Details

analyze22.0ms (0.4%)

Algorithm

1×

Search

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

Compiler

Compiled 25 to 17 computations (32% saved)

sample1.3s (20.6%)

Results

675.0ms	5944×	body	256	valid
280.0ms	1021×	body	1024	valid
266.0ms	1247×	body	512	valid
18.0ms	181×	body	256	invalid
15.0ms	44×	body	2048	valid

preprocess26.0ms (0.4%)

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 12 to 8 computations (33.3% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

22.8b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	22.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

localize30.0ms (0.5%)

Local error

Found 6 expressions with local error:

New	Error	Program
	4.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	0.0b	(-.f64 (*.f64 x x) eps)
	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	4.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 26 to 6 computations (76.9% saved)

series12.0ms (0.2%)

Counts

3 → 56

Calls

18 calls:

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

rewrite68.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

931×	`pow1_binary64`
871×	`add-log-exp_binary64`
871×	`log1p-expm1-u_binary64`
871×	`expm1-log1p-u_binary64`
849×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
1	162	28
2	2412	28

Stop Event

1×	node limit

Counts

3 → 97

Calls

Call 1

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

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (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 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))))))))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

706×	`unswap-sqr_binary64`
524×	`fma-def_binary64`
423×	`associate-/l/_binary64`
379×	`associate-/r/_binary64`
310×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	968
1	331	939
2	990	925
3	3948	911
4	6345	911

Stop Event

1×	node limit

Counts

153 → 151

Calls

Call 1

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

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

eval45.0ms (0.7%)

Compiler: Compiled 2547 to 1189 computations (53.3% saved)

prune35.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	142	9	151
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	142	10	152

Error

0.0b

Counts

152 → 10

Alt Table

Click to see full alt table

Status	Error	Program
	26.7b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
▶	38.0b	(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
	58.8b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
▶	36.8b	(*.f64 1/2 (/.f64 eps x))
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	61.3b	(-.f64 x x)
▶	61.7b	(*.f64 2 x)
	50.6b	(fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 (pow.f64 eps 4) 5/128) (pow.f64 x 7)))))
▶	0.4b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))
✓	22.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 262 to 164 computations (37.4% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

Compiler

Compiled 60 to 9 computations (85% saved)

series12.0ms (0.2%)

Counts

2 → 32

Calls

12 calls:

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

rewrite87.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
508×	`log-prod_binary64`
308×	`fma-neg_binary64`
272×	`pow2_binary64`
185×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	261	24
2	4003	22

Stop Event

1×	node limit

Counts

2 → 194

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

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

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-def_binary64`
511×	`cancel-sign-sub-inv_binary64`
392×	`fma-neg_binary64`
356×	`associate-l_binary64`
351×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	962
1	400	841
2	1346	803
3	6178	785

Stop Event

1×	node limit

Counts

226 → 230

Calls

Call 1

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

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

localize3.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize5.0ms (0.1%)

Compiler: Compiled 13 to 6 computations (53.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	11.3b	(/.f64 eps (*.f64 x x))
	0.2b	(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
✓	0.2b	(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
✓	11.3b	(/.f64 eps (*.f64 x x))

Compiler

Compiled 46 to 18 computations (60.9% saved)

series9.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite83.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

648×	`log-prod_binary64`
404×	`prod-diff_binary64`
320×	`pow2_binary64`
240×	`pow-unpow_binary64`
226×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	249	24
2	3608	24

Stop Event

1×	node limit

Counts

2 → 140

Calls

Call 1

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

Outputs

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

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1240×	`associate-*l/_binary64`
1008×	`associate-/l/_binary64`
620×	`associate-/r/_binary64`
569×	`unswap-sqr_binary64`
307×	`sqr-pow_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	588
1	39	588
2	91	588
3	305	570
4	1799	534
5	2493	534
6	3409	534
7	3596	534
8	3825	534
9	4097	534

Stop Event

1×	node limit

Counts

188 → 148

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

localize16.0ms (0.3%)

Local error

Found 8 expressions with local error:

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

Compiler

Compiled 81 to 12 computations (85.2% saved)

series18.0ms (0.3%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps))
1.0ms	eps	@	-inf	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps))
1.0ms	x	@	0	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps))
1.0ms	eps	@	inf	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps))
1.0ms	eps	@	-inf	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))

rewrite102.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`fma-def_binary64`
587×	`log-prod_binary64`
316×	`fma-neg_binary64`
218×	`egg-rr`
208×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	301	27
2	4496	25

Stop Event

1×	node limit

Counts

2 → 256

Calls

Call 1

Inputs

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 -1 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (neg.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps))) (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4)) (pow.f64 (-.f64 (*.f64 x x) eps) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 1 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (cbrt.f64 (-.f64 (*.f64 x x) eps)) (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4)) (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (*.f64 0 (/.f64 1 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (*.f64 (/.f64 1 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 0 (/.f64 1 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))) (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 0) (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))) (cbrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule 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simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
496×	`cancel-sign-sub-inv_binary64`
427×	`fma-neg_binary64`
361×	`times-frac_binary64`
350×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	995
1	446	858
2	1459	810
3	6288	792

Stop Event

1×	node limit

Counts

288 → 302

Calls

Call 1

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

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

eval313.0ms (5.1%)

Compiler: Compiled 21375 to 7444 computations (65.2% saved)

prune133.0ms (2.2%)

Pruning

14 alts after pruning (9 fresh and 5 done)

	Pruned	Kept	Total
New	877	6	883
Fresh	1	3	4
Picked	1	0	1
Done	0	5	5
Total	879	14	893

Error

Counts

893 → 14

Alt Table

Click to see full alt table

Status	Error	Program
▶	24.8b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
	36.0b	(/.f64 1 (-.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 1 x))))
	13.7b	(/.f64 1 (*.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (/.f64 1 eps)))
✓	61.7b	(*.f64 2 x)
	26.7b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	38.0b	(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
▶	58.8b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
✓	36.8b	(*.f64 1/2 (/.f64 eps x))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	61.3b	(-.f64 x x)
▶	35.9b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
▶	0.4b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)))
	36.9b	(/.f64 1/2 (/.f64 x eps))
✓	22.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 299 to 184 computations (38.5% saved)

localize29.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)))
	0.0b	(+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2))
	0.0b	(pow.f64 (-.f64 (*.f64 x x) eps) 1/4)
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.0b	(pow.f64 (-.f64 (*.f64 x x) eps) 1/4)
✓	0.0b	(+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)))
✓	0.5b	(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)

