Details

analyze20.0ms (0.3%)

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)

sample1.9s (26.6%)

Results

1.1s	5938×	body	256	valid
463.0ms	1125×	body	1024	valid
320.0ms	1160×	body	512	valid
22.0ms	173×	body	256	invalid
13.0ms	33×	body	2048	valid

preprocess43.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

144×	`fma-neg_binary64`
96×	`fma-def_binary64`
54×	`cancel-sign-sub-inv_binary64`
44×	`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	353	24
7	506	24
8	608	24
9	660	24
10	670	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)

simplify27.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	361	12
9	439	12
10	495	12
11	499	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

22.3b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	22.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	4.7b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 26 to 6 computations (76.9% saved)

series103.0ms (1.5%)

Counts

3 → 56

Calls

18 calls:

Time	Variable		Point	Expression
93.0ms	x	@	0	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms	x	@	inf	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms	eps	@	inf	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms	eps	@	0	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms	eps	@	inf	(sqrt.f64 (-.f64 (*.f64 x x) eps))

rewrite82.0ms (1.2%)

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	2429	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 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(.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 expm1.f64 (log1p.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.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 +.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 expm1.f64 (log1p.f64 (-.f64 (.f64 x x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (.f64 x x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (.f64 x x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 -.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 expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(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 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 expm1.f64 (log1p.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.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 +.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 expm1.f64 (log1p.f64 (-.f64 (*.f64 x x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (*.f64 x x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (*.f64 x x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 -.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 expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(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 exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))))

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

704×	`unswap-sqr_binary64`
524×	`fma-def_binary64`
425×	`associate-/l/_binary64`
381×	`associate-/r/_binary64`
310×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	968
1	331	939
2	999	925
3	3977	911
4	6396	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 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)))
(+.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)
(fma.f64 (sqrt.f64 -1) (neg.f64 (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))
(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)))
(fma.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (/.f64 (.f64 x x) (sqrt.f64 -1))) (fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 -1)) x))
(-.f64 x (fma.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x (/.f64 (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 x (/.f64 (sqrt.f64 -1) x))) x) (fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) (.f64 1/8 (*.f64 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(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 1/8 eps) eps) (pow.f64 x 3)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 1/8 (/.f64 (/.f64 (pow.f64 x 3) eps) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 eps x) (/.f64 1/8 (/.f64 (/.f64 (pow.f64 x 3) eps) eps))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 (.f64 eps eps) -1/8) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 (fma.f64 1/16 (pow.f64 eps 4) (.f64 (pow.f64 eps 4) 1/64)) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (+.f64 (/.f64 eps x) (/.f64 (*.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7))) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 1/8 (/.f64 (/.f64 (pow.f64 x 3) eps) eps))))
(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)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 (pow.f64 eps 4) 5/128) (pow.f64 x 7)))))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(fma.f64 -1/2 (/.f64 eps x) (*.f64 x 2))
(fma.f64 x 2 (*.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (/.f64 eps (/.f64 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) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (/.f64 (.f64 eps (.f64 eps -1/8)) (pow.f64 x 3))))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (/.f64 eps (/.f64 (pow.f64 x 3) (*.f64 eps -1/8)))))
(fma.f64 x 2 (.f64 (/.f64 eps x) (+.f64 -1/2 (/.f64 (.f64 eps -1/8) (*.f64 x x)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (*.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16))))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (/.f64 eps (/.f64 (pow.f64 x 3) (*.f64 eps -1/8))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (fma.f64 x 2 (/.f64 eps (/.f64 (pow.f64 x 3) (*.f64 eps -1/8))))))
(*.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 1/2 (/.f64 eps x) (/.f64 (.f64 (.f64 1/8 eps) eps) (pow.f64 x 3)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 1/8 (/.f64 (/.f64 (pow.f64 x 3) eps) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 eps x) (/.f64 1/8 (/.f64 (/.f64 (pow.f64 x 3) eps) eps))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 4) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 x 6))))) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (/.f64 (pow.f64 eps 4) (/.f64 x (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (/.f64 1/16 (pow.f64 x 6))))) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (.f64 (/.f64 (pow.f64 eps 4) x) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (/.f64 1/16 (pow.f64 x 6)))) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (.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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 (.f64 eps 1/8) (pow.f64 x 3)) eps)) (.f64 (/.f64 1/2 x) (+.f64 (.f64 (pow.f64 eps 4) (+.f64 (/.f64 1/64 (pow.f64 x 6)) (/.f64 1/16 (pow.f64 x 6)))) eps)))
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.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 x (/.f64 (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 (pow.f64 eps 3))) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (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 (pow.f64 eps 3))) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (fma.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x (/.f64 (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 (.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 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (*.f64 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) 1/16)))))
(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 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 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))) (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x (/.f64 (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))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) -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 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) -1/8 x)))
(*.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 1/2 (/.f64 eps x) (/.f64 (.f64 (.f64 1/8 eps) eps) (pow.f64 x 3))) x)
(-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 1/8 (/.f64 (/.f64 (pow.f64 x 3) eps) eps))) x)
(-.f64 (.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.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))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 eps x) (/.f64 1/8 (/.f64 (/.f64 (pow.f64 x 3) eps) eps)))) x)
(-.f64 (.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x)))) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 x))
(fma.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (.f64 x x))) (-.f64 (*.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3)) 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))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) -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 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 x)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) -1/8 x)))

