Details

analyze42.0ms (1.2%)

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 (40.9%)

Results

572.0ms	5204×	body	128	valid
406.0ms	1147×	body	1024	valid
321.0ms	1188×	body	512	valid
130.0ms	670×	body	256	valid
24.0ms	47×	body	2048	valid
9.0ms	94×	body	128	invalid

preprocess39.0ms (1.1%)

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 (0.3%)

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)))

eval0.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

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

21.4b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.4b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 20 to 12 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	2.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series10.0ms (0.3%)

Counts

3 → 56

Calls

18 calls:

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

rewrite54.0ms (1.5%)

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	28
1	162	28
2	2412	28

Stop Event

1×	node limit

Counts

3 → 104

Calls

Call 1

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

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

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

417×	`fma-def_binary64`
402×	`associate-/l/_binary64`
271×	`times-frac_binary64`
202×	`associate-r_binary64`
201×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	884
1	299	852
2	884	844
3	3527	827

Stop Event

1×	node limit

Counts

160 → 156

Calls

Call 1

Inputs
(*.f64 -1 (sqrt.f64 (neg.f64 eps)))
(+.f64 (*.f64 -1 (sqrt.f64 (neg.f64 eps))) x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (.f64 -1 (sqrt.f64 (neg.f64 eps))) x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (.f64 -1 (sqrt.f64 (neg.f64 eps))) (+.f64 x (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 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 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 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 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 4) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 x 6))))) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(sqrt.f64 (neg.f64 eps))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (+.f64 (sqrt.f64 (neg.f64 eps)) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(*.f64 -1 x)
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 -1 x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 -1 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1 x))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(*.f64 -1 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(*.f64 -1 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(*.f64 -1 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))

Outputs
(*.f64 -1 (sqrt.f64 (neg.f64 eps)))
(neg.f64 (sqrt.f64 (neg.f64 eps)))
(+.f64 (*.f64 -1 (sqrt.f64 (neg.f64 eps))) x)
(fma.f64 -1 (sqrt.f64 (neg.f64 eps)) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (.f64 -1 (sqrt.f64 (neg.f64 eps))) x))
(fma.f64 -1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (fma.f64 -1 (sqrt.f64 (neg.f64 eps)) x))
(fma.f64 -1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 (fma.f64 -1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) x) (sqrt.f64 (neg.f64 eps)))
(-.f64 x (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) 1/2 (sqrt.f64 (neg.f64 eps))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (.f64 -1 (sqrt.f64 (neg.f64 eps))) (+.f64 x (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))))
(fma.f64 -1/2 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps))) (+.f64 (fma.f64 -1 (sqrt.f64 (neg.f64 eps)) x) (/.f64 (.f64 1/8 (pow.f64 x 4)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(fma.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) (sqrt.f64 (neg.f64 eps))))
(-.f64 (fma.f64 -1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (fma.f64 (/.f64 -1/8 eps) (/.f64 (pow.f64 x 4) (sqrt.f64 (neg.f64 eps))) x)) (sqrt.f64 (neg.f64 eps)))
(+.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps))) (+.f64 -1/2 (.f64 1/8 (/.f64 (.f64 x x) (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)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (.f64 1/2 (/.f64 eps x)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.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 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x))))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 (.f64 eps eps) -1/8) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 (fma.f64 1/16 (pow.f64 eps 4) (.f64 (pow.f64 eps 4) 1/64)) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (*.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 1/2 (+.f64 (/.f64 eps x) (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7))) (*.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 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 (pow.f64 eps 4) 5/128) (pow.f64 x 7)))))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(fma.f64 -1/2 (/.f64 eps x) (*.f64 x 2))
(fma.f64 x 2 (*.f64 -1/2 (/.f64 eps x)))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 x 2 (fma.f64 (.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (.f64 -1/2 (/.f64 eps x))))
(fma.f64 x 2 (.f64 (/.f64 eps x) (+.f64 -1/2 (/.f64 (.f64 eps -1/8) (*.f64 x x)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 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))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (/.f64 (.f64 (pow.f64 eps 3) -1/16) (pow.f64 x 5)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 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 1/8 (/.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 (/.f64 eps (pow.f64 x 3)) eps) (.f64 1/2 (/.f64 eps x)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.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 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x))))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 4) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 x 6))))) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (/.f64 (pow.f64 eps 4) (/.f64 x (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (/.f64 1/16 (pow.f64 x 6))))) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (.f64 (/.f64 (pow.f64 eps 4) x) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (/.f64 1/16 (pow.f64 x 6)))) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (/.f64 1/16 (pow.f64 x 6))) (/.f64 (pow.f64 eps 4) x)) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(+.f64 (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))) (.f64 (/.f64 1/2 x) (+.f64 eps (.f64 (pow.f64 eps 4) (+.f64 (/.f64 1/64 (pow.f64 x 6)) (/.f64 1/16 (pow.f64 x 6)))))))
(sqrt.f64 (neg.f64 eps))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (sqrt.f64 (neg.f64 eps)))
(fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 eps)))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) 1/2 (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (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 (.f64 x x) (sqrt.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 eps))) (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/8))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) 1/2 (fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/8 (sqrt.f64 (neg.f64 eps))))
(+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps))) (+.f64 1/2 (.f64 -1/8 (/.f64 (.f64 x x) (neg.f64 eps))))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (+.f64 (sqrt.f64 (neg.f64 eps)) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))))
(fma.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps))) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/8))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) 1/2 (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/8 (sqrt.f64 (neg.f64 eps)))))
(fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) 1/2 (fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/8 (sqrt.f64 (neg.f64 eps)))))
(fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 eps))) (+.f64 1/2 (.f64 -1/8 (/.f64 (.f64 x x) (neg.f64 eps)))))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(fma.f64 -1/2 (/.f64 eps x) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 -1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) x))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) -1/8 x))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) -1/8 x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 -1 x))
(fma.f64 1/2 (/.f64 eps x) (neg.f64 x))
(-.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 -1 x)))
(fma.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (neg.f64 x)))
(-.f64 (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x))) x)
(fma.f64 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/2 (/.f64 eps x) (neg.f64 x)))
(-.f64 (.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x))))) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1 x))))
(fma.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (neg.f64 x))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))) x))
(-.f64 (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))) x)
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))) x)
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(fma.f64 -1/2 (/.f64 eps x) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 -1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) x))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) -1/8 x))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) -1/8 x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 x)))
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))

