Details

analyze40.0ms (1.4%)

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 (54.9%)

Results

587.0ms	5173×	body	128	valid
437.0ms	1115×	body	1024	valid
321.0ms	1166×	body	512	valid
147.0ms	758×	body	256	valid
22.0ms	44×	body	2048	valid
17.0ms	87×	body	128	invalid

preprocess25.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 10 to 6 computations (40% saved)

simplify15.0ms (0.5%)

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)))

prune2.0ms (0.1%)

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

26.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	6.2b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series8.0ms (0.3%)

Counts

2 → 40

Calls

12 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)))

rewrite52.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

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

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

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 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 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 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 +.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 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)))))) (#(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 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))))))

simplify46.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

681×	`unswap-sqr_binary64`
321×	`associate-/l/_binary64`
263×	`fma-def_binary64`
233×	`associate-/r/_binary64`
217×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	77	567
1	223	539
2	667	531
3	2775	518
4	4554	516

Stop Event

1×	node limit

Counts

119 → 109

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

prune82.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	4	110

Error

Counts

110 → 4

Alt Table

Status	Error	Program
	27.0b	(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.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)))
✓	26.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 1908 to 778 computations (59.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series13.0ms (0.5%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	inf	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.0ms	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))))

rewrite73.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 177

Calls

Call 1

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

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

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(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 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))))))))) (#(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 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))))))

simplify33.0ms (1.2%)

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))))

prune160.0ms (5.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	258	4	262

Error

Counts

262 → 4

Alt Table

Status	Error	Program
▶	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)
	27.0b	(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	26.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 6780 to 1791 computations (73.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	0.1b	(/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps)
✓	0.3b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)

series13.0ms (0.5%)

Counts

3 → 48

Calls

18 calls:

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

rewrite58.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

846×	`prod-diff_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
111×	`add-sqr-sqrt_binary64`
106×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	218	33
2	3022	33

Stop Event

1×	node limit

Counts

3 → 113

Calls

Call 1

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

Outputs

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

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

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

simplify40.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

941×	`fma-def_binary64`
591×	`times-frac_binary64`
419×	`associate-/l*_binary64`
380×	`associate-/r*_binary64`
202×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	1233
1	489	1184
2	1608	1093

Stop Event

1×	node limit

Counts

161 → 168

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

prune78.0ms (2.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	168	4	172

Error

Counts

172 → 4

Alt Table

Status	Error	Program
✓	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)
▶	27.0b	(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	26.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 3205 to 1438 computations (55.1% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.4b	(cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)
	6.2b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series55.0ms (1.9%)

Counts

2 → 8

Calls

12 calls:

Time	Variable		Point	Expression
14.0ms	eps	@	0	(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)
14.0ms	eps	@	inf	(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)
9.0ms	x	@	0	(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)
4.0ms	x	@	0	(cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
4.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)

rewrite69.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`fma-def_binary64`
447×	`log-prod_binary64`
222×	`fma-neg_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	228	26
2	2874	24

Stop Event

1×	node limit

Counts

2 → 146

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)
(cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 1 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (cbrt.f64 (-.f64 (*.f64 x x) eps)) (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (+.f64 (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))) (cbrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 3) (fma.f64 x x (fma.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 (*.f64 x x) eps)))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 3/2) (fma.f64 x x (fma.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (pow.f64 (cbrt.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 2) (cbrt.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 2)) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 x 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simplify51.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
364×	`distribute-lft-in_binary64`
364×	`distribute-rgt-in_binary64`
194×	`associate-+l+_binary64`
152×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1709
1	400	1611
2	1562	1418

Stop Event

1×	node limit

Counts

154 → 162

Calls

Call 1

Inputs
(*.f64 -1 (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 2/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3)))) x) (.f64 -1 (sqrt.f64 (neg.f64 eps))))
(+.f64 (.f64 (+.f64 (.f64 -1/3 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 1/3) (.f64 (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/3) (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))) (cbrt.f64 -1))))) (cbrt.f64 -1))))) (pow.f64 x 2)) (+.f64 (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 2/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3)))) x) (.f64 -1 (sqrt.f64 (neg.f64 eps)))))
(+.f64 (.f64 (+.f64 (.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 8)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 8)) 1/3) (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))))))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/3) (/.f64 (+.f64 (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/9) (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))) (cbrt.f64 -1))))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/9) (.f64 (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/3) (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))) (cbrt.f64 -1))))) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)))) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/9) (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3)))) (.f64 -1/3 (+.f64 (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))))))))))) (pow.f64 x 3)) (+.f64 (.f64 (+.f64 (.f64 -1/3 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 1/3) (.f64 (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/3) (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))) (cbrt.f64 -1))))) (cbrt.f64 -1))))) (pow.f64 x 2)) (+.f64 (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 2/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3)))) x) (.f64 -1 (sqrt.f64 (neg.f64 eps))))))
(*.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 1/3) (cbrt.f64 -1))
(+.f64 (.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 1/3) (cbrt.f64 -1)) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3) x))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/3) (/.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))) (pow.f64 x 2)) (pow.f64 (cbrt.f64 -1) 2)))) (+.f64 (.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 1/3) (cbrt.f64 -1)) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3) x)))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/3) (/.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))) (pow.f64 x 2)) (pow.f64 (cbrt.f64 -1) 2)))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/3) (/.f64 (.f64 (+.f64 (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/9) (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))) (pow.f64 x 3)) (pow.f64 (cbrt.f64 -1) 2)))) (+.f64 (.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 1/3) (cbrt.f64 -1)) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/9) (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3) x))))))