eval48.0ms (0.7%)

Compiler: Compiled 2547 to 1184 computations (53.5% saved)

prune29.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	143	8	151
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	143	9	152

Error

0.0b

Counts

152 → 9

Alt Table

Click to see full alt table

Status	Error	Program
	25.6b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
▶	38.9b	(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
	59.0b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
▶	37.6b	(*.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))))
▶	61.7b	(*.f64 x 2)
✓	22.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	0.4b	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 1 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
	61.3b	(-.f64 x x)

Compiler

Compiled 194 to 114 computations (41.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.1%)

Counts

2 → 32

Calls

12 calls:

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

rewrite109.0ms (1.5%)

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	4073	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 expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(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 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 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)))))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	962
1	400	841
2	1374	803
3	6258	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 -1 (/.f64 (sqrt.f64 (/.f64 1 eps)) (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 -1 (/.f64 (sqrt.f64 (/.f64 1 eps)) (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 -1 (/.f64 (sqrt.f64 (/.f64 1 eps)) (sqrt.f64 -1))) -1/2) (*.f64 x x))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (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) (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 eps 1/2) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.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 (.f64 1/16 (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 x 5) (pow.f64 eps 3)))))
(fma.f64 1/2 (/.f64 eps x) (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 1/8 (/.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 (*.f64 1/16 (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 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.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 (*.f64 eps -1/2) x))
(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 eps (/.f64 (pow.f64 x 3) (*.f64 eps -1/8)))))
(+.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 eps 1/2) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.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 (.f64 1/16 (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 x 5) (pow.f64 eps 3)))))
(fma.f64 1/2 (/.f64 eps x) (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 1/8 (/.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 (*.f64 1/16 (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 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.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 (sqrt.f64 (/.f64 1 eps)) (.f64 1/2 (.f64 (/.f64 x (sqrt.f64 -1)) x)) (fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x))
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x (sqrt.f64 -1)) x)) 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 (sqrt.f64 (/.f64 1 eps)) (.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 -1)) x)) (fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)))
(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 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (*.f64 (/.f64 x (sqrt.f64 -1)) x)) 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 (*.f64 eps -1/2) x))
(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 eps (/.f64 (pow.f64 x 3) (*.f64 eps -1/8)))))
(+.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 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (fma.f64 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (/.f64 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 eps 1/2) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.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 (.f64 1/16 (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 x 5) (pow.f64 eps 3)))))
(fma.f64 1/2 (/.f64 eps x) (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 1/8 (/.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 (*.f64 1/16 (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 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.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 (*.f64 eps -1/2) x))
(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 eps (/.f64 (pow.f64 x 3) (*.f64 eps -1/8)))))
(+.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 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (fma.f64 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (/.f64 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))

localize3.0ms (0%)

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

localize6.0ms (0.1%)

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

localize18.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
✓	13.3b	(/.f64 (.f64 eps 1/8) (.f64 x x))

