Details

analyze41.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.8%	87.2%	0
0%	12.8%	87.2%	1
0%	12.8%	87.2%	2
6.4%	6.4%	87.2%	3
6.4%	4.8%	88.8%	4
7.2%	3.2%	89.6%	5
7.2%	2.4%	90.4%	6
7.6%	1.6%	90.8%	7
7.6%	1.2%	91.2%	8
7.8%	0.8%	91.4%	9
7.8%	0.6%	91.5%	10
7.9%	0.4%	91.7%	11
8%	0.3%	91.7%	12
8.1%	0.2%	91.7%	13
8.1%	0.2%	91.8%	14

Compiler

Compiled 25 to 17 computations (32% saved)

sample1.5s (56.5%)

Results

599.0ms	5185×	body	128	valid
406.0ms	1166×	body	1024	valid
302.0ms	1092×	body	512	valid
155.0ms	780×	body	256	valid
14.0ms	33×	body	2048	valid
8.0ms	75×	body	128	invalid

Compiler

Compiled 50 to 34 computations (32% saved)

preprocess25.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

144×	`fma-neg_binary64`
96×	`fma-def_binary64`
54×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
26×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	349	24
7	501	24
8	603	24
9	655	24
10	665	24
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 eps (sqrt.f64 (-.f64 (*.f64 eps eps) x)))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 eps (sqrt.f64 (-.f64 (*.f64 eps eps) x)))
(-.f64 eps (sqrt.f64 (fma.f64 eps eps (neg.f64 x))))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

107×	`fma-def_binary64`
72×	`fma-neg_binary64`
29×	`cancel-sign-sub-inv_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

25.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	4.5b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series8.0ms (0.3%)

Counts

2 → 40

Calls

12 calls:

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

rewrite44.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

871×	`log1p-expm1-u_binary64`
871×	`expm1-log1p-u_binary64`
88×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
85×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	162	19
2	2412	19

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)

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

Outputs

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

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

simplify28.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary64`
638×	`associate-/r*_binary64`
426×	`associate-*l/_binary64`
319×	`cancel-sign-sub-inv_binary64`
210×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	523
1	160	515
2	447	513
3	1671	503

Stop Event

1×	node limit

Counts

119 → 107

Calls

Call 1

Inputs
(*.f64 -1 (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (+.f64 (sqrt.f64 (neg.f64 eps)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(-.f64 (+.f64 x (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(*.f64 -1 eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(*.f64 -1 eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(*.f64 -1 eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (pow.f64 x 2) eps)

Outputs
(*.f64 -1 (sqrt.f64 (neg.f64 eps)))
(neg.f64 (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (+.f64 (sqrt.f64 (neg.f64 eps)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(-.f64 x (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps))))))
(-.f64 x (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 eps))))
(-.f64 x (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (neg.f64 eps))))
(fma.f64 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) -1/2 (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 (+.f64 x (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(-.f64 (+.f64 x (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))))))
(-.f64 (fma.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) x) (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 eps))))
(-.f64 (fma.f64 (/.f64 -1/8 eps) (/.f64 (pow.f64 x 4) (sqrt.f64 (neg.f64 eps))) x) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (neg.f64 eps))))
(+.f64 x (-.f64 (.f64 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) (-.f64 (.f64 1/8 (/.f64 x (/.f64 (neg.f64 eps) x))) 1/2)) (sqrt.f64 (neg.f64 eps))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 1/2 eps) x)
(/.f64 1/2 (/.f64 x eps))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 1/2 eps) x))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps))))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps (*.f64 x x)) 1/8)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps (*.f64 x x)) 1/8))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps (*.f64 x x)) 1/8)))))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 x 2) (/.f64 (.f64 1/2 eps) x))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(fma.f64 x 2 (/.f64 -1/2 (/.f64 x eps)))
(fma.f64 x 2 (*.f64 (/.f64 -1/2 x) eps))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (*.f64 1/2 eps) x)))
(+.f64 (fma.f64 x 2 (.f64 (/.f64 eps x) -1/2)) (.f64 -1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (.f64 (.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8)))
(fma.f64 x 2 (.f64 (/.f64 eps x) (-.f64 -1/2 (.f64 (/.f64 eps (*.f64 x x)) 1/8))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (fma.f64 (.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 1/2 eps) x)
(/.f64 1/2 (/.f64 x eps))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 1/2 eps) x))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps))))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps (*.f64 x x)) 1/8)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps (*.f64 x x)) 1/8))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps (*.f64 x x)) 1/8)))))
(*.f64 -1 eps)
(neg.f64 eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(pow.f64 x 2)
(*.f64 x x)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(pow.f64 x 2)
(*.f64 x x)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(pow.f64 x 2)
(*.f64 x x)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(*.f64 -1 eps)
(neg.f64 eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(*.f64 -1 eps)
(neg.f64 eps)
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(-.f64 (pow.f64 x 2) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))

