1 (pow.f64 x 6))) (*.f64 32/121 (/.f64 1 (pow.f64 x 2)))))
2/11
(-.f64 2/11 (*.f64 32/121 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 2/11 (.f64 512/1331 (/.f64 1 (pow.f64 x 4)))) (.f64 32/121 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 2/11 (.f64 512/1331 (/.f64 1 (pow.f64 x 4)))) (+.f64 (.f64 8192/14641 (/.f64 1 (pow.f64 x 6))) (*.f64 32/121 (/.f64 1 (pow.f64 x 2)))))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (pow.f64 x 2))

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 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(+.f64 (.f64 121/2048 (pow.f64 x 6)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 121/2048 (pow.f64 x 6) (fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4))))
(fma.f64 1/8 (.f64 x x) (fma.f64 121/2048 (pow.f64 x 6) (.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 121/2048 (pow.f64 x 6) (.f64 1/8 (.f64 x x))))
(+.f64 (.f64 121/2048 (pow.f64 x 6)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 -1331/32768 (pow.f64 x 8)) (.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 121/2048 (pow.f64 x 6) (fma.f64 1/8 (.f64 x x) (fma.f64 -1331/32768 (pow.f64 x 8) (.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 121/2048 (pow.f64 x 6) (fma.f64 1/8 (.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (.f64 -1331/32768 (pow.f64 x 8)))))
(fma.f64 1/8 (.f64 x x) (fma.f64 121/2048 (pow.f64 x 6) (fma.f64 -1331/32768 (pow.f64 x 8) (.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1331/32768 -11/128) (fma.f64 121/2048 (pow.f64 x 6) (.f64 1/8 (.f64 x x))))
(fma.f64 1/8 (.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 121/2048 (pow.f64 x 6) (.f64 -1331/32768 (pow.f64 x 8)))))
2/11
(-.f64 2/11 (*.f64 32/121 (/.f64 1 (pow.f64 x 2))))
(-.f64 2/11 (/.f64 32/121 (*.f64 x x)))
(+.f64 2/11 (/.f64 -32/121 (*.f64 x x)))
(-.f64 (+.f64 2/11 (.f64 512/1331 (/.f64 1 (pow.f64 x 4)))) (.f64 32/121 (/.f64 1 (pow.f64 x 2))))
(+.f64 2/11 (-.f64 (/.f64 512/1331 (pow.f64 x 4)) (/.f64 32/121 (*.f64 x x))))
(+.f64 (/.f64 512/1331 (pow.f64 x 4)) (+.f64 2/11 (/.f64 -32/121 (*.f64 x x))))
(+.f64 (+.f64 2/11 (/.f64 512/1331 (pow.f64 x 4))) (/.f64 -32/121 (*.f64 x x)))
(+.f64 (+.f64 2/11 (/.f64 -32/121 (*.f64 x x))) (/.f64 512/1331 (pow.f64 x 4)))
(+.f64 2/11 (+.f64 (/.f64 512/1331 (pow.f64 x 4)) (/.f64 -32/121 (*.f64 x x))))
(-.f64 (+.f64 2/11 (.f64 512/1331 (/.f64 1 (pow.f64 x 4)))) (+.f64 (.f64 8192/14641 (/.f64 1 (pow.f64 x 6))) (*.f64 32/121 (/.f64 1 (pow.f64 x 2)))))
(+.f64 2/11 (-.f64 (/.f64 512/1331 (pow.f64 x 4)) (+.f64 (/.f64 32/121 (*.f64 x x)) (/.f64 8192/14641 (pow.f64 x 6)))))
(+.f64 (/.f64 512/1331 (pow.f64 x 4)) (+.f64 (+.f64 2/11 (/.f64 -8192/14641 (pow.f64 x 6))) (/.f64 -32/121 (*.f64 x x))))
(+.f64 2/11 (+.f64 (/.f64 512/1331 (pow.f64 x 4)) (+.f64 (/.f64 -32/121 (*.f64 x x)) (/.f64 -8192/14641 (pow.f64 x 6)))))
(+.f64 2/11 (-.f64 (+.f64 (/.f64 512/1331 (pow.f64 x 4)) (/.f64 -32/121 (*.f64 x x))) (/.f64 8192/14641 (pow.f64 x 6))))
2/11
(-.f64 2/11 (*.f64 32/121 (/.f64 1 (pow.f64 x 2))))
(-.f64 2/11 (/.f64 32/121 (*.f64 x x)))
(+.f64 2/11 (/.f64 -32/121 (*.f64 x x)))
(-.f64 (+.f64 2/11 (.f64 512/1331 (/.f64 1 (pow.f64 x 4)))) (.f64 32/121 (/.f64 1 (pow.f64 x 2))))
(+.f64 2/11 (-.f64 (/.f64 512/1331 (pow.f64 x 4)) (/.f64 32/121 (*.f64 x x))))
(+.f64 (/.f64 512/1331 (pow.f64 x 4)) (+.f64 2/11 (/.f64 -32/121 (*.f64 x x))))
(+.f64 (+.f64 2/11 (/.f64 512/1331 (pow.f64 x 4))) (/.f64 -32/121 (*.f64 x x)))
(+.f64 (+.f64 2/11 (/.f64 -32/121 (*.f64 x x))) (/.f64 512/1331 (pow.f64 x 4)))
(+.f64 2/11 (+.f64 (/.f64 512/1331 (pow.f64 x 4)) (/.f64 -32/121 (*.f64 x x))))
(-.f64 (+.f64 2/11 (.f64 512/1331 (/.f64 1 (pow.f64 x 4)))) (+.f64 (.f64 8192/14641 (/.f64 1 (pow.f64 x 6))) (*.f64 32/121 (/.f64 1 (pow.f64 x 2)))))
(+.f64 2/11 (-.f64 (/.f64 512/1331 (pow.f64 x 4)) (+.f64 (/.f64 32/121 (*.f64 x x)) (/.f64 8192/14641 (pow.f64 x 6)))))
(+.f64 (/.f64 512/1331 (pow.f64 x 4)) (+.f64 (+.f64 2/11 (/.f64 -8192/14641 (pow.f64 x 6))) (/.f64 -32/121 (*.f64 x x))))
(+.f64 2/11 (+.f64 (/.f64 512/1331 (pow.f64 x 4)) (+.f64 (/.f64 -32/121 (*.f64 x x)) (/.f64 -8192/14641 (pow.f64 x 6)))))
(+.f64 2/11 (-.f64 (+.f64 (/.f64 512/1331 (pow.f64 x 4)) (/.f64 -32/121 (*.f64 x x))) (/.f64 8192/14641 (pow.f64 x 6))))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))
(/.f64 8 (pow.f64 x 2))
(/.f64 8 (*.f64 x x))