Compiler

Compiled 44 to 22 computations (50% saved)

series10.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite261.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

688×	`log-prod_binary64`
393×	`prod-diff_binary64`
285×	`log-div_binary64`
231×	`pow1/3_binary64`
224×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	253	27
2	3851	27

Stop Event

1×	node limit

Counts

2 → 135

Calls

Call 1

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

Outputs

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

simplify114.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1175×	`associate-/l/_binary64`
690×	`associate-/r/_binary64`
591×	`unswap-sqr_binary64`
407×	`sqr-pow_binary64`
313×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	660
1	43	660
2	101	660
3	325	642
4	1987	606
5	2721	606
6	3667	606
7	3854	606
8	4083	606
9	4357	606
10	7270	606

Stop Event

1×	node limit

Counts

183 → 143

Calls

Call 1

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

localize38.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 73 to 14 computations (80.8% saved)

series9.0ms (0.1%)

Counts

2 → 32

Calls

12 calls:

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

rewrite119.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

789×	`fma-def_binary64`
561×	`log-prod_binary64`
315×	`fma-neg_binary64`
225×	`egg-rr`
202×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	296	27
2	4380	25

Stop Event

1×	node limit

Counts

2 → 253

Calls

Call 1

Inputs
(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 1 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 1 (+.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 (-.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 (sqrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (sqrt.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 (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))))) 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simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

524×	`associate-l_binary64`
482×	`associate-r_binary64`
449×	`associate-+l+_binary64`
439×	`times-frac_binary64`
370×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	171	1152
1	543	949
2	1958	881
3	7866	871

Stop Event

1×	node limit

Counts

285 → 301

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

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

eval275.0ms (3.9%)

Compiler: Compiled 21941 to 7251 computations (67% saved)

prune186.0ms (2.6%)

Pruning

15 alts after pruning (9 fresh and 6 done)

	Pruned	Kept	Total
New	871	6	877
Fresh	0	3	3
Picked	0	1	1
Done	0	5	5
Total	871	15	886

Error

Counts

886 → 15

Alt Table

Click to see full alt table

Status	Error	Program
	25.6b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	38.9b	(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
	59.0b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
✓	37.6b	(*.f64 1/2 (/.f64 eps x))
▶	61.3b	(-.f64 x x)
	41.6b	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x))))
▶	37.6b	(/.f64 1/2 (/.f64 x eps))
	37.7b	(*.f64 eps (/.f64 1/2 x))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	61.7b	(*.f64 x 2)
▶	36.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
▶	23.8b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
▶	0.8b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3))))
✓	22.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.4b	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 1 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))

Compiler

Compiled 325 to 191 computations (41.2% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3))))
✓	0.6b	(cbrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.7b	(pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3)

Compiler

Compiled 84 to 22 computations (73.8% saved)

series23.0ms (0.3%)

Counts

3 → 32

Calls

18 calls:

Time	Variable		Point	Expression
7.0ms	x	@	0	(pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3)
4.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3)
3.0ms	eps	@	0	(pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3)
1.0ms	eps	@	inf	(pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3)

rewrite102.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

774×	`fma-def_binary64`
570×	`log-prod_binary64`
332×	`fma-neg_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	34
1	328	28
2	4549	27

Stop Event

1×	node limit

Counts

3 → 295

Calls

Call 1

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

Outputs

((#(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) (+.f64 (neg.f64 eps) eps))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 eps) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (-.f64 (*.f64 x x) eps))) (cbrt.f64 (exp.f64 (-.f64 (*.f64 x x) eps))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (*.f64 x x) eps)))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x x) eps)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 (*.f64 x x) eps))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 6) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x 4))) (/.f64 (pow.f64 eps 3) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.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 (-.f64 (*.f64 x x) eps) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))) (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 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simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

939×	`times-frac_binary64`
488×	`associate-/l*_binary64`
448×	`associate-/r*_binary64`
354×	`distribute-lft-in_binary64`
354×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	1632
1	879	1407
2	3120	1347