Compiler

Compiled 78 to 25 computations (67.9% saved)

series37.0ms (0.6%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)
6.0ms	eps	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)))
5.0ms	eps	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)))
4.0ms	eps	@	inf	(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)
2.0ms	x	@	inf	(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)

rewrite100.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

696×	`fma-def_binary64`
589×	`log-prod_binary64`
310×	`fma-neg_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	333	43
2	4691	40

Stop Event

1×	node limit

Counts

4 → 241

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)))
(+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2))
(pow.f64 (-.f64 (*.f64 x x) eps) 1/4)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 1)))) (#(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 (hypot.f64 x (sqrt.f64 (neg.f64 eps))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 (.f64 x x) eps)) (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (cbrt.f64 (-.f64 (.f64 x x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (.f64 (cbrt.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 (pow.f64 (-.f64 (.f64 x x) eps) 1/8) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/8) (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (pow.f64 (-.f64 (.f64 x x) eps) 1/8)) (pow.f64 (-.f64 (.f64 x x) eps) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.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) (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.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 (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (.f64 eps eps))) (hypot.f64 x (sqrt.f64 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 x 6) (pow.f64 eps 3))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (-.f64 (.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 (neg.f64 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 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (sqrt.f64 (neg.f64 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 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 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 (neg.f64 (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 x (.f64 -1 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 (neg.f64 (cbrt.f64 (-.f64 (.f64 x x) eps))) (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)) (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 1 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (cbrt.f64 (-.f64 (.f64 x x) eps)) (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))) (cbrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 x x) (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 eps (/.f64 1 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (pow.f64 (cbrt.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 2) (cbrt.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 eps) 2) (.f64 (cbrt.f64 eps) (/.f64 1 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 eps) (.f64 (sqrt.f64 eps) (/.f64 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(pow.f64 (-.f64 (.f64 x x) eps) 3/2)) (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (-.f64 (.f64 x x) eps) 3/2)) (+.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 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 (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)) (-.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 x) (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 x)) (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (pow.f64 (-.f64 (.f64 x x) eps) 1/4) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))) 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (hypot.f64 x (sqrt.f64 (neg.f64 eps))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 (.f64 x x) eps)) (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (cbrt.f64 (-.f64 (.f64 x x) eps)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)) (pow.f64 (-.f64 (.f64 x x) eps) 1/4)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/8) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/8) (pow.f64 (-.f64 (.f64 x x) eps) 1/4)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (pow.f64 (-.f64 (.f64 x x) eps) 1/8)) (pow.f64 (-.f64 (.f64 x x) eps) 1/8) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x 4))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) eps) 2))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 x x) eps))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 (neg.f64 eps))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) eps) 2)) 1/2) (pow.f64 (cbrt.f64 (-.f64 (.f64 x x) eps)) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (cbrt.f64 (pow.f64 (-.f64 (.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 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (-.f64 (.f64 x x) eps) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4))) (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (-.f64 (.f64 x x) eps) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)) (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/8) (pow.f64 (-.f64 (.f64 x x) eps) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/4) (pow.f64 (-.f64 (.f64 x x) eps) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) eps) 2)) 1/4) (pow.f64 (cbrt.f64 (-.f64 (.f64 x x) eps)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))) 1/4) (pow.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (.f64 x x) eps) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4)) 1))))))

simplify157.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

790×	`distribute-rgt-in_binary64`
586×	`fma-def_binary64`
349×	`associate-r_binary64`
329×	`associate-+r+_binary64`
325×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	455	5280
1	1546	4673
2	5980	4227