prune58.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Error

0.0b

Counts

108 → 4

Alt Table

Status	Error	Program
	25.8b	(-.f64 x (sqrt.f64 (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	0.4b	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 1 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
✓	25.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 1829 to 700 computations (61.7% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

series13.0ms (0.5%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
2.0ms	eps	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	x	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	x	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	eps	@	inf	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

rewrite70.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
308×	`fma-neg_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	261	24
2	4003	24

Stop Event

1×	node limit

Counts

2 → 177

Calls

Call 1

Inputs
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

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

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simplify37.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

759×	`cancel-sign-sub-inv_binary64`
355×	`fma-neg_binary64`
304×	`times-frac_binary64`
279×	`distribute-neg-frac_binary64`
214×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	786
1	202	759
2	613	751
3	2862	717

Stop Event

1×	node limit

Counts

209 → 206

Calls

Call 1

Inputs
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (+.f64 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (.f64 1/8 (/.f64 (*.f64 eps (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(sqrt.f64 (neg.f64 eps))
(+.f64 (sqrt.f64 (neg.f64 eps)) x)
(+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))

Outputs
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 eps (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2) x)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (*.f64 (/.f64 eps (neg.f64 eps)) x))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (*.f64 x (/.f64 eps (neg.f64 eps))))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (neg.f64 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 eps (.f64 x x)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 eps (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2) x)))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (.f64 x x)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (*.f64 (/.f64 eps (neg.f64 eps)) x))
(-.f64 (fma.f64 (/.f64 -1/2 eps) (/.f64 (.f64 eps x) (/.f64 (sqrt.f64 (neg.f64 eps)) x)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (.f64 x (/.f64 eps (neg.f64 eps))))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) -1/2 (*.f64 1 x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (+.f64 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (.f64 1/8 (/.f64 (*.f64 eps (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 eps (.f64 x x)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (+.f64 (/.f64 eps (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2) x)) (/.f64 (.f64 1/8 (.f64 eps (pow.f64 x 4))) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (.f64 x x)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (pow.f64 x 4)) (.f64 (/.f64 eps (neg.f64 eps)) x)))
(-.f64 (fma.f64 (/.f64 -1/2 eps) (/.f64 (.f64 eps x) (/.f64 (sqrt.f64 (neg.f64 eps)) x)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (fma.f64 1/8 (.f64 (pow.f64 x 4) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (*.f64 x (/.f64 eps (neg.f64 eps)))))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) -1/2 (fma.f64 (.f64 (pow.f64 x 4) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) -1/8 (.f64 1 x))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 1/2 eps) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 x 2) (.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (*.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8)))
(fma.f64 x 2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (*.f64 (/.f64 eps x) -1/2)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(-.f64 (fma.f64 x 2 (.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (/.f64 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 1/2 eps) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(sqrt.f64 (neg.f64 eps))
(+.f64 (sqrt.f64 (neg.f64 eps)) x)
(+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(+.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) x) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps)))))
(+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) x))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(-.f64 (+.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) x) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps))))) (/.f64 (*.f64 1/8 (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) x)) (/.f64 (*.f64 1/8 (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))
(fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/8 (+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) x)))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 x 2) (.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (*.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8)))
(fma.f64 x 2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (*.f64 (/.f64 eps x) -1/2)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(-.f64 (fma.f64 x 2 (.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (/.f64 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 1/2 eps) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 x 2) (.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (*.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8)))
(fma.f64 x 2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (*.f64 (/.f64 eps x) -1/2)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(-.f64 (fma.f64 x 2 (.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (/.f64 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))

prune134.0ms (5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	252	5	257

Error

Counts

257 → 5

Alt Table

Status	Error	Program
	25.8b	(-.f64 x (sqrt.f64 (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
▶	0.4b	(*.f64 eps (/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	0.6b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2))
✓	25.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 6508 to 1588 computations (75.6% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	0.2b	(/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
✓	0.3b	(*.f64 eps (/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))

series14.0ms (0.5%)