Outputs
(*.f64 -1 (sqrt.f64 (neg.f64 eps)))
(neg.f64 (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 2/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3)))) x) (.f64 -1 (sqrt.f64 (neg.f64 eps))))
(fma.f64 (.f64 (.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/18) (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/18)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 4))) 1) x (neg.f64 (sqrt.f64 (neg.f64 eps))))
(fma.f64 (.f64 (.f64 (pow.f64 (.f64 (neg.f64 eps) (neg.f64 eps)) 1/18) (pow.f64 (.f64 (neg.f64 eps) (neg.f64 eps)) 1/18)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 4))) x (neg.f64 (sqrt.f64 (neg.f64 eps))))
(fma.f64 (.f64 (.f64 (pow.f64 (.f64 eps eps) 1/18) (pow.f64 (.f64 eps eps) 1/18)) (cbrt.f64 (*.f64 -1 (cbrt.f64 -1)))) x (neg.f64 (sqrt.f64 (neg.f64 eps))))
(+.f64 (.f64 (+.f64 (.f64 -1/3 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 1/3) (.f64 (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/3) (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))) (cbrt.f64 -1))))) (cbrt.f64 -1))))) (pow.f64 x 2)) (+.f64 (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 2/3 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3)))) x) (.f64 -1 (sqrt.f64 (neg.f64 eps)))))
(fma.f64 (fma.f64 -1/3 (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) (/.f64 1/2 (sqrt.f64 (neg.f64 eps)))) (fma.f64 2/9 (.f64 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) (.f64 (cbrt.f64 (sqrt.f64 (neg.f64 eps))) (.f64 (cbrt.f64 -1) (fma.f64 1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (.f64 -2/3 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) (/.f64 1/2 (sqrt.f64 (neg.f64 eps))))) (cbrt.f64 -1)))))))) (.f64 x x) (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/18) (pow.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 4) 1/18)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 4))) 1) x (neg.f64 (sqrt.f64 (neg.f64 eps)))))
(fma.f64 (fma.f64 -1/3 (fma.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18))) (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (/.f64 1/2 (sqrt.f64 (neg.f64 eps)))) (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) 2/9 (.f64 (fma.f64 -2/3 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (fma.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18))) (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (/.f64 1/2 (sqrt.f64 (neg.f64 eps))))) (cbrt.f64 -1)) (.f64 (.f64 (pow.f64 (/.f64 (/.f64 1 (neg.f64 eps)) (neg.f64 eps)) 1/18) (pow.f64 (/.f64 (/.f64 1 (neg.f64 eps)) (neg.f64 eps)) 1/18)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))) 1/9))) (.f64 (cbrt.f64 -1) (cbrt.f64 (sqrt.f64 (neg.f64 eps))))))) (.f64 x x) (fma.f64 (.f64 (.f64 (pow.f64 (.f64 (neg.f64 eps) (neg.f64 eps)) 1/18) (pow.f64 (*.f64 (neg.f64 eps) (neg.f64 eps)) 1/18)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 4))) x (neg.f64 (sqrt.f64 (neg.f64 eps)))))
(-.f64 (.f64 x (+.f64 (.f64 (.f64 (pow.f64 (.f64 eps eps) 1/18) (pow.f64 (.f64 eps eps) 1/18)) (cbrt.f64 (.f64 -1 (cbrt.f64 -1)))) (.f64 (fma.f64 (cbrt.f64 -1) (.f64 (cbrt.f64 (sqrt.f64 (neg.f64 eps))) (fma.f64 -2/3 (.f64 (/.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (cbrt.f64 -1)) (fma.f64 1/3 (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (/.f64 1/2 (sqrt.f64 (neg.f64 eps))))) (.f64 (cbrt.f64 (/.f64 -1 (cbrt.f64 -1))) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (.f64 eps eps)) 1/18) (pow.f64 (/.f64 1 (.f64 eps eps)) 1/18)))))) (fma.f64 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 2/9) (fma.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) -1/9 (/.f64 -1/6 (sqrt.f64 (neg.f64 eps)))))) x))) (sqrt.f64 (neg.f64 eps)))
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(*.f64 (cbrt.f64 -1) (cbrt.f64 (sqrt.f64 (neg.f64 eps))))
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(fma.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 (neg.f64 eps))) (/.f64 (fma.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18))) (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (/.f64 1/2 (sqrt.f64 (neg.f64 eps)))) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 x x)))) (fma.f64 1/3 (.f64 x (.f64 (.f64 (pow.f64 (/.f64 1 (neg.f64 eps)) 1/18) (pow.f64 (/.f64 1 (neg.f64 eps)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (.f64 (cbrt.f64 -1) (cbrt.f64 (sqrt.f64 (neg.f64 eps))))))
(fma.f64 (cbrt.f64 (/.f64 -1 eps)) (/.f64 (fma.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) -1/9 (/.f64 -1/6 (sqrt.f64 (neg.f64 eps)))) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 x x))) (fma.f64 1/3 (.f64 x (.f64 (.f64 (pow.f64 (/.f64 -1 eps) 1/18) (pow.f64 (/.f64 -1 eps) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 8))))) (*.f64 (cbrt.f64 -1) (cbrt.f64 (sqrt.f64 (neg.f64 eps))))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/3) (/.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))) (pow.f64 x 2)) (pow.f64 (cbrt.f64 -1) 2)))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/3) (/.f64 (.f64 (+.f64 (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/9) (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 1/2 (/.f64 1 (sqrt.f64 (neg.f64 eps))))) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))) (pow.f64 x 3)) (pow.f64 (cbrt.f64 -1) 2)))) (+.f64 (.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) 1/3) (cbrt.f64 -1)) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/9) (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3) x))))))
(fma.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) (/.f64 1/2 (sqrt.f64 (neg.f64 eps)))) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 x x)))) (fma.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 (fma.f64 1/27 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/3 (.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) (/.f64 1/2 (sqrt.f64 (neg.f64 eps))))))) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 x 3)))) (fma.f64 (cbrt.f64 (sqrt.f64 (neg.f64 eps))) (cbrt.f64 -1) (.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) 1/18)) (.f64 x (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))))))))
(+.f64 (fma.f64 1/3 (.f64 x (.f64 (.f64 (pow.f64 (/.f64 1 (neg.f64 eps)) 1/18) (pow.f64 (/.f64 1 (neg.f64 eps)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (.f64 (cbrt.f64 -1) (cbrt.f64 (sqrt.f64 (neg.f64 eps))))) (.f64 (.f64 -1/3 (cbrt.f64 (/.f64 1 (neg.f64 eps)))) (+.f64 (/.f64 (fma.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18))) (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (/.f64 1/2 (sqrt.f64 (neg.f64 eps)))) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 x x))) (/.f64 (fma.f64 -2/3 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/18)) (.f64 (fma.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18))) (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (/.f64 1/2 (sqrt.f64 (neg.f64 eps)))) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))))) (/.f64 (*.f64 1/27 (cbrt.f64 (/.f64 1 (neg.f64 eps)))) (pow.f64 (cbrt.f64 -1) 2))) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 x 3))))))
(fma.f64 (.f64 -1/3 (cbrt.f64 (/.f64 -1 eps))) (fma.f64 (/.f64 (fma.f64 1/3 (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (/.f64 1/2 (sqrt.f64 (neg.f64 eps)))) (pow.f64 (cbrt.f64 -1) 2)) (.f64 x x) (.f64 (/.f64 (fma.f64 -2/3 (.f64 (fma.f64 1/3 (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (pow.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) 1/18)) (/.f64 1/2 (sqrt.f64 (neg.f64 eps)))) (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/18) (.f64 (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) 1/18) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))))) (.f64 (cbrt.f64 (/.f64 -1 eps)) (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)))) (pow.f64 (cbrt.f64 -1) 2)) (pow.f64 x 3))) (fma.f64 1/3 (.f64 x (.f64 (.f64 (pow.f64 (/.f64 -1 eps) 1/18) (pow.f64 (/.f64 -1 eps) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 8))))) (*.f64 (cbrt.f64 -1) (cbrt.f64 (sqrt.f64 (neg.f64 eps))))))