Stop Event

1×	node limit

Counts

337 → 394

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 -1) (sqrt.f64 eps))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(+.f64 (.f64 (+.f64 (.f64 1/16 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (.f64 -3/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (sqrt.f64 -1)))) (pow.f64 x 4)) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps))))
(+.f64 (.f64 (+.f64 (.f64 1/16 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (.f64 -3/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (sqrt.f64 -1)))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 3/64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (sqrt.f64 -1))) (.f64 -7/64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (sqrt.f64 -1)))) (pow.f64 x 6)) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 -1/384 (pow.f64 eps 3)) (+.f64 (.f64 -1/12 (pow.f64 eps 3)) (.f64 1/32 (pow.f64 eps 3)))) (pow.f64 x 5))) (+.f64 (.f64 -1/2 (/.f64 (.f64 eps (+.f64 (.f64 1/32 (pow.f64 eps 2)) (*.f64 -1/8 (pow.f64 eps 2)))) (pow.f64 x 5))) x)))))
(*.f64 -1 x)
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 -1 x))
(+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 -1 x))))
(+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (.f64 eps (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2)))) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1 x) (.f64 -2 (/.f64 (+.f64 (.f64 -1/384 (pow.f64 eps 3)) (+.f64 (.f64 -1/12 (pow.f64 eps 3)) (.f64 1/32 (pow.f64 eps 3)))) (pow.f64 x 5))))))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (pow.f64 x 2)) eps)))
(+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (pow.f64 x 4)) (pow.f64 eps 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (pow.f64 eps 2))) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (pow.f64 x 2)) eps)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (pow.f64 x 2))) (pow.f64 eps 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (pow.f64 x 4)) (pow.f64 eps 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (+.f64 (.f64 1/32 (pow.f64 x 6)) (+.f64 (.f64 -1/384 (pow.f64 x 6)) (.f64 -1/12 (pow.f64 x 6))))) (pow.f64 eps 3))) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (pow.f64 eps 2))) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (pow.f64 x 2)) eps)))))))
(*.f64 (sqrt.f64 eps) (sqrt.f64 -1))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (+.f64 (.f64 1/16 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 4)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (.f64 (sqrt.f64 eps) (sqrt.f64 -1)))))
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x
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(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 eps)) x))
(+.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (+.f64 (.f64 1/16 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 4)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 eps)) x))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 -1) (.f64 (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4))) (pow.f64 x 2))))) (.f64 2 (.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/32 (pow.f64 x 6)) (+.f64 (.f64 1/12 (pow.f64 x 6)) (.f64 1/384 (pow.f64 x 6)))))))) (pow.f64 eps 3))) (+.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (+.f64 (.f64 1/16 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 4)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)) x)))))
(pow.f64 (*.f64 -1 eps) 1/4)
(+.f64 (pow.f64 (.f64 -1 eps) 1/4) (.f64 -1/4 (*.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4) (pow.f64 x 2))))
(+.f64 (pow.f64 (.f64 -1 eps) 1/4) (+.f64 (.f64 -1/4 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4) (pow.f64 x 2))) (.f64 -3/32 (*.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4) (pow.f64 x 4)))))
(+.f64 (pow.f64 (.f64 -1 eps) 1/4) (+.f64 (.f64 -1/4 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4) (pow.f64 x 2))) (+.f64 (.f64 -7/128 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 11)) 1/4) (pow.f64 x 6))) (.f64 -3/32 (*.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4) (pow.f64 x 4))))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (.f64 -1/4 (.f64 eps (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 x) (.f64 -1/4 (*.f64 eps (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 (+.f64 (.f64 -1/384 (pow.f64 eps 3)) (+.f64 (.f64 -1/12 (pow.f64 eps 3)) (.f64 1/32 (pow.f64 eps 3)))) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (sqrt.f64 x) (.f64 -1/4 (*.f64 eps (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 x))
(+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 x)) (.f64 -1/4 (.f64 (.f64 eps (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2)))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 x)) (.f64 -1/4 (.f64 (.f64 eps (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/384 (pow.f64 eps 3)) (+.f64 (.f64 -1/12 (pow.f64 eps 3)) (.f64 1/32 (pow.f64 eps 3))))) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 (.f64 (sqrt.f64 -1) (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2)))) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 x)) (.f64 -1/4 (.f64 (*.f64 eps (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))
(*.f64 (pow.f64 1 1/4) (sqrt.f64 x))
(+.f64 (.f64 -1/4 (.f64 eps (.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (.f64 (pow.f64 1 1/4) (sqrt.f64 x)))
(+.f64 (.f64 -1/4 (.f64 eps (.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 1 1/4) (sqrt.f64 x)) (.f64 -3/32 (.f64 (pow.f64 eps 2) (*.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))
(+.f64 (.f64 -1/4 (.f64 eps (.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 1 1/4) (sqrt.f64 x)) (+.f64 (.f64 -7/128 (.f64 (pow.f64 eps 3) (.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))))) (.f64 -3/32 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps))))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (.f64 -1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) eps)))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (pow.f64 eps 2)) (.f64 -1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) eps))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (.f64 -1/12 (pow.f64 x 6)) (+.f64 (.f64 1/32 (pow.f64 x 6)) (.f64 -1/384 (pow.f64 x 6))))) (pow.f64 eps 3)) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (pow.f64 eps 2)) (.f64 -1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) eps)))))
(pow.f64 (*.f64 -1 eps) 1/4)
(+.f64 (pow.f64 (.f64 -1 eps) 1/4) (.f64 -1/4 (*.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4) (pow.f64 x 2))))
(+.f64 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (+.f64 (pow.f64 (.f64 -1 eps) 1/4) (.f64 -1/4 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4) (pow.f64 x 2)))))
(+.f64 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (+.f64 (pow.f64 (.f64 -1 eps) 1/4) (+.f64 (.f64 -1/4 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4) (pow.f64 x 2))) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 11)) 1/4) (+.f64 (.f64 -1/32 (pow.f64 x 6)) (+.f64 (.f64 1/12 (pow.f64 x 6)) (*.f64 1/384 (pow.f64 x 6)))))))))