Counts

3 → 48

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	inf	(/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
2.0ms	eps	@	-inf	(/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
1.0ms	eps	@	inf	(*.f64 eps (/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
1.0ms	eps	@	-inf	(*.f64 eps (/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
1.0ms	x	@	0	(/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))

rewrite52.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

920×	`log1p-expm1-u_binary64`
920×	`expm1-log1p-u_binary64`
106×	`add-sqr-sqrt_binary64`
102×	`*-un-lft-identity_binary64`
102×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	212	33
2	2843	33

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

Inputs
(*.f64 eps (/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))

Outputs

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

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

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

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-neg_binary64`
395×	`times-frac_binary64`
284×	`associate-/l*_binary64`
265×	`associate-/r*_binary64`
225×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1177
1	288	1121
2	898	1105
3	3892	1075

Stop Event

1×	node limit

Counts

137 → 139

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (+.f64 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (.f64 1/8 (/.f64 (*.f64 eps (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(/.f64 1 (sqrt.f64 (neg.f64 eps)))
(-.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (*.f64 1/8 (/.f64 eps (pow.f64 x 3)))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))))
(*.f64 2 (/.f64 x eps))
(-.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 (/.f64 x eps)) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 eps (pow.f64 x 3)))))
(-.f64 (.f64 2 (/.f64 x eps)) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (*.f64 1/8 (/.f64 eps (pow.f64 x 3)))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))))
(sqrt.f64 (neg.f64 eps))
(+.f64 (sqrt.f64 (neg.f64 eps)) x)
(+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))