prune180.0ms (6.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	271	4	275

Error

Counts

275 → 4

Alt Table

Status	Error	Program
✓	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)
✓	27.0b	(pow.f64 (cbrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 3)
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	26.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 7427 to 3210 computations (56.8% saved)

regimes91.0ms (3.2%)

Accuracy

Total -25.0b remaining (-8236.8%)

Threshold costs -25.0b (-8236.8%)

Counts

35 → 1

Compiler

Compiled 492 to 218 computations (55.7% 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))))

end54.0ms (1.9%)

Stop Event

1×

done

Compiler

Compiled 89 to 29 computations (67.4% 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

analyze40.0ms (1.4%)

sample1.5s (54.9%)

preprocess25.0ms (0.9%)

simplify15.0ms (0.5%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite52.0ms (1.9%)

simplify46.0ms (1.6%)

prune82.0ms (2.9%)

localize8.0ms (0.3%)

series13.0ms (0.5%)

rewrite73.0ms (2.6%)

simplify33.0ms (1.2%)

prune160.0ms (5.7%)

localize8.0ms (0.3%)

series13.0ms (0.5%)

rewrite58.0ms (2.1%)

simplify40.0ms (1.4%)

prune78.0ms (2.8%)

localize7.0ms (0.3%)

series55.0ms (1.9%)

rewrite69.0ms (2.5%)

simplify51.0ms (1.8%)

prune180.0ms (6.4%)

regimes91.0ms (3.2%)

simplify2.0ms (0.1%)

end54.0ms (1.9%)

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