Outputs
(*.f64 (sqrt.f64 -1) (sqrt.f64 eps))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(fma.f64 -1/2 (.f64 (sqrt.f64 -1) (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 eps)))) (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))))
(.f64 (sqrt.f64 -1) (+.f64 (.f64 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 eps)))) -1/2) (sqrt.f64 eps)))
(+.f64 (.f64 (+.f64 (.f64 1/16 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (.f64 -3/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (sqrt.f64 -1)))) (pow.f64 x 4)) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps))))
(fma.f64 (fma.f64 1/16 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) (.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) (sqrt.f64 -1))) (pow.f64 x 4) (fma.f64 -1/2 (.f64 (sqrt.f64 -1) (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 eps)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps))))
(fma.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) -1/8) (pow.f64 x 4) (fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (.f64 (sqrt.f64 -1) (.f64 x x))))))
(fma.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) -1/8) (pow.f64 x 4) (.f64 (sqrt.f64 -1) (+.f64 (.f64 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 eps)))) -1/2) (sqrt.f64 eps))))
(+.f64 (.f64 (+.f64 (.f64 1/16 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (.f64 -3/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (sqrt.f64 -1)))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 3/64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (sqrt.f64 -1))) (.f64 -7/64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (sqrt.f64 -1)))) (pow.f64 x 6)) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 -1) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 eps)))) (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))))
(fma.f64 (fma.f64 1/16 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) (.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) (sqrt.f64 -1))) (pow.f64 x 4) (fma.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 5)))) -1/16) (pow.f64 x 6) (fma.f64 -1/2 (.f64 (sqrt.f64 -1) (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 eps)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))))
(fma.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) -1/8) (pow.f64 x 4) (fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (.f64 (sqrt.f64 -1) -1/16)) (pow.f64 x 6) (fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))))))
(fma.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) -1/8) (pow.f64 x 4) (fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (.f64 (sqrt.f64 -1) -1/16)) (pow.f64 x 6) (.f64 (sqrt.f64 -1) (+.f64 (.f64 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 eps)))) -1/2) (sqrt.f64 eps)))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(fma.f64 -1/2 (/.f64 eps x) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 (/.f64 (.f64 (.f64 eps eps) -3/32) (pow.f64 x 3)) (fma.f64 1/16 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -3/32)) (fma.f64 1/16 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) x)))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (+.f64 (.f64 -1/384 (pow.f64 eps 3)) (+.f64 (.f64 -1/12 (pow.f64 eps 3)) (.f64 1/32 (pow.f64 eps 3)))) (pow.f64 x 5))) (+.f64 (.f64 -1/2 (/.f64 (.f64 eps (+.f64 (.f64 1/32 (pow.f64 eps 2)) (*.f64 -1/8 (pow.f64 eps 2)))) (pow.f64 x 5))) x)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 (.f64 eps eps) -3/32) (pow.f64 x 3)) (fma.f64 2 (/.f64 (fma.f64 -1/384 (pow.f64 eps 3) (.f64 (pow.f64 eps 3) -5/96)) (pow.f64 x 5)) (fma.f64 -1/2 (/.f64 eps (/.f64 (pow.f64 x 5) (.f64 (.f64 eps eps) -3/32))) x)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 2 (/.f64 (.f64 eps eps) (/.f64 (pow.f64 x 3) -3/32)) (fma.f64 2 (/.f64 (.f64 (pow.f64 eps 3) -7/128) (pow.f64 x 5)) (fma.f64 -1/2 (/.f64 (*.f64 (pow.f64 eps 3) -3/32) (pow.f64 x 5)) x)))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 -1 x))
(fma.f64 1/2 (/.f64 eps x) (neg.f64 x))
(-.f64 (*.f64 (/.f64 eps x) 1/2) x)
(+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 -1 x))))
(fma.f64 -2 (/.f64 (.f64 (.f64 eps eps) -3/32) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 -1/16 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) (neg.f64 x))))
(fma.f64 (/.f64 (.f64 eps eps) (/.f64 (pow.f64 x 3) -3/32)) -2 (-.f64 (fma.f64 (/.f64 eps x) 1/2 (/.f64 (.f64 (*.f64 -1/16 eps) eps) (pow.f64 x 3))) x))
(-.f64 (fma.f64 (/.f64 (.f64 eps eps) (/.f64 (pow.f64 x 3) -3/32)) -2 (fma.f64 (/.f64 eps x) 1/2 (/.f64 (.f64 (*.f64 -1/16 eps) eps) (pow.f64 x 3)))) x)
(+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (.f64 eps (+.f64 (.f64 1/32 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2)))) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1 x) (.f64 -2 (/.f64 (+.f64 (.f64 -1/384 (pow.f64 eps 3)) (+.f64 (.f64 -1/12 (pow.f64 eps 3)) (.f64 1/32 (pow.f64 eps 3)))) (pow.f64 x 5))))))))
(fma.f64 -2 (/.f64 (.f64 (.f64 eps eps) -3/32) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps (/.f64 (pow.f64 x 5) (.f64 (.f64 eps eps) -3/32))) (fma.f64 1/2 (/.f64 eps x) (fma.f64 -1/16 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 -1 x (.f64 (/.f64 (fma.f64 -1/384 (pow.f64 eps 3) (*.f64 (pow.f64 eps 3) -5/96)) (pow.f64 x 5)) -2))))))
(fma.f64 (/.f64 (.f64 eps eps) (/.f64 (pow.f64 x 3) -3/32)) -2 (fma.f64 (/.f64 (.f64 (pow.f64 eps 3) -3/32) (pow.f64 x 5)) 1/2 (fma.f64 (/.f64 eps x) 1/2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/16 (fma.f64 (/.f64 (*.f64 (pow.f64 eps 3) -7/128) (pow.f64 x 5)) -2 (neg.f64 x))))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(fma.f64 -1/2 (/.f64 eps x) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 -1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) x))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 -1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) x)))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) 2)
(pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4)) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) 2) (pow.f64 x 2)) eps)))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) 2) (.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) 2) (/.f64 eps (.f64 x x)))))
(fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) 2) (/.f64 eps (*.f64 x x))) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) 2))
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x
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x
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(fma.f64 -1/4 (*.f64 eps (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))
(+.f64 (.f64 -1/4 (.f64 eps (.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 1 1/4) (sqrt.f64 x)) (.f64 -3/32 (.f64 (pow.f64 eps 2) (*.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))
(fma.f64 (.f64 (.f64 eps eps) -3/32) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (+.f64 (sqrt.f64 x) (.f64 (.f64 -1/4 eps) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 (.f64 eps (.f64 eps -3/32)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 -1/4 (*.f64 eps (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x)))
(+.f64 (.f64 -1/4 (.f64 eps (.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 1 1/4) (sqrt.f64 x)) (+.f64 (.f64 -7/128 (.f64 (pow.f64 eps 3) (.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 11)))))) (.f64 -3/32 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 1 1/4) (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))))
(fma.f64 (.f64 (.f64 eps eps) -3/32) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 (fma.f64 -1/384 (pow.f64 eps 3) (.f64 (pow.f64 eps 3) -5/96)) (sqrt.f64 (/.f64 1 (pow.f64 x 11))) (+.f64 (sqrt.f64 x) (.f64 (*.f64 -1/4 eps) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 (.f64 eps (.f64 eps -3/32)) (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 (.f64 (pow.f64 eps 3) -7/128) (sqrt.f64 (/.f64 1 (pow.f64 x 11))) (fma.f64 -1/4 (.f64 eps (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 x))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps)))
(*.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (.f64 -1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) eps)))
(+.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) (.f64 -1/4 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) (/.f64 eps (.f64 x x)))))
(fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) eps) (.f64 x x)) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))))
(fma.f64 -1/4 (.f64 (/.f64 (.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4)) eps) (.f64 x x)) (.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4)))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (pow.f64 eps 2)) (.f64 -1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) eps))))
(+.f64 (+.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) (/.f64 (.f64 eps eps) (.f64 (pow.f64 x 4) -3/32)))) (.f64 -1/4 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) (/.f64 eps (.f64 x x)))))
(+.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) (fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) eps) (.f64 x x)) (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) eps) (/.f64 (.f64 (pow.f64 x 4) -3/32) eps))))
(+.f64 (.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4)) (fma.f64 -1/4 (.f64 (/.f64 (.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4)) eps) (.f64 x x)) (/.f64 (.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4)) (.f64 (/.f64 eps (pow.f64 x 4)) (/.f64 eps -3/32)))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (.f64 -1/12 (pow.f64 x 6)) (+.f64 (.f64 1/32 (pow.f64 x 6)) (.f64 -1/384 (pow.f64 x 6))))) (pow.f64 eps 3)) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 1 eps)))))) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (pow.f64 eps 2)) (.f64 -1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 1 eps)))))) (pow.f64 x 2)) eps)))))
(+.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) (+.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) (/.f64 (pow.f64 eps 3) (fma.f64 1/32 (pow.f64 x 6) (.f64 (pow.f64 x 6) -11/128)))) (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) (/.f64 (.f64 eps eps) (.f64 (pow.f64 x 4) -3/32)))) (.f64 -1/4 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (neg.f64 (neg.f64 (log.f64 eps))))) (/.f64 eps (*.f64 x x))))))
(+.f64 (fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) eps) (.f64 x x)) (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) eps) (/.f64 (.f64 (pow.f64 x 4) -3/32) eps))) (+.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 eps))) (/.f64 (pow.f64 eps 3) (*.f64 (pow.f64 x 6) -7/128)))))
(+.f64 (.f64 (/.f64 (.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4)) (.f64 eps eps)) (+.f64 (.f64 (pow.f64 x 4) -3/32) (/.f64 (.f64 (pow.f64 x 6) -7/128) eps))) (fma.f64 -1/4 (.f64 (/.f64 (.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4)) eps) (.f64 x x)) (*.f64 (pow.f64 -1 1/4) (pow.f64 eps 1/4))))
(pow.f64 (*.f64 -1 eps) 1/4)
(pow.f64 (neg.f64 eps) 1/4)
(+.f64 (pow.f64 (.f64 -1 eps) 1/4) (.f64 -1/4 (*.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4) (pow.f64 x 2))))
(+.f64 (pow.f64 (neg.f64 eps) 1/4) (.f64 -1/4 (.f64 (*.f64 x x) (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4))))
(fma.f64 -1/4 (.f64 x (.f64 x (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4))) (pow.f64 (neg.f64 eps) 1/4))
(+.f64 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (+.f64 (pow.f64 (.f64 -1 eps) 1/4) (.f64 -1/4 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4) (pow.f64 x 2)))))
(+.f64 (pow.f64 (neg.f64 eps) 1/4) (fma.f64 -1/4 (.f64 (.f64 x x) (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4)) (.f64 -3/32 (.f64 (pow.f64 x 4) (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4)))))
(fma.f64 (.f64 (pow.f64 x 4) -3/32) (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4) (fma.f64 -1/4 (.f64 x (*.f64 x (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4))) (pow.f64 (neg.f64 eps) 1/4)))
(+.f64 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (.f64 1/32 (pow.f64 x 4)))) (+.f64 (pow.f64 (.f64 -1 eps) 1/4) (+.f64 (.f64 -1/4 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4) (pow.f64 x 2))) (.f64 -1 (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 11)) 1/4) (+.f64 (.f64 -1/32 (pow.f64 x 6)) (+.f64 (.f64 1/12 (pow.f64 x 6)) (*.f64 1/384 (pow.f64 x 6)))))))))
(+.f64 (pow.f64 (neg.f64 eps) 1/4) (fma.f64 -1/4 (.f64 (.f64 x x) (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4)) (fma.f64 -7/128 (.f64 (pow.f64 x 6) (pow.f64 (/.f64 -1 (pow.f64 eps 11)) 1/4)) (.f64 -3/32 (*.f64 (pow.f64 x 4) (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4))))))
(+.f64 (fma.f64 -1/4 (.f64 x (.f64 x (pow.f64 (/.f64 -1 (pow.f64 eps 3)) 1/4))) (pow.f64 (neg.f64 eps) 1/4)) (fma.f64 -3/32 (.f64 (pow.f64 x 4) (pow.f64 (/.f64 -1 (pow.f64 eps 7)) 1/4)) (.f64 (pow.f64 (/.f64 -1 (pow.f64 eps 11)) 1/4) (*.f64 (pow.f64 x 6) -7/128))))