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (/.f64 8 x) x)
✓	0.5b	(/.f64 1 (/.f64 (/.f64 8 x) x))

Compiler

Compiled 19 to 13 computations (31.6% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 1 (/.f64 (/.f64 8 x) x))
1.0ms	x	@	0	(/.f64 1 (/.f64 (/.f64 8 x) x))
0.0ms	x	@	-inf	(/.f64 1 (/.f64 (/.f64 8 x) x))

rewrite92.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

729×	`pow1_binary64`
685×	`add-log-exp_binary64`
685×	`log1p-expm1-u_binary64`
685×	`expm1-log1p-u_binary64`
671×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	153	7
2	1979	7

Stop Event

1×	node limit

Counts

1 → 42

Calls

Call 1

Inputs
(/.f64 1 (/.f64 (/.f64 8 x) x))

Outputs

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

simplify188.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
559×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
446×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	23	84
3	44	84
4	104	84
5	318	84
6	1268	84
7	2140	84
8	2304	84
9	2488	84
10	2696	84
11	2991	84
12	3382	84
13	3865	84
14	4431	84
15	5119	84
16	5950	84
17	6346	84
18	6640	84
19	6920	84
20	6994	84
21	7030	84
22	7971	84

Stop Event

1×	node limit

Counts

54 → 44

Calls

Call 1

Inputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))

Outputs
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 1/8 x))

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 1 (sqrt.f64 1/2))

Compiler

Compiled 9 to 9 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite78.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

443×	`pow1_binary64`
438×	`add-sqr-sqrt_binary64`
426×	`*-un-lft-identity_binary64`
418×	`add-log-exp_binary64`
418×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	104	6
2	1124	6

Stop Event

1×	node limit

Counts

1 → 28

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 1/2))

Outputs

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

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

28 → 28

Calls

Call 1

Inputs

Outputs

localize13.0ms (0.2%)

Compiler: Compiled 15 to 15 computations (0% saved)

localize27.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 x)))
✓	0.4b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))

Compiler

Compiled 26 to 21 computations (19.2% saved)

series4.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

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

rewrite82.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

931×	`pow1_binary64`
870×	`add-log-exp_binary64`
870×	`log1p-expm1-u_binary64`
870×	`expm1-log1p-u_binary64`
854×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	180	21
2	2356	21

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

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

Outputs

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

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

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

721×	`associate-/l*_binary64`
675×	`associate-/r*_binary64`
662×	`distribute-neg-frac_binary64`
337×	`associate-l_binary64`
292×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	408
1	108	400
2	329	384
3	1167	384
4	5324	384