eval44.0ms (1.2%)

Compiler: Compiled 2500 to 1025 computations (59% saved)

prune152.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	152	5	157

Error

Counts

157 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	21.4b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	0.6b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))
	22.0b	(-.f64 x (sqrt.f64 (.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))))))
	39.7b	(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))

Compiler

Compiled 176 to 88 computations (50% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
	0.0b	(sqrt.f64 (-.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 (0.4%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	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))))
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))))

rewrite72.0ms (2%)

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
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Outputs

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

simplify31.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
416×	`times-frac_binary64`
318×	`associate-r_binary64`
315×	`associate-/l*_binary64`
305×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	854
1	372	822
2	1263	747

Stop Event

1×	node limit

Counts

209 → 211

Calls

Call 1

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

eval97.0ms (2.7%)

Compiler: Compiled 7877 to 2102 computations (73.3% saved)

prune542.0ms (15%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	304	1	305
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	305	5	310

Error

Counts

310 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	14.4b	(.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (.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))))
✓	21.4b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	0.6b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))
	22.0b	(-.f64 x (sqrt.f64 (.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))))))

Compiler

Compiled 192 to 89 computations (53.6% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.2b	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps))
✓	0.4b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))

series7.0ms (0.2%)

Counts

2 → 32

Calls

12 calls:

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

rewrite59.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
145×	`*-un-lft-identity_binary64`
145×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	301	27
2	4496	27

Stop Event

1×	node limit

Counts

2 → 95

Calls

Call 1

Inputs

(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (-.f64 (*.f64 x x) (*.f64 x x)) eps)))

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

simplify31.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-def_binary64`
530×	`times-frac_binary64`
364×	`associate-/l*_binary64`
353×	`associate-/r*_binary64`
321×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	892
1	419	842
2	1404	755

Stop Event

1×	node limit

Counts

127 → 139

Calls

Call 1

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

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

eval68.0ms (1.9%)

Compiler: Compiled 5561 to 2044 computations (63.2% saved)

prune283.0ms (7.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	243	5	248

Error

Counts

248 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	14.4b	(.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (.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))))
✓	21.4b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.6b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))
	22.0b	(-.f64 x (sqrt.f64 (.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))))))