localize3.0ms (0%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.1b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
	0.0b	(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
✓	0.0b	(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
✓	4.1b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))

Compiler

Compiled 29 to 13 computations (55.2% saved)

series7.0ms (0.1%)

Counts

2 → 30

Calls

12 calls:

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

rewrite84.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

490×	`log-prod_binary64`
468×	`fma-def_binary64`
370×	`exp-prod_binary64`
313×	`pow-prod-down_binary64`
266×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	191	19
2	2939	19

Stop Event

1×	node limit

Counts

2 → 168

Calls

Call 1

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

Outputs

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

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
2×	`associate-*r/_binary64`
2×	`associate-*l/_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	192
1	14	192
2	21	192
3	29	192
4	31	192

Stop Event

1×

saturated

Counts

198 → 173

Calls

Call 1

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

Outputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
x
(*.f64 -1/2 (/.f64 eps x))
(*.f64 (/.f64 eps x) -1/2)
(*.f64 eps (/.f64 -1/2 x))
(*.f64 -1/2 (/.f64 eps x))
(*.f64 (/.f64 eps x) -1/2)
(*.f64 eps (/.f64 -1/2 x))
(*.f64 -1/2 (/.f64 eps x))
(*.f64 (/.f64 eps x) -1/2)
(*.f64 eps (/.f64 -1/2 x))
x
x

localize18.0ms (0.3%)

Local error

Found 6 expressions with local error:

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

Compiler

Compiled 67 to 21 computations (68.7% saved)

series7.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite72.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`fma-def_binary64`
658×	`log-prod_binary64`
400×	`fma-neg_binary64`
233×	`log-div_binary64`
233×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	311	25
2	4802	25

Stop Event

1×	node limit

Counts

2 → 127

Calls

Call 1

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

Outputs

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

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

758×	`associate-/l*_binary64`
592×	`associate-+l+_binary64`
566×	`fma-def_binary64`
440×	`associate-/r*_binary64`
328×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	804
1	133	804
2	369	804
3	1214	795
4	5584	795
5	6638	795
6	7100	795

Stop Event

1×	node limit

Counts

175 → 148

Calls

Call 1

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

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

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 48 to 9 computations (81.3% saved)

series15.0ms (0.2%)

Counts

2 → 26

Calls

12 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
2.0ms	eps	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
1.0ms	eps	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
1.0ms	eps	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
1.0ms	x	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))

rewrite58.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

444×	`log-prod_binary64`
417×	`fma-def_binary64`
295×	`fma-neg_binary64`
286×	`pow-prod-down_binary64`
229×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	255	15
2	3949	15

Stop Event

1×	node limit

Counts

2 → 94

Calls

Call 1

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

Outputs

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

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

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-neg_binary64`
561×	`cancel-sign-sub-inv_binary64`
473×	`unswap-sqr_binary64`
411×	`div-sub_binary64`
310×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	513
1	168	450
2	543	406
3	2389	387
4	5981	387

Stop Event

1×	node limit

Counts

120 → 114

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 (sqrt.f64 -1) 4) eps))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 -1) 3))))))
(/.f64 eps x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x))
(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 x 3)) (+.f64 (.f64 -1 (*.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (+.f64 (/.f64 eps x) (+.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3)) (.f64 -1 (*.f64 (/.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 eps 5)))))))
(/.f64 eps x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x))
(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 x 3)) (+.f64 (.f64 -1 (*.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (+.f64 (/.f64 eps x) (+.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3)) (.f64 -1 (*.f64 (sqrt.f64 (pow.f64 eps 5)) (/.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))))
(/.f64 eps x)
(*.f64 (sqrt.f64 eps) (sqrt.f64 -1))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
x
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
x
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
x