Stop Event

1×	node limit

Counts

327 → 350

Calls

Call 1

Inputs
(.f64 -1 (.f64 eps (pow.f64 1 1/3)))
(+.f64 (.f64 (+.f64 (.f64 1/3 (pow.f64 1 1/3)) (.f64 2/3 (pow.f64 1 1/3))) (pow.f64 x 2)) (.f64 -1 (*.f64 eps (pow.f64 1 1/3))))
(+.f64 (.f64 (+.f64 (.f64 -2/9 (.f64 (/.f64 1 eps) (pow.f64 1 1/3))) (+.f64 (.f64 (pow.f64 (.f64 eps 1) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))))))) (.f64 1/9 (.f64 (/.f64 1 eps) (pow.f64 1 1/3))))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 1/3 (pow.f64 1 1/3)) (.f64 2/3 (pow.f64 1 1/3))) (pow.f64 x 2)) (.f64 -1 (*.f64 eps (pow.f64 1 1/3)))))
(+.f64 (.f64 (+.f64 (.f64 -2/27 (.f64 (/.f64 1 (.f64 (pow.f64 eps 2) (pow.f64 (cbrt.f64 -1) 6))) (pow.f64 1 1/3))) (+.f64 (.f64 5/81 (.f64 (/.f64 1 (.f64 (pow.f64 eps 2) (pow.f64 (cbrt.f64 -1) 6))) (pow.f64 1 1/3))) (+.f64 (.f64 (pow.f64 (.f64 eps 1) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 10/81 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 7)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 7)))) (.f64 -2/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 7)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 7))))))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 2)) 1/3) (/.f64 (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))))) (pow.f64 (cbrt.f64 -1) 2))))))) (pow.f64 x 6)) (+.f64 (.f64 (+.f64 (.f64 -2/9 (.f64 (/.f64 1 eps) (pow.f64 1 1/3))) (+.f64 (.f64 (pow.f64 (.f64 eps 1) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))))))) (.f64 1/9 (.f64 (/.f64 1 eps) (pow.f64 1 1/3))))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 1/3 (pow.f64 1 1/3)) (.f64 2/3 (pow.f64 1 1/3))) (pow.f64 x 2)) (.f64 -1 (*.f64 eps (pow.f64 1 1/3))))))
(*.f64 (pow.f64 1 1/3) (pow.f64 x 2))
(+.f64 (.f64 eps (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -1/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)))) (.f64 (pow.f64 1 1/3) (pow.f64 x 2)))
(+.f64 (.f64 eps (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -1/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)))) (+.f64 (.f64 (pow.f64 1 1/3) (pow.f64 x 2)) (.f64 (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (+.f64 (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)))) (+.f64 (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)) (*.f64 2/9 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)))) (pow.f64 eps 2))))
(+.f64 (.f64 eps (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -1/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)))) (+.f64 (.f64 (pow.f64 1 1/3) (pow.f64 x 2)) (+.f64 (.f64 (pow.f64 eps 3) (+.f64 (.f64 -1/3 (.f64 (+.f64 (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9))) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/9))) (+.f64 (.f64 2/27 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3))) (+.f64 (.f64 -1/3 (.f64 (+.f64 (.f64 -1/27 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)) (.f64 2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)))) (pow.f64 1 1/3))) (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (+.f64 (.f64 2/27 (.f64 (pow.f64 1 1/9) (/.f64 1 (pow.f64 x 2)))) (.f64 -2/3 (.f64 (+.f64 (.f64 -1/27 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)) (.f64 2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)))) (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3))))))))) (.f64 (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (+.f64 (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)))) (+.f64 (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)) (.f64 2/9 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)))) (pow.f64 eps 2)))))
(.f64 (pow.f64 (.f64 eps 1) 1/3) (cbrt.f64 -1))
(+.f64 (.f64 (pow.f64 (.f64 eps 1) 1/3) (cbrt.f64 -1)) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 2)) 1/3) (/.f64 (pow.f64 x 2) (pow.f64 (cbrt.f64 -1) 2)))))
(+.f64 (.f64 (pow.f64 (.f64 eps 1) 1/3) (cbrt.f64 -1)) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 5)) 1/3) (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 -1) 5)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 2)) 1/3) (/.f64 (pow.f64 x 2) (pow.f64 (cbrt.f64 -1) 2))))))
(+.f64 (.f64 (pow.f64 (.f64 eps 1) 1/3) (cbrt.f64 -1)) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 5)) 1/3) (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 -1) 5)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 2)) 1/3) (/.f64 (pow.f64 x 2) (pow.f64 (cbrt.f64 -1) 2)))) (.f64 5/81 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 8)) 1/3) (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 -1) 8)))))))
(pow.f64 (pow.f64 x 2) 1/3)
(+.f64 (pow.f64 (pow.f64 x 2) 1/3) (.f64 -1/3 (.f64 eps (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/9))))
(+.f64 (.f64 -1/9 (.f64 (pow.f64 eps 2) (pow.f64 (/.f64 1 (pow.f64 x 14)) 1/9))) (+.f64 (pow.f64 (pow.f64 x 2) 1/3) (.f64 -1/3 (.f64 eps (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/9)))))
(+.f64 (.f64 -1/9 (.f64 (pow.f64 eps 2) (pow.f64 (/.f64 1 (pow.f64 x 14)) 1/9))) (+.f64 (.f64 -1/3 (.f64 (.f64 (+.f64 (.f64 -1/27 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)) (.f64 2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)))) (pow.f64 eps 3)) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3))) (+.f64 (pow.f64 (pow.f64 x 2) 1/3) (.f64 -1/3 (.f64 eps (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/9))))))
(*.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))))))