Compiler

Compiled 170 to 78 computations (54.1% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	0.2b	(pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2)
✓	0.5b	(.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
✓	13.5b	(/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2)))

series46.0ms (1.3%)

Counts

4 → 82

Calls

24 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	-inf	(.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
5.0ms	eps	@	inf	(.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
5.0ms	x	@	0	(.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
4.0ms	eps	@	inf	(/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2)))
3.0ms	eps	@	-inf	(/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2)))

rewrite42.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

183×	`add-sqr-sqrt_binary64`
176×	`pow1_binary64`
174×	`*-un-lft-identity_binary64`
172×	`add-log-exp_binary64`
172×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	87
1	366	73

Stop Event

1×	node limit

Counts

4 → 111

Calls

Call 1

Inputs
(/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2)))
(.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2)
(*.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 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 0 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))) (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 eps (/.f64 1 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 eps (/.f64 1 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))) (pow.f64 (cbrt.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))) 2) (cbrt.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 eps) 2) (.f64 (cbrt.f64 eps) (/.f64 1 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 eps) (hypot.f64 (pow.f64 (fma.f64 x x eps) 3/4) (pow.f64 x 3/2))) (/.f64 (sqrt.f64 eps) (hypot.f64 (pow.f64 (fma.f64 x x eps) 3/4) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 eps) (.f64 (sqrt.f64 eps) (/.f64 1 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) eps)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 eps) 2) 1) (/.f64 (cbrt.f64 eps) (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 eps) 1) (/.f64 (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 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) 2)) (/.f64 eps (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 eps) 2) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) 2)) (cbrt.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 eps) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) 2)) (/.f64 (sqrt.f64 eps) (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (hypot.f64 (pow.f64 (fma.f64 x x eps) 3/4) (pow.f64 x 3/2))) (/.f64 eps (hypot.f64 (pow.f64 (fma.f64 x x eps) 3/4) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 eps) 2) (hypot.f64 (pow.f64 (fma.f64 x x eps) 3/4) (pow.f64 x 3/2))) (/.f64 (cbrt.f64 eps) (hypot.f64 (pow.f64 (fma.f64 x x eps) 3/4) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 eps (+.f64 (pow.f64 x 9) (pow.f64 (fma.f64 x x eps) 9/2))) (-.f64 (+.f64 (pow.f64 x 6) (pow.f64 (fma.f64 x x eps) 3)) (pow.f64 (.f64 x (hypot.f64 x (sqrt.f64 eps))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 eps (-.f64 (pow.f64 x 6) (pow.f64 (fma.f64 x x eps) 3))) (-.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 eps) (hypot.f64 (pow.f64 (fma.f64 x x eps) 3/4) (pow.f64 x 3/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)) eps) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (fma.f64 x x (fma.f64 x x eps)) (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))) (.f64 (.f64 x (neg.f64 (hypot.f64 x (sqrt.f64 eps)))) (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) (fma.f64 x x (fma.f64 x x eps))) (.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) (.f64 x (neg.f64 (hypot.f64 x (sqrt.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x eps)) (.f64 x (hypot.f64 x (sqrt.f64 eps))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 eps (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)) (-.f64 (fma.f64 x x (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 (fma.f64 x x eps)) (.f64 x (hypot.f64 x (sqrt.f64 eps)))) (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)) eps))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)) (.f64 eps (-.f64 (fma.f64 x x (fma.f64 x x eps)) (.f64 x (hypot.f64 x (sqrt.f64 eps)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x x (fma.f64 x x eps)) 3) (pow.f64 (.f64 x (hypot.f64 x (sqrt.f64 eps))) 3)) (.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)) eps) (+.f64 (pow.f64 (fma.f64 x x (fma.f64 x x eps)) 2) (.f64 (.f64 x (hypot.f64 x (sqrt.f64 eps))) (+.f64 (fma.f64 x x (fma.f64 x x eps)) (.f64 x (hypot.f64 x (sqrt.f64 eps))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x x (fma.f64 x x eps)) 2) (.f64 (fma.f64 x x eps) (.f64 x x))) (.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)) eps) (+.f64 (fma.f64 x x (fma.f64 x x eps)) (.f64 x (hypot.f64 x (sqrt.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 eps (-.f64 (fma.f64 x x (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 (.f64 eps (-.f64 (fma.f64 x x (fma.f64 x x eps)) (.f64 x (hypot.f64 x (sqrt.f64 eps))))) (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 eps (-.f64 (fma.f64 x x (fma.f64 x x eps)) (.f64 x (hypot.f64 x (sqrt.f64 eps)))))) (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 eps (-.f64 (pow.f64 (fma.f64 x x (fma.f64 x x eps)) 3) (pow.f64 (.f64 x (hypot.f64 x (sqrt.f64 eps))) 3))) (.f64 (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x eps) 3/2)) (+.f64 (pow.f64 (fma.f64 x x (fma.f64 x x eps)) 2) (.f64 (.f64 x (hypot.f64 x (sqrt.f64 eps))) (+.f64 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (fma.f64 x x eps) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x eps) (hypot.f64 x (sqrt.f64 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x eps) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (sqrt.f64 eps)) (fma.f64 x x eps))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (fma.f64 x x eps) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x eps)) 2) (.f64 (cbrt.f64 (fma.f64 x x eps)) (hypot.f64 x (sqrt.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x eps) 3/4) (pow.f64 (fma.f64 x x eps) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 x (sqrt.f64 eps)) 3/2) (pow.f64 (hypot.f64 x (sqrt.f64 eps)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 3/2) (pow.f64 (fma.f64 x x eps) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x eps)) 2) 3/2) (pow.f64 (cbrt.f64 (fma.f64 x x eps)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (fma.f64 x x eps) (cbrt.f64 (fma.f64 x x eps))) (cbrt.f64 (hypot.f64 x (sqrt.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (fma.f64 x x eps) (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 sqrt.f64 (pow.f64 (fma.f64 x x eps) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (fma.f64 x x eps) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 x x eps) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x eps) 9/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 3/2 (log.f64 (fma.f64 x x eps))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 3/2 (log.f64 (fma.f64 x x eps))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (fma.f64 x x eps) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (fma.f64 x x eps) 3/2)))))))
((#(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 pow.f64 (.f64 x (hypot.f64 x (sqrt.f64 eps))) 1)))) (#(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 (pow.f64 (.f64 x (hypot.f64 x (sqrt.f64 eps))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (fma.f64 x x eps) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.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 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 expm1.f64 (log1p.f64 (.f64 x (hypot.f64 x (sqrt.f64 eps)))))))))