Outputs
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16)))))
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (*.f64 (/.f64 eps (neg.f64 eps)) x))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 x (neg.f64 (/.f64 eps eps))))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (neg.f64 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (fma.f64 1/2 (/.f64 eps (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) (.f64 x x))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (fma.f64 1/2 (/.f64 eps (/.f64 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) x) x)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (*.f64 (/.f64 eps (neg.f64 eps)) x))
(-.f64 (fma.f64 1/2 (/.f64 x (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) (*.f64 eps x))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 x (neg.f64 (/.f64 eps eps))))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) -1/2 (.f64 1 x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (+.f64 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (.f64 1/8 (/.f64 (*.f64 eps (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)))))
(-.f64 (fma.f64 1/2 (/.f64 eps (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) (.f64 x x))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (+.f64 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5) (pow.f64 x 4))))))
(-.f64 (fma.f64 1/2 (/.f64 eps (/.f64 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) x) x)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (pow.f64 x 4)) (.f64 (/.f64 eps (neg.f64 eps)) x)))
(-.f64 (fma.f64 1/2 (/.f64 x (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) (.f64 eps x))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (fma.f64 1/8 (/.f64 (.f64 eps (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (/.f64 x (neg.f64 (/.f64 eps eps)))))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) -1/2 (fma.f64 (/.f64 (.f64 eps (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) -1/8 (*.f64 1 x))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16)))))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 x 2) (.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3))))
(-.f64 (fma.f64 x 2 (.f64 (/.f64 eps x) -1/2)) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (.f64 (.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16)))))
(/.f64 1 (sqrt.f64 (neg.f64 eps)))
(-.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (/.f64 x (neg.f64 eps)))
(-.f64 (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (-.f64 (.f64 1/2 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))))
(-.f64 (fma.f64 1/2 (/.f64 x (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) x)) (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (/.f64 x (neg.f64 eps)))
(fma.f64 1/2 (*.f64 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) x) (-.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (/.f64 x (neg.f64 eps))))
(-.f64 (fma.f64 1/2 (*.f64 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) x) (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (/.f64 x (neg.f64 eps)))
(-.f64 (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))))
(+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (-.f64 (.f64 1/2 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))))
(-.f64 (fma.f64 1/2 (/.f64 x (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) x)) (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (/.f64 x (neg.f64 eps))))
(-.f64 (fma.f64 1/2 (*.f64 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) x) (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (/.f64 x (neg.f64 eps))))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (*.f64 1/8 (/.f64 eps (pow.f64 x 3))))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (*.f64 1/8 (/.f64 eps (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (fma.f64 1/16 (/.f64 (.f64 eps eps) (pow.f64 x 5)) (.f64 1/8 (/.f64 eps (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (*.f64 1/16 (/.f64 eps (/.f64 (pow.f64 x 5) eps)))))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (fma.f64 1/16 (*.f64 (/.f64 eps (pow.f64 x 5)) eps) (/.f64 1/2 x)))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7)) (+.f64 (/.f64 1/2 x) (fma.f64 1/16 (/.f64 (.f64 eps eps) (pow.f64 x 5)) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))))
(+.f64 (fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (*.f64 1/16 (/.f64 eps (/.f64 (pow.f64 x 5) eps)))) (fma.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7)) (/.f64 1/2 x)))
(fma.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7)) (fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (fma.f64 1/16 (*.f64 (/.f64 eps (pow.f64 x 5)) eps) (/.f64 1/2 x))))
(*.f64 2 (/.f64 x eps))
(-.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 1 x)))
(fma.f64 2 (/.f64 x eps) (neg.f64 (/.f64 1/2 x)))
(fma.f64 2 (/.f64 x eps) (/.f64 -1/2 x))
(fma.f64 (/.f64 2 eps) x (/.f64 -1/2 x))
(-.f64 (.f64 2 (/.f64 x eps)) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 eps (pow.f64 x 3)))))
(-.f64 (.f64 2 (/.f64 x eps)) (+.f64 (/.f64 1/2 x) (.f64 1/8 (/.f64 eps (pow.f64 x 3)))))
(+.f64 (fma.f64 2 (/.f64 x eps) (/.f64 -1/2 x)) (*.f64 -1/8 (/.f64 eps (pow.f64 x 3))))
(+.f64 (/.f64 -1/2 x) (fma.f64 2 (/.f64 x eps) (*.f64 (/.f64 eps (pow.f64 x 3)) -1/8)))
(fma.f64 2 (/.f64 x eps) (fma.f64 (/.f64 eps (pow.f64 x 3)) -1/8 (/.f64 -1/2 x)))
(-.f64 (.f64 2 (/.f64 x eps)) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))))
(-.f64 (.f64 2 (/.f64 x eps)) (+.f64 (/.f64 1/2 x) (fma.f64 1/16 (/.f64 (.f64 eps eps) (pow.f64 x 5)) (*.f64 1/8 (/.f64 eps (pow.f64 x 3))))))
(-.f64 (fma.f64 2 (/.f64 x eps) (/.f64 -1/2 x)) (fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (*.f64 1/16 (/.f64 eps (/.f64 (pow.f64 x 5) eps)))))
(-.f64 (fma.f64 2 (/.f64 x eps) (/.f64 -1/2 x)) (fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/16 (/.f64 (pow.f64 x 5) (*.f64 eps eps)))))
(-.f64 (fma.f64 (/.f64 2 eps) x (/.f64 -1/2 x)) (fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/16 (/.f64 (pow.f64 x 5) (*.f64 eps eps)))))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (*.f64 1/8 (/.f64 eps (pow.f64 x 3))))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (*.f64 1/8 (/.f64 eps (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (fma.f64 1/16 (/.f64 (.f64 eps eps) (pow.f64 x 5)) (.f64 1/8 (/.f64 eps (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (*.f64 1/16 (/.f64 eps (/.f64 (pow.f64 x 5) eps)))))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (fma.f64 1/16 (*.f64 (/.f64 eps (pow.f64 x 5)) eps) (/.f64 1/2 x)))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 5))) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7)) (+.f64 (/.f64 1/2 x) (fma.f64 1/16 (/.f64 (.f64 eps eps) (pow.f64 x 5)) (.f64 1/8 (/.f64 eps (pow.f64 x 3))))))
(+.f64 (fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (*.f64 1/16 (/.f64 eps (/.f64 (pow.f64 x 5) eps)))) (fma.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7)) (/.f64 1/2 x)))
(fma.f64 5/128 (/.f64 (pow.f64 eps 3) (pow.f64 x 7)) (fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (fma.f64 1/16 (*.f64 (/.f64 eps (pow.f64 x 5)) eps) (/.f64 1/2 x))))
(sqrt.f64 (neg.f64 eps))
(+.f64 (sqrt.f64 (neg.f64 eps)) x)
(+.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(+.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps)))))
(+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) x))
(+.f64 x (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) (sqrt.f64 (neg.f64 eps))))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(+.f64 (+.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps))))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) x) (*.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/8)))
(fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/8 (+.f64 x (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) (sqrt.f64 (neg.f64 eps)))))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 x 2) (.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3))))
(-.f64 (fma.f64 x 2 (.f64 (/.f64 eps x) -1/2)) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (.f64 (.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16)))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16)))))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 x 2) (.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3))))
(-.f64 (fma.f64 x 2 (.f64 (/.f64 eps x) -1/2)) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (.f64 (.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 1/8 (*.f64 eps eps)) (pow.f64 x 3)))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16)))))