Stop Event

1×	node limit

Counts

66 → 64

Calls

Call 1

Inputs
(-.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 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(-.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 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(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 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.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 (+.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 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.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 (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 (sqrt.f64 1/2) x))))
(-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 1 (-.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.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 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x)))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) 1) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (+.f64 1 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x)) (-.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x)) (-.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))))
(+.f64 1 (-.f64 (-.f64 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x) (sqrt.f64 1/2)) (/.f64 1/4 (*.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 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(+.f64 1 (-.f64 (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x))) (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))))))
(-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) 1) (+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))))
(+.f64 1 (+.f64 (-.f64 (-.f64 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x) (sqrt.f64 1/2)) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x)) (-.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/128 (pow.f64 x 3)) (pow.f64 (sqrt.f64 1/2) 5)))))
(+.f64 1 (+.f64 (-.f64 (-.f64 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x) (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (/.f64 (/.f64 -1/128 (pow.f64 x 3)) (pow.f64 (sqrt.f64 1/2) 5))))
(-.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 (sqrt.f64 1/2) x))))
(-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 1 (-.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.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 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x)))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) 1) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (+.f64 1 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x)) (-.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x)) (-.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))))
(+.f64 1 (-.f64 (-.f64 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x) (sqrt.f64 1/2)) (/.f64 1/4 (*.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 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(+.f64 1 (-.f64 (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x))) (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))))))
(-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) 1) (+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (.f64 (sqrt.f64 1/2) x))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))))
(+.f64 1 (+.f64 (-.f64 (-.f64 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x) (sqrt.f64 1/2)) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (.f64 x x)) (-.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/128 (pow.f64 x 3)) (pow.f64 (sqrt.f64 1/2) 5)))))
(+.f64 1 (+.f64 (-.f64 (-.f64 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x) (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (/.f64 (/.f64 -1/128 (pow.f64 x 3)) (pow.f64 (sqrt.f64 1/2) 5))))
(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 (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 (sqrt.f64 1/2) x))) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 -1/32 (.f64 (sqrt.f64 1/2) (.f64 1/2 (.f64 x x))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x)))
(+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x))))
(-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x) (sqrt.f64 1/2)))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.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 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (/.f64 1/32 (.f64 (sqrt.f64 1/2) (.f64 1/2 (*.f64 x x)))))))
(+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (-.f64 (sqrt.f64 1/2) (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x))))
(+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 (/.f64 1/128 (pow.f64 x 3)) (pow.f64 (sqrt.f64 1/2) 5)) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)))))
(+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)))))
(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 (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 (sqrt.f64 1/2) x))) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 -1/32 (.f64 (sqrt.f64 1/2) (.f64 1/2 (.f64 x x))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x)))
(+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x))))
(-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x) (sqrt.f64 1/2)))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.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 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))) (/.f64 1/32 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (/.f64 1/32 (.f64 (sqrt.f64 1/2) (.f64 1/2 (*.f64 x x)))))))
(+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (-.f64 (sqrt.f64 1/2) (/.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) x) x))))
(+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 (/.f64 1/128 (pow.f64 x 3)) (pow.f64 (sqrt.f64 1/2) 5)) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (.f64 x x)))))
(+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 1/128 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)))))

eval140.0ms (1.8%)

Compiler: Compiled 3918 to 3313 computations (15.4% saved)

prune44.0ms (0.6%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	308	1	309
Fresh	0	2	2
Picked	0	1	1
Done	1	6	7
Total	309	10	319

Error

Counts

319 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	34.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
✓	33.8b	(-.f64 1 (sqrt.f64 1/2))
✓	24.4b	(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
✓	34.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
▶	34.1b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x))))
✓	29.0b	(.f64 1/8 (.f64 x x))
	56.8b	2/11
✓	33.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))
✓	33.4b	(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
▶	33.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))

Compiler

Compiled 91 to 79 computations (13.2% saved)

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))
✓	0.1b	(/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))
✓	1.0b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))

Compiler

Compiled 51 to 39 computations (23.5% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite78.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

854×	`prod-diff_binary64`
529×	`log-prod_binary64`
383×	`fma-def_binary64`
215×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	255	43
2	3481	43

Stop Event

1×	node limit

Counts

3 → 102

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) 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 (-.f64 (/.f64 -1/2 x) x))))))) (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) 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 (-.f64 (/.f64 -1/2 x) x)))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))) 3/2)) (/.f64 1 (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) (-.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) 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(neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))))) (-.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) 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 (-.f64 (/.f64 -1/2 x) x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))) 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) (-.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x 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x) 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 (-.f64 (/.f64 -1/2 x) x)))))) (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))))) (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))) 1/4)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))) 1/4) 1)))))

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

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

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

684×	`times-frac_binary64`
626×	`associate-/l*_binary64`
525×	`associate-*l/_binary64`
428×	`associate-*r/_binary64`
345×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	854
1	338	748
2	1126	732
3	3424	716

Stop Event

1×	node limit

Counts

138 → 145

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 1/2)))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 1 (.f64 1/2 (/.f64 x (sqrt.f64 1/2))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (.f64 (-.f64 2 (.f64 1/8 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (pow.f64 x 3)) (sqrt.f64 1/2))) (*.f64 1/2 (/.f64 x (sqrt.f64 1/2)))))) (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 (+.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 1/4 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 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 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))
(*.f64 -1 x)
(+.f64 (.f64 2 (pow.f64 x 3)) (.f64 -1 x))
(+.f64 (.f64 2 (pow.f64 x 3)) (+.f64 (.f64 -1 x) (*.f64 -4 (pow.f64 x 5))))
(+.f64 (.f64 2 (pow.f64 x 3)) (+.f64 (.f64 8 (pow.f64 x 7)) (+.f64 (.f64 -1 x) (.f64 -4 (pow.f64 x 5)))))
(/.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 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))))
(/.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 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1/2 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (.f64 -1/2 (/.f64 x (sqrt.f64 1/2))) (.f64 1/2 (/.f64 (.f64 (-.f64 2 (*.f64 1/8 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (pow.f64 x 3)) (sqrt.f64 1/2))))))
(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 (.f64 1/2 (/.f64 (-.f64 1/4 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (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))))))
(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))))))

Outputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 1/2)))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)))
(-.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) 1) (sqrt.f64 1/2))
(fma.f64 (/.f64 1/2 (sqrt.f64 1/2)) x (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 1 (.f64 1/2 (/.f64 x (sqrt.f64 1/2))))) (sqrt.f64 1/2))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (+.f64 1 (.f64 1/2 (/.f64 x (sqrt.f64 1/2))))) (sqrt.f64 1/2))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) 1) (-.f64 (.f64 1/4 (/.f64 (.f64 x x) (sqrt.f64 1/2))) (sqrt.f64 1/2)))
(-.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) 1)) (sqrt.f64 1/2))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (*.f64 (/.f64 x (sqrt.f64 1/2)) (+.f64 1/2 (/.f64 x 4))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (.f64 (-.f64 2 (.f64 1/8 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (pow.f64 x 3)) (sqrt.f64 1/2))) (*.f64 1/2 (/.f64 x (sqrt.f64 1/2)))))) (sqrt.f64 1/2))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (+.f64 1 (fma.f64 -1/2 (/.f64 (-.f64 2 (/.f64 1/8 (pow.f64 (sqrt.f64 1/2) 4))) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (.f64 1/2 (/.f64 x (sqrt.f64 1/2)))))) (sqrt.f64 1/2))
(+.f64 (.f64 1/4 (/.f64 (.f64 x x) (sqrt.f64 1/2))) (+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) (/.f64 (*.f64 -3/4 (pow.f64 x 3)) (sqrt.f64 1/2))) (-.f64 1 (sqrt.f64 1/2))))
(+.f64 1 (-.f64 (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) (fma.f64 1/2 (/.f64 x (sqrt.f64 1/2)) (*.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (pow.f64 x 3)))) (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (+.f64 (.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (pow.f64 x 3)) (.f64 (/.f64 x (sqrt.f64 1/2)) (+.f64 1/2 (/.f64 x 4)))) (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 (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 (sqrt.f64 1/2) x)) (/.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 1/4 (.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 (-.f64 1/4 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 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 1/4 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4))) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.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 1/4 (.f64 (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 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x)))) (-.f64 (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (+.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))) (/.f64 (/.f64 -3/32 (sqrt.f64 1/2)) (pow.f64 x 3))))
(-.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 (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 (sqrt.f64 1/2) x)) (/.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 1/4 (.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (-.f64 (/.f64 1/4 (*.f64 (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 1/4 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4))) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.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 1/4 (.f64 (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 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x)))) (-.f64 (/.f64 -3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (+.f64 (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))) (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))) (/.f64 (/.f64 -3/32 (sqrt.f64 1/2)) (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 2 (pow.f64 x 3)) (.f64 -1 x))
(fma.f64 2 (pow.f64 x 3) (neg.f64 x))
(-.f64 (*.f64 2 (pow.f64 x 3)) x)
(+.f64 (.f64 2 (pow.f64 x 3)) (+.f64 (.f64 -1 x) (*.f64 -4 (pow.f64 x 5))))
(fma.f64 2 (pow.f64 x 3) (fma.f64 -1 x (*.f64 -4 (pow.f64 x 5))))
(fma.f64 2 (pow.f64 x 3) (-.f64 (*.f64 -4 (pow.f64 x 5)) x))
(-.f64 (fma.f64 2 (pow.f64 x 3) (*.f64 -4 (pow.f64 x 5))) x)
(+.f64 (.f64 2 (pow.f64 x 3)) (+.f64 (.f64 8 (pow.f64 x 7)) (+.f64 (.f64 -1 x) (.f64 -4 (pow.f64 x 5)))))
(fma.f64 2 (pow.f64 x 3) (fma.f64 8 (pow.f64 x 7) (fma.f64 -1 x (*.f64 -4 (pow.f64 x 5)))))
(fma.f64 2 (pow.f64 x 3) (fma.f64 8 (pow.f64 x 7) (-.f64 (*.f64 -4 (pow.f64 x 5)) x)))
(fma.f64 2 (pow.f64 x 3) (-.f64 (fma.f64 -4 (pow.f64 x 5) (*.f64 8 (pow.f64 x 7))) x))
(fma.f64 2 (pow.f64 x 3) (fma.f64 -4 (pow.f64 x 5) (fma.f64 8 (pow.f64 x 7) (neg.f64 x))))
(/.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 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 5)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 -1/2 x) (/.f64 1/8 (pow.f64 x 5))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (-.f64 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 7))) (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 5)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 1/16 (pow.f64 x 7)) (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 5)))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/16 (pow.f64 x 7)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 5)))))
(/.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 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 5)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 -1/2 x) (/.f64 1/8 (pow.f64 x 5))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (-.f64 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 7))) (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 5)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 1/16 (pow.f64 x 7)) (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 5)))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/16 (pow.f64 x 7)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 5)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (*.f64 (/.f64 x (sqrt.f64 1/2)) -1/2))
(fma.f64 (/.f64 x (sqrt.f64 1/2)) -1/2 (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1/2 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (.f64 (/.f64 x (sqrt.f64 1/2)) -1/2)))
(+.f64 (sqrt.f64 1/2) (fma.f64 (/.f64 x (sqrt.f64 1/2)) -1/2 (.f64 -1/4 (/.f64 (.f64 x x) (sqrt.f64 1/2)))))
(fma.f64 (/.f64 x (sqrt.f64 1/2)) -1/2 (fma.f64 -1/4 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (*.f64 (/.f64 x (sqrt.f64 1/2)) (+.f64 -1/2 (/.f64 x -4))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (.f64 -1/2 (/.f64 x (sqrt.f64 1/2))) (.f64 1/2 (/.f64 (.f64 (-.f64 2 (*.f64 1/8 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (pow.f64 x 3)) (sqrt.f64 1/2))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (fma.f64 -1/2 (/.f64 x (sqrt.f64 1/2)) (.f64 1/2 (/.f64 (-.f64 2 (/.f64 1/8 (pow.f64 (sqrt.f64 1/2) 4))) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/4 (/.f64 (.f64 x x) (sqrt.f64 1/2))) (fma.f64 (/.f64 x (sqrt.f64 1/2)) -1/2 (/.f64 (*.f64 3/4 (pow.f64 x 3)) (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 (/.f64 x (sqrt.f64 1/2)) -1/2 (fma.f64 -1/4 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) (*.f64 (/.f64 3/4 (sqrt.f64 1/2)) (pow.f64 x 3)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 (/.f64 x (sqrt.f64 1/2)) (+.f64 -1/2 (/.f64 x -4))) (.f64 (/.f64 3/4 (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 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.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 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.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 1/4 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x))) (/.f64 1/16 (.f64 (sqrt.f64 1/2) (*.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (*.f64 x x)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 1/4 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (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 (fma.f64 1/2 (/.f64 (-.f64 1/4 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4))) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2)) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.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 1/4 (.f64 (sqrt.f64 1/2) x)))))
(+.f64 (-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x))) (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x)))) (/.f64 3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (/.f64 3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))))))
(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 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.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 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.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 1/4 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x))) (/.f64 1/16 (.f64 (sqrt.f64 1/2) (*.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (*.f64 x 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 (fma.f64 1/2 (/.f64 (-.f64 1/4 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4))) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2)) (+.f64 (/.f64 1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.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 1/4 (.f64 (sqrt.f64 1/2) x)))))
(+.f64 (-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x))) (/.f64 1/16 (.f64 (sqrt.f64 1/2) (.f64 x x)))) (/.f64 3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (/.f64 3/32 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (.f64 (sqrt.f64 1/2) x)) (/.f64 -1/16 (.f64 (sqrt.f64 1/2) (.f64 x x))))))