simplify67.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

449×	`fma-def_binary64`
286×	`associate-r_binary64`
237×	`times-frac_binary64`
206×	`associate-/r*_binary64`
202×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	414	4653
1	1369	4176

Stop Event

1×	node limit

Counts

193 → 252

Calls

Call 1

Inputs
(/.f64 eps (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)))
(+.f64 (.f64 3/2 (/.f64 (.f64 (pow.f64 eps 2) x) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2))) (/.f64 eps (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3))))
(+.f64 (.f64 3/2 (/.f64 (.f64 (pow.f64 eps 2) x) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2))) (+.f64 (/.f64 eps (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3))) (.f64 -1 (.f64 (pow.f64 eps 3) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2) x))) (*.f64 -9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 3))))))))
(+.f64 (.f64 -1 (.f64 (pow.f64 eps 4) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2) (pow.f64 x 3)))) (+.f64 (.f64 3/2 (/.f64 (.f64 (+.f64 (.f64 3/8 (/.f64 1 (.f64 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2) x))) (.f64 -9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 3)))) x) (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)))) (.f64 9/16 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 3))))))) (+.f64 (.f64 3/2 (/.f64 (.f64 (pow.f64 eps 2) x) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2))) (+.f64 (/.f64 eps (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3))) (.f64 -1 (.f64 (pow.f64 eps 3) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2) x))) (*.f64 -9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 3)))))))))
(/.f64 eps (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 3)))
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(+.f64 (.f64 -1 (pow.f64 x 3)) (.f64 3/2 (*.f64 eps x)))
(+.f64 (.f64 -1 (pow.f64 x 3)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 9/8 (pow.f64 eps 2)) (.f64 -3/4 (pow.f64 eps 2))) x)) (.f64 3/2 (.f64 eps x))))
(+.f64 (.f64 -1 (pow.f64 x 3)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 9/8 (pow.f64 eps 2)) (.f64 -3/4 (pow.f64 eps 2))) x)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 9/8 (pow.f64 eps 3)) (+.f64 (.f64 -1/2 (pow.f64 eps 3)) (.f64 -9/16 (pow.f64 eps 3)))) (pow.f64 x 3))) (.f64 3/2 (.f64 eps x)))))
(pow.f64 x 3)
(+.f64 (.f64 -3/2 (.f64 eps x)) (pow.f64 x 3))
(+.f64 (.f64 -3/2 (.f64 eps x)) (+.f64 (pow.f64 x 3) (*.f64 3/8 (/.f64 (pow.f64 eps 2) x))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 3))) (+.f64 (.f64 -3/2 (.f64 eps x)) (+.f64 (pow.f64 x 3) (.f64 3/8 (/.f64 (pow.f64 eps 2) x)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps))))))
(+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (.f64 -3/2 (/.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) eps)))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -3/4 (pow.f64 x 4)) (.f64 9/8 (pow.f64 x 4))) (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps))))))) (pow.f64 eps 2)) (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (.f64 -3/2 (/.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) eps))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 6)) (+.f64 (.f64 -9/16 (pow.f64 x 6)) (.f64 9/8 (pow.f64 x 6)))) (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps))))))) (pow.f64 eps 3)) (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (.f64 -3/4 (pow.f64 x 4)) (.f64 9/8 (pow.f64 x 4)))) (pow.f64 eps 2)) (.f64 -3/2 (/.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) eps)))))
(sqrt.f64 (*.f64 -1 (pow.f64 eps 3)))
(+.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (.f64 -3/2 (/.f64 (.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (pow.f64 x 2)) eps)))
(+.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (+.f64 (/.f64 (.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (+.f64 (.f64 -3/4 (pow.f64 x 4)) (.f64 9/8 (pow.f64 x 4)))) (pow.f64 eps 2)) (.f64 -3/2 (/.f64 (.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (pow.f64 x 2)) eps))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (+.f64 (.f64 9/16 (pow.f64 x 6)) (+.f64 (.f64 1/2 (pow.f64 x 6)) (.f64 -9/8 (pow.f64 x 6))))) (pow.f64 eps 3))) (+.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (+.f64 (/.f64 (.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (+.f64 (.f64 -3/4 (pow.f64 x 4)) (.f64 9/8 (pow.f64 x 4)))) (pow.f64 eps 2)) (.f64 -3/2 (/.f64 (.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (pow.f64 x 2)) eps)))))
(*.f64 (sqrt.f64 (neg.f64 eps)) x)
(+.f64 (.f64 (sqrt.f64 (neg.f64 eps)) x) (.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps)))))
(+.f64 (.f64 (sqrt.f64 (neg.f64 eps)) x) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps)))) (*.f64 -1/8 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 x 7) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (+.f64 (.f64 (sqrt.f64 (neg.f64 eps)) x) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps)))) (.f64 -1/8 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))))
(pow.f64 x 2)
(+.f64 (*.f64 -1/2 eps) (pow.f64 x 2))
(+.f64 (.f64 -1/2 eps) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (pow.f64 x 2)))
(+.f64 (.f64 -1/2 eps) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (pow.f64 x 2))))
(*.f64 -1 (pow.f64 x 2))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 1/2 eps))
(+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 1/2 eps) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 1/2 eps) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))))))
(pow.f64 x 2)
(+.f64 (*.f64 -1/2 eps) (pow.f64 x 2))
(+.f64 (.f64 -1/2 eps) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (pow.f64 x 2)))
(+.f64 (.f64 -1/2 eps) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (pow.f64 x 2))))