prune64.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	139	5	144

Error

Counts

144 → 5

Alt Table

Status	Error	Program
	25.8b	(-.f64 x (sqrt.f64 (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
✓	0.4b	(*.f64 eps (/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	0.6b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2))
✓	25.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 2464 to 1121 computations (54.5% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	0.1b	(sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2))
✓	0.5b	(pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2)

series20.0ms (0.7%)

Counts

3 → 32

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	-inf	(sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
2.0ms	eps	@	inf	(pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2)
2.0ms	eps	@	inf	(sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
2.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2)
1.0ms	eps	@	0	(pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2)

rewrite54.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
151×	`pow1_binary64`
149×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	44
1	339	29
2	4499	29

Stop Event

1×	node limit

Counts

3 → 122

Calls

Call 1

Inputs

(pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2)

(/.f64 (+.f64 (-.f64 (*.f64 x x) (*.f64 x x)) eps) (pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2))

(sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))

Outputs

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

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

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

simplify32.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-def_binary64`
435×	`times-frac_binary64`
359×	`associate-/l*_binary64`
308×	`associate-/r*_binary64`
254×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1053
1	396	961
2	1310	927

Stop Event

1×	node limit

Counts

154 → 169

Calls

Call 1

Inputs
(sqrt.f64 (neg.f64 eps))
(+.f64 (sqrt.f64 (neg.f64 eps)) x)
(+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(-.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (+.f64 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (.f64 1/8 (/.f64 (*.f64 eps (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(sqrt.f64 (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) x)) (sqrt.f64 (sqrt.f64 (neg.f64 eps))))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) x)) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (pow.f64 x 2))) (sqrt.f64 (sqrt.f64 (neg.f64 eps)))))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) x)) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (pow.f64 x 2))) (sqrt.f64 (sqrt.f64 (neg.f64 eps))))) (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (pow.f64 x 3))))
(*.f64 (sqrt.f64 2) (sqrt.f64 x))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (.f64 1/4 (*.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (+.f64 (.f64 1/4 (.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 eps 2) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))) (.f64 1/32 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (+.f64 (.f64 1/4 (.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 1/64 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 11))))) (+.f64 (.f64 1/32 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 eps 2) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))) (+.f64 (.f64 1/128 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 2) 5)) (sqrt.f64 (/.f64 1 (pow.f64 x 11))))) (.f64 1/32 (*.f64 (/.f64 (pow.f64 eps 3) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))))))))))