localize51.0ms (0.7%)

Local error

Found 3 expressions with local error:

New

Error

Program

0.0b

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

✓

0.1b

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

✓

0.1b

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

Compiler

Compiled 62 to 52 computations (16.1% saved)

series9.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

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

rewrite101.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

599×	`log-prod_binary64`
497×	`prod-diff_binary64`
313×	`fma-def_binary64`
241×	`log-div_binary64`
227×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	277	27
2	3866	27

Stop Event

1×	node limit

Counts

2 → 93

Calls

Call 1

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

Outputs

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

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

872×	`times-frac_binary64`
644×	`fma-def_binary64`
549×	`associate-l_binary64`
415×	`associate-r_binary64`
259×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	1486
1	628	1290
2	2088	1200

Stop Event

1×	node limit

Counts

109 → 117

Calls

Call 1

Inputs
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (/.f64 1/8 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (+.f64 (/.f64 1/2 (.f64 (+.f64 1 (sqrt.f64 1/2)) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))))))
(-.f64 (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (sqrt.f64 1/2)) x))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2))))))
(-.f64 (+.f64 (.f64 1/256 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 5) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (sqrt.f64 1/2)) x))) (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2))))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3))))) (+.f64 (.f64 -1/32 (/.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2))))))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (/.f64 1/8 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (+.f64 (/.f64 1/2 (.f64 (+.f64 (sqrt.f64 1/2) 1) x)) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (.f64 1/256 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 5) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/32 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 3))))) (+.f64 (.f64 1/4 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(*.f64 2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (.f64 2 (+.f64 1 (sqrt.f64 1/2))) (.f64 -1 (/.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))) x)))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (+.f64 (.f64 2 (+.f64 1 (sqrt.f64 1/2))) (.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))))) (pow.f64 x 2))) (+.f64 (.f64 2 (+.f64 1 (sqrt.f64 1/2))) (.f64 -1 (/.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))) x))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))))))) (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 5)))) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (+.f64 (.f64 2 (+.f64 1 (sqrt.f64 1/2))) (.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))))) (pow.f64 x 2))) (+.f64 (.f64 2 (+.f64 1 (sqrt.f64 1/2))) (.f64 -1 (/.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))) x)))))
(*.f64 2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)))
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)) (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (*.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2)))))
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 5))) (+.f64 (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2))))) (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))))) (pow.f64 x 3))) (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (*.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2))))))