Outputs
(/.f64 eps (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)))
(/.f64 eps (+.f64 (pow.f64 (*.f64 x x) 3/2) (pow.f64 x 3)))
(+.f64 (.f64 3/2 (/.f64 (.f64 (pow.f64 eps 2) x) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2))) (/.f64 eps (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3))))
(fma.f64 3/2 (/.f64 (.f64 x (.f64 eps eps)) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2)) (/.f64 eps (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3))))
(fma.f64 3/2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2)) x) (/.f64 eps (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3))))
(+.f64 (.f64 3/2 (/.f64 (.f64 (pow.f64 eps 2) x) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2))) (+.f64 (/.f64 eps (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3))) (.f64 -1 (.f64 (pow.f64 eps 3) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2) x))) (*.f64 -9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 3))))))))
(+.f64 (fma.f64 3/2 (/.f64 (.f64 x (.f64 eps eps)) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2)) (/.f64 eps (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)))) (.f64 (neg.f64 (pow.f64 eps 3)) (+.f64 (/.f64 3/8 (.f64 x (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2))) (/.f64 (.f64 -9/4 (.f64 x x)) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 3)))))
(-.f64 (fma.f64 3/2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2)) x) (/.f64 eps (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)))) (.f64 (pow.f64 eps 3) (fma.f64 -9/4 (/.f64 (.f64 x x) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 3)) (/.f64 3/8 (.f64 x (pow.f64 (+.f64 (pow.f64 (*.f64 x x) 3/2) (pow.f64 x 3)) 2))))))
(+.f64 (.f64 -1 (.f64 (pow.f64 eps 4) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2) (pow.f64 x 3)))) (+.f64 (.f64 3/2 (/.f64 (.f64 (+.f64 (.f64 3/8 (/.f64 1 (.f64 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2) x))) (.f64 -9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 3)))) x) (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)))) (.f64 9/16 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 3))))))) (+.f64 (.f64 3/2 (/.f64 (.f64 (pow.f64 eps 2) x) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2))) (+.f64 (/.f64 eps (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3))) (.f64 -1 (.f64 (pow.f64 eps 3) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 2) x))) (*.f64 -9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (pow.f64 x 2) 3/2) (pow.f64 x 3)) 3)))))))))
(fma.f64 -1 (.f64 (pow.f64 eps 4) (+.f64 (/.f64 1/16 (.f64 (pow.f64 x 3) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2))) (fma.f64 3/2 (/.f64 (+.f64 (/.f64 3/8 (.f64 x (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2))) (/.f64 (.f64 -9/4 (.f64 x x)) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 3))) (/.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) x)) (/.f64 9/16 (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 3))))) (+.f64 (fma.f64 3/2 (/.f64 (.f64 x (.f64 eps eps)) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2)) (/.f64 eps (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)))) (.f64 (neg.f64 (pow.f64 eps 3)) (+.f64 (/.f64 3/8 (.f64 x (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2))) (/.f64 (.f64 -9/4 (.f64 x x)) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 3))))))
(fma.f64 (neg.f64 (pow.f64 eps 4)) (+.f64 (/.f64 1/16 (.f64 (pow.f64 x 3) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2))) (fma.f64 3/2 (.f64 (/.f64 (fma.f64 -9/4 (/.f64 (.f64 x x) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 3)) (/.f64 3/8 (.f64 x (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2)))) (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3))) x) (/.f64 9/16 (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 3)))) (-.f64 (fma.f64 3/2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2)) x) (/.f64 eps (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)))) (.f64 (pow.f64 eps 3) (fma.f64 -9/4 (/.f64 (.f64 x x) (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 3)) (/.f64 3/8 (.f64 x (pow.f64 (+.f64 (pow.f64 (.f64 x x) 3/2) (pow.f64 x 3)) 2)))))))