Outputs
(sqrt.f64 (neg.f64 eps))
(+.f64 (sqrt.f64 (neg.f64 eps)) x)
(+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps))))))
(+.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) x) (/.f64 (.f64 1/2 (.f64 x x)) (sqrt.f64 (neg.f64 eps))))
(+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) x))
(+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) x))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))))) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(+.f64 (+.f64 (+.f64 (sqrt.f64 (neg.f64 eps)) x) (/.f64 (.f64 1/2 (.f64 x x)) (sqrt.f64 (neg.f64 eps)))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 (neg.f64 eps)) x)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) (/.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) (pow.f64 x 4)))))
(fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/8 (+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) x)))
(*.f64 (pow.f64 (sqrt.f64 2) 2) x)
(*.f64 x (pow.f64 (sqrt.f64 2) 2))
(*.f64 x 2)
(-.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) x) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 x (pow.f64 (sqrt.f64 2) 2)) (.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(-.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 x (pow.f64 (sqrt.f64 2) 2)) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (*.f64 1/2 (/.f64 eps x))))
(-.f64 (*.f64 x 2) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 1/2 (/.f64 x eps))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (/.f64 (.f64 -1/8 (.f64 eps eps)) (pow.f64 x 3))))
(-.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 (.f64 x (pow.f64 (sqrt.f64 2) 2)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3))))))
(-.f64 (fma.f64 x 2 (.f64 (/.f64 eps x) -1/2)) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (*.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5)))))
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 eps (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2) x)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 (*.f64 eps x) (neg.f64 eps)))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 x (neg.f64 (/.f64 eps eps))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 eps (.f64 x x)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 eps (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2) x)))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (.f64 x x)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 (*.f64 eps x) (neg.f64 eps)))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 eps (.f64 x x)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (/.f64 x (neg.f64 (/.f64 eps eps))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 x 2)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (+.f64 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (.f64 1/8 (/.f64 (*.f64 eps (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 eps (.f64 x x)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (+.f64 (/.f64 eps (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2) x)) (/.f64 (.f64 1/8 (.f64 eps (pow.f64 x 4))) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (.f64 x x)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (fma.f64 1/8 (/.f64 (.f64 eps (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (/.f64 (.f64 eps x) (neg.f64 eps))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 eps (.f64 x x)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))) (fma.f64 1/8 (*.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) eps) (/.f64 x (neg.f64 (/.f64 eps eps)))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 1/2 (/.f64 x eps)))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 (*.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 (*.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5)))))
(*.f64 2 x)
(*.f64 x (pow.f64 (sqrt.f64 2) 2))
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 x (pow.f64 (sqrt.f64 2) 2)) (.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(-.f64 (.f64 x (pow.f64 (sqrt.f64 2) 2)) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (*.f64 1/2 (/.f64 eps x))))
(-.f64 (*.f64 x 2) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 1/2 (/.f64 x eps))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (/.f64 (.f64 -1/8 (.f64 eps eps)) (pow.f64 x 3))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 (.f64 x (pow.f64 (sqrt.f64 2) 2)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3))))))
(-.f64 (fma.f64 x 2 (.f64 (/.f64 eps x) -1/2)) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(-.f64 (.f64 x 2) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (*.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5)))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 1/2 (/.f64 x eps)))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/2 (/.f64 eps x))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 (*.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 eps x)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (/.f64 (*.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5)))))
(fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5)))))
(sqrt.f64 (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) x)) (sqrt.f64 (sqrt.f64 (neg.f64 eps))))
(fma.f64 1/2 (*.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (sqrt.f64 (sqrt.f64 (neg.f64 eps))))
(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (*.f64 x 1/2) (sqrt.f64 (sqrt.f64 (neg.f64 eps))))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) x)) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (pow.f64 x 2))) (sqrt.f64 (sqrt.f64 (neg.f64 eps)))))
(fma.f64 1/2 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (fma.f64 1/8 (.f64 (*.f64 x x) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (sqrt.f64 (sqrt.f64 (neg.f64 eps)))))
(fma.f64 1/2 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (fma.f64 1/8 (.f64 x (*.f64 x (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))) (sqrt.f64 (sqrt.f64 (neg.f64 eps)))))
(fma.f64 x (.f64 1/2 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (fma.f64 (.f64 x x) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (sqrt.f64 (sqrt.f64 (neg.f64 eps)))))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) x)) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (pow.f64 x 2))) (sqrt.f64 (sqrt.f64 (neg.f64 eps))))) (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (pow.f64 x 3))))
(+.f64 (fma.f64 1/2 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (fma.f64 1/8 (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (sqrt.f64 (sqrt.f64 (neg.f64 eps))))) (.f64 -1/16 (*.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))))))
(+.f64 (fma.f64 1/2 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (fma.f64 1/8 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))) (sqrt.f64 (sqrt.f64 (neg.f64 eps))))) (.f64 (*.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)))) -1/16))
(fma.f64 (.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)))) -1/16 (fma.f64 x (.f64 1/2 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (fma.f64 (.f64 x x) (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (sqrt.f64 (sqrt.f64 (neg.f64 eps))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 x))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (.f64 1/4 (*.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (.f64 (*.f64 1/4 (/.f64 eps (sqrt.f64 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 x) (.f64 (.f64 -1/4 (/.f64 eps (sqrt.f64 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 (/.f64 eps (sqrt.f64 2)) -1/4)))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (+.f64 (.f64 1/4 (.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 eps 2) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))) (.f64 1/32 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (fma.f64 1/4 (.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 1/16 (.f64 (/.f64 (.f64 eps eps) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (.f64 (.f64 1/32 (/.f64 (*.f64 eps eps) (pow.f64 (sqrt.f64 2) 3))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (fma.f64 1/4 (.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/16 (/.f64 eps (/.f64 (sqrt.f64 2) eps))) (.f64 1/32 (.f64 (/.f64 eps (sqrt.f64 2)) (/.f64 eps 2)))))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (fma.f64 1/4 (.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/16 (/.f64 (.f64 eps eps) (sqrt.f64 2)) (.f64 1/64 (/.f64 (.f64 eps eps) (sqrt.f64 2)))))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (+.f64 (.f64 1/4 (.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 1/64 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 11))))) (+.f64 (.f64 1/32 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 eps 2) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))) (+.f64 (.f64 1/128 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 2) 5)) (sqrt.f64 (/.f64 1 (pow.f64 x 11))))) (.f64 1/32 (*.f64 (/.f64 (pow.f64 eps 3) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))))))))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (fma.f64 1/4 (.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 1/64 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (fma.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (/.f64 (.f64 eps eps) (pow.f64 (sqrt.f64 2) 3))) (fma.f64 1/16 (.f64 (/.f64 (.f64 eps eps) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (fma.f64 1/128 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 11))) (/.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 2) 5))) (.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 11))) (/.f64 (pow.f64 eps 3) (sqrt.f64 2))))))))))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (fma.f64 1/4 (.f64 (/.f64 eps (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 1/64 (.f64 (/.f64 (pow.f64 eps 3) (.f64 2 (sqrt.f64 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/16 (/.f64 eps (/.f64 (sqrt.f64 2) eps))) (.f64 1/32 (.f64 (/.f64 eps (sqrt.f64 2)) (/.f64 eps 2))))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 11))) (+.f64 (.f64 1/32 (/.f64 (pow.f64 eps 3) (sqrt.f64 2))) (*.f64 1/128 (/.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 2) 5)))))))))
(-.f64 (fma.f64 (sqrt.f64 2) (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 (/.f64 eps (sqrt.f64 2)) -1/4))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/16 (/.f64 (.f64 eps eps) (sqrt.f64 2)) (.f64 1/64 (/.f64 (.f64 eps eps) (sqrt.f64 2)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 11))) (+.f64 (fma.f64 1/32 (/.f64 (pow.f64 eps 3) (sqrt.f64 2)) (.f64 1/128 (/.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 2) 5)))) (.f64 1/128 (/.f64 (pow.f64 eps 3) (sqrt.f64 2)))))))