Outputs
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (/.f64 1/8 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (+.f64 (/.f64 1/2 (.f64 (+.f64 1 (sqrt.f64 1/2)) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))))))
(+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (.f64 (+.f64 1 (sqrt.f64 1/2)) x))) (/.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 1/2))) (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 1/2))) (.f64 x (+.f64 1/2 (sqrt.f64 1/2)))) (/.f64 1/2 (.f64 (+.f64 1 (sqrt.f64 1/2)) x))))
(+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (fma.f64 (sqrt.f64 1/2) x x))) (/.f64 1/8 (*.f64 (fma.f64 (sqrt.f64 1/2) x x) (+.f64 1/2 (sqrt.f64 1/2)))))
(-.f64 (+.f64 (.f64 1/64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (sqrt.f64 1/2)) x))) (+.f64 (.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))))) (.f64 -1/4 (/.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (+.f64 (sqrt.f64 1/2) 1) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2))))))
(+.f64 (/.f64 1/64 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (pow.f64 (sqrt.f64 1/2) 3) (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 x x))))) (-.f64 (+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/2 (.f64 (+.f64 1 (sqrt.f64 1/2)) x))) (/.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 1/2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (.f64 -1/4 (/.f64 (+.f64 (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))) (.f64 (.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))) (*.f64 x x))))))
(+.f64 (/.f64 1/64 (.f64 (.f64 (+.f64 1 (sqrt.f64 1/2)) (.f64 x x)) (+.f64 (.f64 1/2 (sqrt.f64 1/2)) 1/4))) (+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 1/2))) (.f64 x (+.f64 1/2 (sqrt.f64 1/2)))) (/.f64 1/2 (.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (.f64 (/.f64 (+.f64 (/.f64 1/8 (.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2)))) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))) (.f64 (.f64 x (+.f64 1/2 (sqrt.f64 1/2))) x)) 1/4)))
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(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (+.f64 (.f64 2 (+.f64 1 (sqrt.f64 1/2))) (.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))))) (pow.f64 x 2))) (+.f64 (.f64 2 (+.f64 1 (sqrt.f64 1/2))) (.f64 -1 (/.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))) x))))
(fma.f64 -1 (/.f64 (fma.f64 -1 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1/16 (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 x x)) (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (neg.f64 (/.f64 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) x))))
(-.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) 2 2) (/.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))) x)) (/.f64 (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2)))) (*.f64 x x)))
(-.f64 (/.f64 (+.f64 (+.f64 2 (fma.f64 (sqrt.f64 1/2) 2 (/.f64 1/2 (sqrt.f64 1/2)))) (/.f64 -1/8 (sqrt.f64 1/2))) (*.f64 x x)) (-.f64 (/.f64 (+.f64 2 (fma.f64 (sqrt.f64 1/2) 2 (/.f64 1/2 (sqrt.f64 1/2)))) x) (fma.f64 (sqrt.f64 1/2) 2 2)))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))))))) (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 5)))) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (+.f64 (.f64 2 (+.f64 1 (sqrt.f64 1/2))) (.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))))) (pow.f64 x 2))) (+.f64 (.f64 2 (+.f64 1 (sqrt.f64 1/2))) (.f64 -1 (/.f64 (+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))) x)))))
(fma.f64 -1 (/.f64 (-.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 5)) (fma.f64 -1 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1/16 (pow.f64 (sqrt.f64 1/2) 3)))) (pow.f64 x 3)) (fma.f64 -1 (/.f64 (fma.f64 -1 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1/16 (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 x x)) (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (neg.f64 (/.f64 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) x)))))
(-.f64 (-.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) 2 2) (/.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))) x)) (/.f64 (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2)))) (*.f64 x x))) (/.f64 (-.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 5)) (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))))) (pow.f64 x 3)))
(+.f64 2 (-.f64 (-.f64 (fma.f64 (sqrt.f64 1/2) 2 (/.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))) x)) (/.f64 (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2)))) (*.f64 x x))) (/.f64 (+.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 5)) (/.f64 -1/8 (sqrt.f64 1/2))) (+.f64 2 (fma.f64 (sqrt.f64 1/2) 2 (/.f64 1/2 (sqrt.f64 1/2))))) (pow.f64 x 3))))
(*.f64 2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 (+.f64 1 (sqrt.f64 1/2)) 2)
(fma.f64 (sqrt.f64 1/2) 2 2)
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)))
(fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (neg.f64 (/.f64 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) x)))
(+.f64 (fma.f64 (sqrt.f64 1/2) 2 2) (/.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))) x))
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)) (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (*.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2)))))
(fma.f64 -1 (/.f64 (fma.f64 -1 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1/16 (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 x x)) (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (neg.f64 (/.f64 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) x))))
(-.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) 2 2) (/.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))) x)) (/.f64 (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2)))) (*.f64 x x)))
(-.f64 (/.f64 (+.f64 (+.f64 2 (fma.f64 (sqrt.f64 1/2) 2 (/.f64 1/2 (sqrt.f64 1/2)))) (/.f64 -1/8 (sqrt.f64 1/2))) (*.f64 x x)) (-.f64 (/.f64 (+.f64 2 (fma.f64 (sqrt.f64 1/2) 2 (/.f64 1/2 (sqrt.f64 1/2)))) x) (fma.f64 (sqrt.f64 1/2) 2 2)))
(+.f64 (.f64 2 (+.f64 (sqrt.f64 1/2) 1)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2)))) x)) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 5))) (+.f64 (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (.f64 -2 (+.f64 1 (sqrt.f64 1/2))))) (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))))) (pow.f64 x 3))) (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1 (-.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (*.f64 -2 (+.f64 (sqrt.f64 1/2) 1))))) (pow.f64 x 2))))))
(fma.f64 -1 (/.f64 (-.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 5)) (fma.f64 -1 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1/16 (pow.f64 (sqrt.f64 1/2) 3)))) (pow.f64 x 3)) (fma.f64 -1 (/.f64 (fma.f64 -1 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1/16 (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 x x)) (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (neg.f64 (/.f64 (fma.f64 2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/2 (sqrt.f64 1/2))) x)))))
(-.f64 (-.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) 2 2) (/.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))) x)) (/.f64 (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2)))) (*.f64 x x))) (/.f64 (-.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 5)) (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))))) (pow.f64 x 3)))
(+.f64 2 (-.f64 (-.f64 (fma.f64 (sqrt.f64 1/2) 2 (/.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2))) x)) (/.f64 (+.f64 (/.f64 1/8 (sqrt.f64 1/2)) (+.f64 (fma.f64 (sqrt.f64 1/2) -2 -2) (/.f64 -1/2 (sqrt.f64 1/2)))) (*.f64 x x))) (/.f64 (+.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 5)) (/.f64 -1/8 (sqrt.f64 1/2))) (+.f64 2 (fma.f64 (sqrt.f64 1/2) 2 (/.f64 1/2 (sqrt.f64 1/2))))) (pow.f64 x 3))))

eval581.0ms (7.6%)

