Details

analyze41.0ms (1.6%)

Algorithm

1×

Search

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

Compiler

Compiled 25 to 17 computations (32% saved)

sample1.5s (57.4%)

Results

558.0ms	5097×	body	128	valid
418.0ms	1174×	body	1024	valid
324.0ms	1206×	body	512	valid
148.0ms	741×	body	256	valid
15.0ms	38×	body	2048	valid
8.0ms	86×	body	128	invalid

Compiler

Compiled 50 to 34 computations (32% saved)

preprocess26.0ms (1%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 10 to 6 computations (40% saved)

simplify12.0ms (0.5%)

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)))

prune1.0ms (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

24.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	24.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	2.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series10.0ms (0.4%)

Counts

2 → 32

Calls

12 calls:

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

rewrite49.0ms (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	21
1	162	21
2	2412	21

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

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

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

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

simplify32.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

610×	`cancel-sign-sub-inv_binary64`
318×	`fma-neg_binary64`
230×	`associate-/r/_binary64`
224×	`associate-/l/_binary64`
193×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	711
1	211	697
2	609	687
3	2414	669

Stop Event

1×	node limit

Counts

94 → 107

Calls

Call 1

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

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

prune56.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Error

Counts

108 → 4

Alt Table

Status	Error	Program
✓	24.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	37.7b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
▶	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)))

Compiler

Compiled 1843 to 730 computations (60.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.3b	(/.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
5.0ms	eps	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
2.0ms	eps	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	x	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	x	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	eps	@	inf	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

rewrite68.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 177

Calls

Call 1

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

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

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simplify38.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

209 → 206

Calls

Call 1

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

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

prune119.0ms (4.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	252	1	253
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	253	4	257

Error

Counts

257 → 4

Alt Table

Status	Error	Program
✓	24.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	37.7b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)

Compiler

Compiled 6476 to 1598 computations (75.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
✓	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)

series17.0ms (0.7%)

Counts

4 → 64

Calls

24 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
2.0ms	eps	@	-inf	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)
1.0ms	x	@	-inf	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)
1.0ms	x	@	0	(/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps)
1.0ms	x	@	0	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)

rewrite56.0ms (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	54
1	218	39
2	3022	39

Stop Event

1×	node limit

Counts

4 → 137

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

simplify59.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
519×	`times-frac_binary64`
342×	`associate-/l*_binary64`
319×	`associate-/r*_binary64`
280×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1484
1	339	1437
2	1074	1415
3	4886	1411

Stop Event

1×	node limit

Counts

201 → 208

Calls

Call 1

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

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

prune87.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	208	4	212

Error

Counts

212 → 4

Alt Table

Status	Error	Program
✓	24.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	37.7b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)

Compiler

Compiled 3678 to 1607 computations (56.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
✓	0.2b	(.f64 -1/8 (/.f64 eps (.f64 x x)))
✓	12.0b	(/.f64 eps (*.f64 x x))

series12.0ms (0.5%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/.f64 eps (*.f64 x x))
1.0ms	eps	@	0	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
1.0ms	eps	@	0	(/.f64 eps (*.f64 x x))
1.0ms	eps	@	inf	(/.f64 eps (*.f64 x x))
1.0ms	eps	@	inf	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))

rewrite56.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

219×	`expm1-udef_binary64`
219×	`log1p-udef_binary64`
178×	`log-pow_binary64`
172×	`prod-diff_binary64`
127×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	251	36
2	3497	34

Stop Event

1×	node limit

Counts

3 → 114

Calls

Call 1

Inputs
(/.f64 eps (*.f64 x x))
(.f64 -1/8 (/.f64 eps (.f64 x x)))
(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))

Outputs

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

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

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

simplify87.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1092×	`associate-/l/_binary64`
591×	`unswap-sqr_binary64`
323×	`times-frac_binary64`
308×	`sqr-pow_binary64`
301×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	828
1	45	828
2	104	828
3	346	810
4	2006	774
5	2734	774
6	3675	774
7	3862	774
8	4091	774
9	4366	774

Stop Event

1×	node limit

Counts

186 → 125

Calls

Call 1

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

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

prune69.0ms (2.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	125	4	129

Error

Counts

129 → 4

Alt Table

Status	Error	Program
✓	24.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	37.7b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)

Compiler

Compiled 2264 to 1378 computations (39.1% saved)

regimes105.0ms (4.1%)

Accuracy

Total 0.3b remaining (97.2%)

Threshold costs 0.3b (97.2%)

Counts

61 → 1

Compiler

Compiled 737 to 267 computations (63.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

Outputs

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

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

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

end59.0ms (2.3%)

Stop Event

1×

done

Compiler

Compiled 87 to 50 computations (42.5% saved)

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

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

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

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

Details

analyze41.0ms (1.6%)

sample1.5s (57.4%)

preprocess26.0ms (1%)

simplify12.0ms (0.5%)

prune1.0ms (0.1%)

localize6.0ms (0.2%)

series10.0ms (0.4%)

rewrite49.0ms (1.9%)

simplify32.0ms (1.2%)

prune56.0ms (2.2%)

localize8.0ms (0.3%)

series13.0ms (0.5%)

rewrite68.0ms (2.6%)

simplify38.0ms (1.5%)

prune119.0ms (4.6%)

localize8.0ms (0.3%)

series17.0ms (0.7%)

rewrite56.0ms (2.1%)

simplify59.0ms (2.3%)

prune87.0ms (3.4%)

localize7.0ms (0.3%)

series12.0ms (0.5%)

rewrite56.0ms (2.2%)

simplify87.0ms (3.4%)

prune69.0ms (2.7%)

regimes105.0ms (4.1%)

simplify3.0ms (0.1%)

end59.0ms (2.3%)

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