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

eval799.0ms (12.9%)

Compiler: Compiled 24163 to 11148 computations (53.9% saved)

prune395.0ms (6.4%)

Pruning

20 alts after pruning (12 fresh and 8 done)

	Pruned	Kept	Total
New	890	8	898
Fresh	0	4	4
Picked	0	1	1
Done	2	7	9
Total	892	20	912

Error

Counts

912 → 20

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.8b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
▶	36.0b	(/.f64 1 (-.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 1 x))))
	60.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
	60.5b	(*.f64 -2 x)
	60.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
▶	13.7b	(/.f64 1 (*.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (/.f64 1 eps)))
	61.3b	0
	26.7b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	38.0b	(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
	36.9b	(/.f64 1/2 (/.f64 x eps))
	60.5b	(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
✓	58.8b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
▶	56.7b	(/.f64 eps x)
✓	36.8b	(*.f64 1/2 (/.f64 eps x))
▶	60.5b	(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	35.9b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
✓	0.4b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)))
▶	36.9b	(*.f64 (/.f64 1/2 x) eps)
✓	22.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 353 to 222 computations (37.1% saved)

localize17.0ms (0.3%)

Local error

Found 8 expressions with local error:

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

Compiler

Compiled 49 to 17 computations (65.3% saved)

series53.0ms (0.9%)

Counts

4 → 52

Calls

24 calls:

Time	Variable		Point	Expression
27.0ms	eps	@	inf	(/.f64 1 (*.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (/.f64 1 eps)))
3.0ms	eps	@	inf	(*.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (/.f64 1 eps))
3.0ms	eps	@	-inf	(*.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (/.f64 1 eps))
3.0ms	eps	@	-inf	(/.f64 1 (*.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (/.f64 1 eps)))
1.0ms	eps	@	inf	(+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))

rewrite93.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

599×	`prod-diff_binary64`
508×	`log-prod_binary64`
264×	`pow2_binary64`
216×	`fma-def_binary64`
194×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	50
1	238	39
2	3305	39

Stop Event

1×	node limit

Counts

4 → 172

Calls

Call 1

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

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

simplify139.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

740×	`associate-/l*_binary64`
604×	`fma-neg_binary64`
589×	`associate-/r*_binary64`
437×	`associate-+l+_binary64`
372×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	2115
1	706	1414
2	2667	1282
3	7743	1281

Stop Event

1×	node limit

Counts

224 → 258

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 eps)))
(+.f64 (/.f64 x eps) (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 eps))))
(+.f64 (/.f64 x eps) (+.f64 (.f64 1/2 (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 eps)))))
(+.f64 (/.f64 x eps) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)))) (+.f64 (.f64 1/2 (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 eps))))))
(*.f64 2 (/.f64 x eps))
(+.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(+.f64 (.f64 -1/8 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 4)) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x))))
(+.f64 (.f64 -1/8 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 4)) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 6)) (pow.f64 x 5))) (+.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
(*.f64 -1/2 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(+.f64 (.f64 1/8 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 4)) (pow.f64 x 3))) (*.f64 -1/2 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 6)) (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 4)) (pow.f64 x 3))) (*.f64 -1/2 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 6)) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2))) 2) (.f64 1/16 (.f64 (pow.f64 eps 4) (pow.f64 (sqrt.f64 -1) 8)))) (.f64 eps (pow.f64 x 7)))) (+.f64 (.f64 1/8 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 4)) (pow.f64 x 3))) (*.f64 -1/2 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
(*.f64 2 (/.f64 x eps))
(*.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2)))))
(+.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 4) eps))) (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (sqrt.f64 -1))))) (pow.f64 x 3)) (+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (*.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3))) (*.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 -1 (/.f64 (+.f64 (.f64 -1/32 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 3))) (.f64 -1/32 (.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 5)))))
(+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/4 (.f64 eps (.f64 (+.f64 (.f64 -1/32 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 3))) (.f64 -1/32 (.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 (sqrt.f64 -1) 2)))) (+.f64 (.f64 1/64 (.f64 (pow.f64 (sqrt.f64 -1) 6) (pow.f64 eps 4))) (.f64 1/128 (.f64 (pow.f64 eps 4) (pow.f64 (sqrt.f64 -1) 6))))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 -1 (/.f64 (+.f64 (.f64 -1/32 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 3))) (.f64 -1/32 (.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 5))))))
(*.f64 -2 (/.f64 x (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 -2 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -2 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 x 3))) (.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3))))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sqrt.f64 -1) 4)) (pow.f64 x 5))) (+.f64 (.f64 -2 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (+.f64 (.f64 1/4 (/.f64 (.f64 (+.f64 (.f64 1/4 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1/8 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)))) (.f64 (pow.f64 (sqrt.f64 -1) 2) eps)) (pow.f64 x 5))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 x 3))) (+.f64 (.f64 -2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2))) 2) (.f64 1/16 (.f64 (pow.f64 eps 4) (pow.f64 (sqrt.f64 -1) 8)))) (.f64 eps (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 5))))) (.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3)))))))))
(*.f64 1/2 (/.f64 eps x))
(*.f64 (sqrt.f64 -1) (sqrt.f64 eps))
(+.f64 x (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(+.f64 x (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps))))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 x (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))))
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/2 (/.f64 (*.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)) (pow.f64 x 3)))))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 6) (pow.f64 eps 3)) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)) (pow.f64 x 3))))))
(.f64 -1/2 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)) (pow.f64 x 3))) (.f64 -1/2 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)) (pow.f64 x 3))) (+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 6) (pow.f64 eps 3)) (pow.f64 x 5))) (.f64 -1/2 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x))))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2))) 2) (.f64 1/16 (.f64 (pow.f64 eps 4) (pow.f64 (sqrt.f64 -1) 8)))) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)) (pow.f64 x 3))) (+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 6) (pow.f64 eps 3)) (pow.f64 x 5))) (.f64 -1/2 (/.f64 (*.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)))))
(*.f64 2 x)
(*.f64 (sqrt.f64 eps) (sqrt.f64 -1))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)))))))
x
(+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)) x)
(+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)) (pow.f64 x 3))) x))
(+.f64 (.f64 1/2 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 6) (pow.f64 eps 3)) (pow.f64 x 5))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)) (pow.f64 x 3))) x)))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 -1/2 (/.f64 (*.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)) (pow.f64 x 3))) (+.f64 (.f64 -1 x) (.f64 -1/2 (/.f64 (*.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)) (pow.f64 x 3))) (+.f64 (.f64 -1 x) (+.f64 (.f64 -1/2 (/.f64 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)) x)) (.f64 -1/16 (/.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 6) (pow.f64 eps 3)) (pow.f64 x 5))))))
x