Compiler: Compiled 7249 to 6464 computations (10.8% saved)

prune110.0ms (1.4%)

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	1	1
Picked	0	1	1
Done	0	8	8
Total	292	10	302

Error

Counts

302 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	34.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
✓	33.8b	(-.f64 1 (sqrt.f64 1/2))
✓	24.4b	(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
✓	34.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
✓	34.1b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x))))
✓	29.0b	(.f64 1/8 (.f64 x x))
	56.8b	2/11
✓	33.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))
✓	33.4b	(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
✓	33.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))

Compiler

Compiled 91 to 79 computations (13.2% saved)

regimes254.0ms (3.3%)

Counts

18 → 2

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x))))
(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))
(-.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))))))
(/.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)))))

Outputs
(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x 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)))))

Calls

13 calls:

133.0ms	(hypot.f64 1 x)
28.0ms	x
20.0ms	(/.f64 1 (hypot.f64 1 x))
15.0ms	(/.f64 1 (hypot.f64 1 x))
8.0ms	(hypot.f64 1 x)

Results

Error	Segments	Branch
0.0b	3	`x`
0.0b	2	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
0.0b	2	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
0.0b	2	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
0.0b	2	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
0.0b	2	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
0.0b	2	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
0.0b	2	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
0.0b	2	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
0.0b	2	`(/.f64 1 (hypot.f64 1 x))`
0.0b	2	`(/.f64 1 (hypot.f64 1 x))`
0.0b	2	`(hypot.f64 1 x)`
0.0b	2	`(hypot.f64 1 x)`

Compiler

Compiled 277 to 239 computations (13.7% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000000000001357	11354.242872006991

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes118.0ms (1.6%)

Counts

17 → 2

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x))))
(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))
(-.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))))))
(/.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
(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x 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))))))

Calls

13 calls:

31.0ms	x
14.0ms	(/.f64 1 (hypot.f64 1 x))
14.0ms	(/.f64 1 (hypot.f64 1 x))
8.0ms	(hypot.f64 1 x)
6.0ms	(hypot.f64 1 x)

Results

Error	Segments	Branch
0.0b	3	`x`
0.0b	2	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
0.0b	2	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
0.0b	2	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
0.0b	2	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
0.0b	2	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
0.0b	2	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
0.0b	2	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
0.0b	2	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
0.0b	2	`(/.f64 1 (hypot.f64 1 x))`
0.0b	2	`(/.f64 1 (hypot.f64 1 x))`
0.0b	2	`(hypot.f64 1 x)`
0.0b	2	`(hypot.f64 1 x)`

Compiler

Compiled 257 to 221 computations (14% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000000000001357	11354.242872006991

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes250.0ms (3.3%)

Counts

16 → 3

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x))))
(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))
(-.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
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x))))
(fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x)))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))

Calls

13 calls:

126.0ms	(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
31.0ms	(/.f64 1 (hypot.f64 1 x))
24.0ms	x
16.0ms	(/.f64 1 (hypot.f64 1 x))
7.0ms	(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Results

Error	Segments	Branch
0.2b	3	`x`
0.2b	2	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
0.2b	2	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
0.2b	2	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
0.2b	2	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
0.2b	2	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
0.2b	2	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
0.2b	2	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
0.2b	2	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
0.2b	2	`(/.f64 1 (hypot.f64 1 x))`
0.2b	2	`(/.f64 1 (hypot.f64 1 x))`
0.2b	2	`(hypot.f64 1 x)`
0.2b	2	`(hypot.f64 1 x)`

Compiler

Compiled 239 to 205 computations (14.2% saved)

bsearch46.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
23.0ms	1.1182393929147128e-10	11354.24282797059
23.0ms	-73890.4955567544	-5.209156832581208e-7

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes25.0ms (0.3%)

Counts

13 → 3

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x))))

Outputs
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x))))
(.f64 1/8 (.f64 x x))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))

Calls

1 calls:

22.0ms

Results

Error	Segments	Branch
0.2b	3	`x`

Compiler

Compiled 103 to 87 computations (15.5% saved)

bsearch47.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
23.0ms	1.1182393929147128e-10	11354.24282797059
23.0ms	-73890.4955567544	-5.209156832581208e-7

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes79.0ms (1%)

Counts

12 → 3

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))

Outputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x)))))
(.f64 1/8 (.f64 x x))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))

Calls

1 calls:

75.0ms

Results

Error	Segments	Branch
0.4b	3	`x`

Compiler

Compiled 87 to 73 computations (16.1% saved)

bsearch48.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
23.0ms	1.1182393929147128e-10	11354.24282797059
24.0ms	-73890.4955567544	-5.209156832581208e-7