(/.f64 eps (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 3)))
(/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps)))))))
(/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps)))))
(+.f64 (.f64 3/2 (/.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) (pow.f64 (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 3)) 2))) (/.f64 eps (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 3))))
(fma.f64 3/2 (/.f64 (.f64 (.f64 x x) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps)))))) (pow.f64 (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps)))))) 2)) (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))))))
(fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps))) (/.f64 (pow.f64 (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps)))) 2) (*.f64 x x))) (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps))))))
(+.f64 (.f64 3/2 (/.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) (pow.f64 (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 3)) 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (.f64 -3/4 (pow.f64 x 4)) (.f64 9/8 (pow.f64 x 4)))) (pow.f64 (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 3)) 2)) (.f64 -9/4 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (pow.f64 x 4)) (pow.f64 (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 3)) 3)))) eps)) (/.f64 eps (+.f64 (exp.f64 (.f64 3/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 3)))))
(fma.f64 3/2 (/.f64 (.f64 (.f64 x x) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps)))))) (pow.f64 (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps)))))) 2)) (fma.f64 -1 (/.f64 (+.f64 (/.f64 (.f64 (pow.f64 x 4) 3/8) (/.f64 (pow.f64 (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps)))))) 2) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))))) (/.f64 (.f64 -9/4 (*.f64 (pow.f64 x 4) (pow.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) 2))) (pow.f64 (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps)))))) 3))) eps) (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps)))))))))
(fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps))) (/.f64 (pow.f64 (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps)))) 2) (.f64 x x))) (-.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps))))) (/.f64 (fma.f64 -9/4 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps))) 2) (pow.f64 (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps)))) 3)) (pow.f64 x 4)) (.f64 (/.f64 (.f64 (pow.f64 x 4) 3/8) (pow.f64 (+.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps)))) 2)) (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 -1) (log.f64 eps))))) eps)))
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(+.f64 (+.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (/.f64 (.f64 eps eps) (.f64 (pow.f64 x 4) 3/8)))) (.f64 -3/2 (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (/.f64 eps (.f64 x x)))))
(+.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (fma.f64 -3/2 (.f64 (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) eps) (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) eps) (/.f64 (.f64 (pow.f64 x 4) 3/8) eps))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (+.f64 (.f64 9/16 (pow.f64 x 6)) (+.f64 (.f64 1/2 (pow.f64 x 6)) (.f64 -9/8 (pow.f64 x 6))))) (pow.f64 eps 3))) (+.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (+.f64 (/.f64 (.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (+.f64 (.f64 -3/4 (pow.f64 x 4)) (.f64 9/8 (pow.f64 x 4)))) (pow.f64 eps 2)) (.f64 -3/2 (/.f64 (.f64 (sqrt.f64 (.f64 -1 (pow.f64 eps 3))) (pow.f64 x 2)) eps)))))
(fma.f64 -1 (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (/.f64 (pow.f64 eps 3) (fma.f64 9/16 (pow.f64 x 6) (.f64 (pow.f64 x 6) -5/8)))) (+.f64 (+.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (/.f64 (.f64 eps eps) (.f64 (pow.f64 x 4) 3/8)))) (.f64 -3/2 (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (/.f64 eps (*.f64 x x))))))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (fma.f64 -3/2 (.f64 (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) eps) (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) eps) (/.f64 (.f64 (pow.f64 x 4) 3/8) eps)))) (/.f64 (sqrt.f64 (neg.f64 (pow.f64 eps 3))) (/.f64 (pow.f64 eps 3) (*.f64 (pow.f64 x 6) -1/16))))