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

localize10.0ms (0.2%)

Compiler: Compiled 7 to 3 computations (57.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (/.f64 1/2 x) eps)
✓	0.3b	(*.f64 (/.f64 1/2 x) eps)

Compiler

Compiled 13 to 8 computations (38.5% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite47.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

617×	`pow1_binary64`
573×	`add-log-exp_binary64`
573×	`log1p-expm1-u_binary64`
573×	`expm1-log1p-u_binary64`
562×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1560	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

45 → 23

Calls

Call 1

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

Outputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
✓	0.0b	(-.f64 x (*.f64 -1/2 (/.f64 eps x)))

Compiler

Compiled 20 to 9 computations (55% saved)

series8.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	x	@	inf	(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
0.0ms	x	@	0	(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
0.0ms	eps	@	0	(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
0.0ms	x	@	-inf	(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
0.0ms	eps	@	-inf	(-.f64 x (*.f64 -1/2 (/.f64 eps x)))

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

933×	`pow1_binary64`
873×	`add-log-exp_binary64`
872×	`log1p-expm1-u_binary64`
872×	`expm1-log1p-u_binary64`
856×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	163	10
2	2332	10

Stop Event

1×	node limit

Counts

1 → 37

Calls

Call 1

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

Outputs

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

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`+-commutative_binary64`
1×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	168
1	12	168
2	17	168
3	21	168
4	23	168
5	24	168

Stop Event

1×

saturated

Counts

61 → 41

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
x
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
x
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
x
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(*.f64 1/2 (/.f64 eps x))
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(*.f64 1/2 (/.f64 eps x))
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)

Outputs
(*.f64 1/2 (/.f64 eps x))
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
x
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
x
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
x
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(*.f64 1/2 (/.f64 eps x))
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(*.f64 1/2 (/.f64 eps x))
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)
(+.f64 (*.f64 1/2 (/.f64 eps x)) x)
(fma.f64 1/2 (/.f64 eps x) x)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (-.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 1 x))))
	0.0b	(-.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 1 x)))
✓	0.0b	(-.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 1 x)))
✓	0.2b	(/.f64 1 (-.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 1 x))))

Compiler

Compiled 47 to 30 computations (36.2% saved)

series6.0ms (0.1%)

Counts

2 → 30

Calls

12 calls:

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

rewrite101.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`log-prod_binary64`
391×	`fma-def_binary64`
330×	`pow2_binary64`
229×	`pow1/3_binary64`
229×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	276	25
2	3609	25

Stop Event

1×	node limit

Counts

2 → 216

Calls

Call 1

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

Outputs

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

simplify186.0ms (3%)

Algorithm

1×	egg-herbie

Rules

758×	`associate-/l*_binary64`
600×	`associate-+l+_binary64`
561×	`fma-def_binary64`
445×	`associate-/r*_binary64`
330×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	606
1	130	606
2	362	606
3	1209	597
4	5561	597
5	6615	597
6	7077	597

Stop Event

1×	node limit

Counts

246 → 234

Calls

Call 1

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

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

eval225.0ms (3.7%)

Compiler: Compiled 11172 to 6914 computations (38.1% saved)

prune101.0ms (1.6%)

Pruning

26 alts after pruning (14 fresh and 12 done)

	Pruned	Kept	Total
New	549	7	556
Fresh	0	7	7
Picked	1	0	1
Done	0	12	12
Total	550	26	576

Error

Counts

576 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	60.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
	60.5b	(*.f64 -2 x)
	60.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
✓	13.7b	(/.f64 1 (*.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (/.f64 1 eps)))
	60.7b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
	36.0b	(/.f64 1 (+.f64 (*.f64 2 (/.f64 x eps)) (/.f64 -1/2 x)))
	60.7b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 eps x) 1/2) (.f64 (/.f64 eps x) 1/2))) (-.f64 x (*.f64 (/.f64 eps x) 1/2)))
	36.1b	(/.f64 1 (.f64 (+.f64 x (+.f64 x (.f64 (/.f64 -1/2 x) eps))) (/.f64 1 eps)))
✓	0.4b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)))
	61.3b	0
	26.7b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	38.0b	(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
	60.5b	(/.f64 1 (/.f64 -1/2 x))
	36.9b	(/.f64 1/2 (/.f64 x eps))
	60.5b	(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
✓	58.8b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
✓	56.7b	(/.f64 eps x)
✓	36.8b	(*.f64 1/2 (/.f64 eps x))
✓	60.5b	(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	35.9b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
✓	24.8b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
	37.0b	(/.f64 1 (*.f64 x (/.f64 2 eps)))
✓	36.9b	(*.f64 (/.f64 1/2 x) eps)
	61.7b	x
✓	22.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 310 to 195 computations (37.1% saved)

regimes65.0ms (1.1%)

Counts

26 → 1

Calls

Call 1

Inputs
x
0
(/.f64 eps x)
(*.f64 -2 x)
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(/.f64 1 (/.f64 -1/2 x))
(/.f64 1 (*.f64 x (/.f64 2 eps)))
(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
(/.f64 1 (+.f64 (*.f64 2 (/.f64 x eps)) (/.f64 -1/2 x)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
(/.f64 1 (.f64 (+.f64 x (+.f64 x (.f64 (/.f64 -1/2 x) eps))) (/.f64 1 eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 eps x) 1/2) (.f64 (/.f64 eps x) 1/2))) (-.f64 x (*.f64 (/.f64 eps x) 1/2)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 1 (*.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (/.f64 1 eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) 2)))

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

Calls

4 calls:

16.0ms	x
15.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
15.0ms	eps
12.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

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

Compiler

Compiled 286 to 127 computations (55.6% saved)

regimes106.0ms (1.7%)

Counts

23 → 2

Calls

Call 1

Inputs
x
0
(/.f64 eps x)
(*.f64 -2 x)
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(/.f64 1 (/.f64 -1/2 x))
(/.f64 1 (*.f64 x (/.f64 2 eps)))
(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
(/.f64 1 (+.f64 (*.f64 2 (/.f64 x eps)) (/.f64 -1/2 x)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
(/.f64 1 (.f64 (+.f64 x (+.f64 x (.f64 (/.f64 -1/2 x) eps))) (/.f64 1 eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 eps x) 1/2) (.f64 (/.f64 eps x) 1/2))) (-.f64 x (*.f64 (/.f64 eps x) 1/2)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))