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes65.0ms (0.8%)

Counts

11 → 3

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 x (/.f64 1/2 x))))))

Outputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(.f64 1/8 (.f64 x x))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))

Calls

1 calls:

62.0ms

Results

Error	Segments	Branch
0.5b	3	`x`

Compiler

Compiled 75 to 63 computations (16% saved)

bsearch47.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
23.0ms	1.1182393929147128e-10	11354.24282797059
24.0ms	-73890.4955567544	-5.209156832581208e-7

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes19.0ms (0.2%)

Counts

9 → 3

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))

Outputs
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(.f64 1/8 (.f64 x x))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))

Calls

1 calls:

16.0ms

Results

Error	Segments	Branch
0.6b	3	`x`

Compiler

Compiled 55 to 46 computations (16.4% saved)

bsearch46.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
22.0ms	1.1182393929147128e-10	11354.24282797059
24.0ms	-73890.4955567544	-5.209156832581208e-7

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes16.0ms (0.2%)

Counts

6 → 3

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))

Outputs
(-.f64 1 (sqrt.f64 1/2))
(.f64 1/8 (.f64 x x))
(-.f64 1 (sqrt.f64 1/2))

Calls

1 calls:

14.0ms

Results

Error	Segments	Branch
1.0b	3	`x`

Compiler

Compiled 33 to 26 computations (21.2% saved)

bsearch52.0ms (0.7%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
26.0ms	1.1182393929147128e-10	11354.24282797059
26.0ms	-73890.4955567544	-5.209156832581208e-7

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes5.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))

Outputs
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
24.4b	1	`x`

Compiler

Compiled 25 to 18 computations (28% saved)

regimes12.0ms (0.2%)

Accuracy

Total -37.8b remaining (-157.5%)

Threshold costs -37.8b (-157.5%)

Counts

3 → 3

Calls

Call 1

Inputs
2/11
(.f64 1/8 (.f64 x x))
(/.f64 1 (/.f64 (/.f64 8 x) x))

Outputs
2/11
(.f64 1/8 (.f64 x x))
2/11

Calls

1 calls:

11.0ms

Results

Error	Segments	Branch
24.0b	3	`x`

Compiler

Compiled 16 to 11 computations (31.3% saved)

bsearch46.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
23.0ms	1.1182393929147128e-10	11354.24282797059
23.0ms	-73890.4955567544	-5.209156832581208e-7

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify23.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
12×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	403
1	87	403
2	110	403
3	122	403
4	128	403

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (hypot.f64 1 x) 2) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x 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))))))
(if (<=.f64 (hypot.f64 1 x) 2) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x 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)))))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (-.f64 1 (sqrt.f64 1/2))))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(if (<=.f64 x -5077716190423895/68719476736) 2/11 (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) 2/11))
2/11

Outputs
(if (<=.f64 (hypot.f64 1 x) 2) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x 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))))))
(if (<=.f64 (hypot.f64 1 x) 2) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x 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))))))
(if (<=.f64 (hypot.f64 1 x) 2) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x 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)))))))
(if (<=.f64 (hypot.f64 1 x) 2) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x 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)))))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 8651958237470621/77371252455336267181195264) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x))) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (+.f64 1/2 (/.f64 1/2 x)))) (if (<=.f64 x 8651958237470621/77371252455336267181195264) (fma.f64 -11/128 (pow.f64 x 4) (.f64 1/8 (.f64 x x))) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (-.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 8651958237470621/77371252455336267181195264) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (+.f64 1/2 (/.f64 1/2 x)))) (if (<=.f64 x 8651958237470621/77371252455336267181195264) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -5077716190423895/68719476736) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (/.f64 -1/2 x) x))))) (if (<=.f64 x 8651958237470621/77371252455336267181195264) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -5077716190423895/68719476736) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (if (<=.f64 x 8651958237470621/77371252455336267181195264) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -5077716190423895/68719476736) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (if (<=.f64 x 8651958237470621/77371252455336267181195264) (.f64 1/8 (.f64 x x)) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -5077716190423895/68719476736) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) (-.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 x -5077716190423895/68719476736) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 8651958237470621/77371252455336267181195264) (.f64 1/8 (.f64 x x)) (-.f64 1 (sqrt.f64 1/2))))
(/.f64 1 (+.f64 11/2 (/.f64 (/.f64 8 x) x)))
(if (<=.f64 x -5077716190423895/68719476736) 2/11 (if (<=.f64 x 8859605235169915904/79228162514264337593543950336) (.f64 1/8 (.f64 x x)) 2/11))
(if (<=.f64 x -5077716190423895/68719476736) 2/11 (if (<=.f64 x 8651958237470621/77371252455336267181195264) (.f64 1/8 (.f64 x x)) 2/11))
2/11

Compiler

Compiled 285 to 235 computations (17.5% saved)

soundness97.0ms (1.3%)

Algorithm

3×	egg-herbie

Rules

544×	`fma-def_binary64`
347×	`associate-*l/_binary64`
338×	`times-frac_binary64`
330×	`associate-*r/_binary64`
323×	`fma-neg_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
0	140	918
1	424	841
2	1268	824
3	3912	824
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
1×	node limit
1×	saturated

Compiler

Compiled 180 to 161 computations (10.6% saved)

end153.0ms (2%)

Compiler: Compiled 275 to 217 computations (21.1% saved)