(*.f64 (sqrt.f64 (neg.f64 eps)) x)
(*.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 (sqrt.f64 (neg.f64 eps)) x) (.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps)))))
(fma.f64 (sqrt.f64 (neg.f64 eps)) x (/.f64 (*.f64 1/2 (pow.f64 x 3)) (sqrt.f64 (neg.f64 eps))))
(fma.f64 x (sqrt.f64 (neg.f64 eps)) (/.f64 (*.f64 1/2 (pow.f64 x 3)) (sqrt.f64 (neg.f64 eps))))
(+.f64 (.f64 (sqrt.f64 (neg.f64 eps)) x) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps)))) (*.f64 -1/8 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))))
(fma.f64 (sqrt.f64 (neg.f64 eps)) x (fma.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps))) (/.f64 (*.f64 -1/8 (pow.f64 x 5)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))
(fma.f64 x (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps))) (/.f64 -1/8 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 x 7) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (+.f64 (.f64 (sqrt.f64 (neg.f64 eps)) x) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps)))) (.f64 -1/8 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))))
(fma.f64 1/16 (/.f64 (pow.f64 x 7) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (fma.f64 (sqrt.f64 (neg.f64 eps)) x (fma.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps))) (/.f64 (*.f64 -1/8 (pow.f64 x 5)) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))))
(fma.f64 1/16 (/.f64 (pow.f64 x 7) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (fma.f64 x (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 (neg.f64 eps))) (/.f64 -1/8 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 3) (pow.f64 x 5))))))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1/2 eps) (pow.f64 x 2))
(fma.f64 -1/2 eps (*.f64 x x))
(fma.f64 eps -1/2 (*.f64 x x))
(+.f64 (.f64 -1/2 eps) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (pow.f64 x 2)))
(fma.f64 -1/2 eps (fma.f64 -1/8 (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 x x)))
(fma.f64 eps -1/2 (fma.f64 -1/8 (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 x x)))
(+.f64 (.f64 -1/2 eps) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (pow.f64 x 2))))
(fma.f64 -1/2 eps (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)) (fma.f64 -1/8 (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 x x))))
(fma.f64 eps -1/2 (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)) (fma.f64 -1/8 (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 x x))))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 1/2 eps))
(fma.f64 -1 (.f64 x x) (.f64 eps 1/2))
(-.f64 (.f64 eps 1/2) (.f64 x x))
(+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 1/2 eps) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)))))
(fma.f64 -1 (.f64 x x) (fma.f64 1/2 eps (.f64 1/8 (/.f64 (.f64 eps eps) (.f64 x x)))))
(-.f64 (fma.f64 eps 1/2 (.f64 1/8 (.f64 (/.f64 eps x) (/.f64 eps x)))) (*.f64 x x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 1/2 eps) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)) (fma.f64 -1 (.f64 x x) (fma.f64 1/2 eps (.f64 1/8 (/.f64 (.f64 eps eps) (.f64 x x))))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)) (-.f64 (fma.f64 eps 1/2 (.f64 1/8 (.f64 (/.f64 eps x) (/.f64 eps x)))) (*.f64 x x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1/2 eps) (pow.f64 x 2))
(fma.f64 -1/2 eps (*.f64 x x))
(fma.f64 eps -1/2 (*.f64 x x))
(+.f64 (.f64 -1/2 eps) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (pow.f64 x 2)))
(fma.f64 -1/2 eps (fma.f64 -1/8 (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 x x)))
(fma.f64 eps -1/2 (fma.f64 -1/8 (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 x x)))
(+.f64 (.f64 -1/2 eps) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (pow.f64 x 2))))
(fma.f64 -1/2 eps (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)) (fma.f64 -1/8 (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 x x))))
(fma.f64 eps -1/2 (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)) (fma.f64 -1/8 (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 x x))))