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

Calls

4 calls:

40.0ms	eps
21.0ms	x
20.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
19.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Error	Segments	Branch
6.9b	2	`x`
10.5b	4	`eps`
0.8b	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
0.8b	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 234 to 112 computations (52.1% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-6.493829368476583e-154	0.0

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes74.0ms (1.2%)

Counts

21 → 2

Calls

Call 1

Inputs
x
0
(/.f64 eps x)
(*.f64 -2 x)
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(/.f64 1 (/.f64 -1/2 x))
(/.f64 1 (*.f64 x (/.f64 2 eps)))
(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
(/.f64 1 (+.f64 (*.f64 2 (/.f64 x eps)) (/.f64 -1/2 x)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
(/.f64 1 (.f64 (+.f64 x (+.f64 x (.f64 (/.f64 -1/2 x) eps))) (/.f64 1 eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 eps x) 1/2) (.f64 (/.f64 eps x) 1/2))) (-.f64 x (*.f64 (/.f64 eps x) 1/2)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))

Outputs
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))

Calls

2 calls:

39.0ms	eps
29.0ms	x

Results

Error	Segments	Branch
7.8b	2	`x`
12.3b	4	`eps`

Compiler

Compiled 191 to 95 computations (50.3% saved)

bsearch88.0ms (1.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
88.0ms	2.3338073781067357e-98	1.1167570773510935e-97

Compiler

Compiled 195 to 118 computations (39.5% saved)

regimes29.0ms (0.5%)

Counts

20 → 1

Calls

Call 1

Inputs
x
0
(/.f64 eps x)
(*.f64 -2 x)
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(/.f64 1 (/.f64 -1/2 x))
(/.f64 1 (*.f64 x (/.f64 2 eps)))
(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
(/.f64 1 (+.f64 (*.f64 2 (/.f64 x eps)) (/.f64 -1/2 x)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
(/.f64 1 (.f64 (+.f64 x (+.f64 x (.f64 (/.f64 -1/2 x) eps))) (/.f64 1 eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 eps x) 1/2) (.f64 (/.f64 eps x) 1/2))) (-.f64 x (*.f64 (/.f64 eps x) 1/2)))

Outputs
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))

Calls

2 calls:

11.0ms	x
10.0ms	eps

Results

Error	Segments	Branch
35.9b	1	`x`
35.9b	1	`eps`

Compiler

Compiled 186 to 92 computations (50.5% saved)

regimes26.0ms (0.4%)

Counts

18 → 1

Calls

Call 1

Inputs
x
0
(/.f64 eps x)
(*.f64 -2 x)
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(/.f64 1 (/.f64 -1/2 x))
(/.f64 1 (*.f64 x (/.f64 2 eps)))
(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
(/.f64 1 (+.f64 (*.f64 2 (/.f64 x eps)) (/.f64 -1/2 x)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x)))))
(/.f64 1 (.f64 (+.f64 x (+.f64 x (.f64 (/.f64 -1/2 x) eps))) (/.f64 1 eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))

Outputs
(/.f64 1 (+.f64 (*.f64 2 (/.f64 x eps)) (/.f64 -1/2 x)))

Calls

2 calls:

11.0ms	x
10.0ms	eps

Results

Error	Segments	Branch
36.0b	1	`x`
36.0b	1	`eps`

Compiler

Compiled 144 to 77 computations (46.5% saved)

regimes19.0ms (0.3%)

Counts

13 → 1

Calls

Call 1

Inputs
x
0
(/.f64 eps x)
(*.f64 -2 x)
(*.f64 (/.f64 1/2 x) eps)
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(/.f64 1 (/.f64 -1/2 x))
(/.f64 1 (*.f64 x (/.f64 2 eps)))
(-.f64 x (*.f64 -1/2 (/.f64 eps x)))
(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)

Outputs
(*.f64 1/2 (/.f64 eps x))

Calls

2 calls:

9.0ms	x
7.0ms	eps

Results

Error	Segments	Branch
36.8b	1	`x`
36.8b	1	`eps`

Compiler

Compiled 75 to 44 computations (41.3% saved)

regimes11.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

Inputs
x
0
(/.f64 eps x)
(*.f64 -2 x)
(*.f64 (/.f64 1/2 x) eps)

Outputs
(*.f64 (/.f64 1/2 x) eps)

Calls

2 calls:

5.0ms	eps
4.0ms	x

Results

Error	Segments	Branch
36.9b	1	`x`
36.9b	1	`eps`

Compiler

Compiled 21 to 13 computations (38.1% saved)

regimes12.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
x
0
(/.f64 eps x)
(*.f64 -2 x)

Outputs
(/.f64 eps x)

Calls

2 calls:

6.0ms	x
4.0ms	eps

Results

Error	Segments	Branch
56.7b	1	`x`
56.7b	1	`eps`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes7.0ms (0.1%)

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

Counts

2 → 1

Calls

Call 1

Inputs
x
0

Outputs
0

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

Error	Segments	Branch
61.3b	1	`x`
61.3b	1	`eps`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	190
1	62	190
2	77	190
3	86	190
4	90	190

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))))
(if (<=.f64 x 925947145615270272/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 1 (+.f64 (*.f64 2 (/.f64 x eps)) (/.f64 -1/2 x)))
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(/.f64 eps x)
0
x

Outputs
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 x (*.f64 -1/2 (/.f64 eps x))))))
(if (<=.f64 x 925947145615270272/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))))
(if (<=.f64 x 7233962075119299/307828173409331868845930000782371982852185463050511302093346042220669701339821957901673955116288403443801781174272) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 x (*.f64 -1/2 (/.f64 eps x))))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 x (*.f64 -1/2 (/.f64 eps x)))))
(/.f64 1 (+.f64 (*.f64 2 (/.f64 x eps)) (/.f64 -1/2 x)))
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 eps x) 1/2)
(*.f64 (/.f64 1/2 x) eps)
(*.f64 eps (/.f64 1/2 x))
(/.f64 eps x)
0
x

end70.0ms (1.1%)

Stop Event

1×

fuel

Compiler

Compiled 280 to 131 computations (53.2% 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

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