prune88.0ms (3.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	216	5	221

Error

Counts

221 → 5

Alt Table

Status	Error	Program
	25.8b	(-.f64 x (sqrt.f64 (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
✓	0.4b	(*.f64 eps (/.f64 1 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.6b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) 2))
✓	25.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 5138 to 1665 computations (67.6% saved)

regimes202.0ms (7.6%)

Accuracy

Total 0.3b remaining (97.4%)

Threshold costs 0.3b (97.4%)

Counts

90 → 1

Compiler

Compiled 1276 to 431 computations (66.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	23	19
2	35	19
3	43	19
4	45	19

Stop Event

1×

saturated

Calls

Call 1

Inputs
(neg.f64 (/.f64 eps (neg.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))))

Outputs

(neg.f64 (/.f64 eps (neg.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))))

(/.f64 (neg.f64 eps) (neg.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))

(/.f64 (neg.f64 eps) (-.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))

end72.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 122 to 66 computations (45.9% saved)

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	349	24
7	501	24
8	603	24
9	655	24
10	665	24
0	2	2

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	349	24
7	501	24
8	603	24
9	655	24
10	665	24
0	2	2

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12

Details

analyze41.0ms (1.6%)

sample1.5s (56.5%)

preprocess25.0ms (0.9%)

simplify12.0ms (0.4%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite44.0ms (1.7%)

simplify28.0ms (1.1%)

prune58.0ms (2.2%)

localize9.0ms (0.3%)

series13.0ms (0.5%)

rewrite70.0ms (2.6%)

simplify37.0ms (1.4%)

prune134.0ms (5%)

localize7.0ms (0.3%)

series14.0ms (0.5%)

rewrite52.0ms (2%)

simplify47.0ms (1.8%)

prune64.0ms (2.4%)

localize12.0ms (0.5%)

series20.0ms (0.7%)

rewrite54.0ms (2%)

simplify32.0ms (1.2%)

prune88.0ms (3.3%)

regimes202.0ms (7.6%)

simplify2.0ms (0.1%)

end72.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	349	24
7	501	24
8	603	24
9	655	24
10	665	24
0	2	2

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12