eval170.0ms (4.7%)

Compiler: Compiled 12484 to 6185 computations (50.5% saved)

prune127.0ms (3.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	252	5	257

Error

Counts

257 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	14.4b	(.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (.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))))
✓	21.4b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.6b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))
	22.0b	(-.f64 x (sqrt.f64 (.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))))))

Compiler

Compiled 111 to 52 computations (53.2% saved)

regimes18.0ms (0.5%)

Accuracy

Total -61.8b remaining (-20010.5%)

Threshold costs -61.8b (-20010.5%)

Counts

6 → 1

Calls

Call 1

Inputs
(.f64 (/.f64 eps (+.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x (neg.f64 eps)) 3/2))) (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))
(-.f64 x (sqrt.f64 (.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))))))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

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

Results

Time	Error	Segments	Branch
5.0ms	0.3b	1	`x`
6.0ms	0.3b	1	`eps`
5.0ms	0.3b	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 132 to 49 computations (62.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	19	27
2	30	27
3	36	27
4	39	27

Stop Event

1×

saturated

Calls

Call 1

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

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

end19.0ms (0.5%)

Stop Event

1×

fuel

Compiler

Compiled 40 to 18 computations (55% 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

analyze42.0ms (1.2%)

sample1.5s (40.9%)

preprocess39.0ms (1.1%)

simplify12.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series10.0ms (0.3%)

rewrite54.0ms (1.5%)

simplify41.0ms (1.1%)

eval44.0ms (1.2%)

prune152.0ms (4.2%)

localize8.0ms (0.2%)

series13.0ms (0.4%)

rewrite72.0ms (2%)

simplify31.0ms (0.9%)

eval97.0ms (2.7%)

prune542.0ms (15%)

localize13.0ms (0.4%)

series7.0ms (0.2%)

rewrite59.0ms (1.6%)

simplify31.0ms (0.8%)

eval68.0ms (1.9%)

prune283.0ms (7.8%)

localize17.0ms (0.5%)

series46.0ms (1.3%)

rewrite42.0ms (1.2%)

simplify67.0ms (1.8%)

eval170.0ms (4.7%)

prune127.0ms (3.5%)

regimes18.0ms (0.5%)

simplify2.0ms (0.1%)

end19.0ms (0.5%)

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