Outputs
(.f64 -1 (.f64 eps (pow.f64 1 1/3)))
(neg.f64 eps)
(+.f64 (.f64 (+.f64 (.f64 1/3 (pow.f64 1 1/3)) (.f64 2/3 (pow.f64 1 1/3))) (pow.f64 x 2)) (.f64 -1 (*.f64 eps (pow.f64 1 1/3))))
(+.f64 (neg.f64 eps) (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (.f64 (+.f64 (.f64 -2/9 (.f64 (/.f64 1 eps) (pow.f64 1 1/3))) (+.f64 (.f64 (pow.f64 (.f64 eps 1) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))))))) (.f64 1/9 (.f64 (/.f64 1 eps) (pow.f64 1 1/3))))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 1/3 (pow.f64 1 1/3)) (.f64 2/3 (pow.f64 1 1/3))) (pow.f64 x 2)) (.f64 -1 (*.f64 eps (pow.f64 1 1/3)))))
(fma.f64 (fma.f64 -2/9 (/.f64 1 eps) (fma.f64 (cbrt.f64 eps) (.f64 (cbrt.f64 -1) (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 4))) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))) -1/9)) (.f64 (/.f64 1 eps) 1/9))) (pow.f64 x 4) (+.f64 (neg.f64 eps) (*.f64 x x)))
(-.f64 (fma.f64 (+.f64 (/.f64 -2/9 eps) (fma.f64 (.f64 (cbrt.f64 eps) (cbrt.f64 -1)) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 4))) -1/9) (.f64 -1 (cbrt.f64 -1))) (/.f64 1/9 eps))) (pow.f64 x 4) (.f64 x x)) eps)
(-.f64 (fma.f64 (+.f64 (.f64 (cbrt.f64 -1) (.f64 (.f64 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 4))) (cbrt.f64 -1)) 1/9) (cbrt.f64 eps))) (.f64 (/.f64 1 eps) -1/9)) (pow.f64 x 4) (*.f64 x x)) eps)
(+.f64 (.f64 (+.f64 (.f64 -2/27 (.f64 (/.f64 1 (.f64 (pow.f64 eps 2) (pow.f64 (cbrt.f64 -1) 6))) (pow.f64 1 1/3))) (+.f64 (.f64 5/81 (.f64 (/.f64 1 (.f64 (pow.f64 eps 2) (pow.f64 (cbrt.f64 -1) 6))) (pow.f64 1 1/3))) (+.f64 (.f64 (pow.f64 (.f64 eps 1) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 10/81 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 7)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 7)))) (.f64 -2/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 7)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 7))))))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 2)) 1/3) (/.f64 (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))))) (pow.f64 (cbrt.f64 -1) 2))))))) (pow.f64 x 6)) (+.f64 (.f64 (+.f64 (.f64 -2/9 (.f64 (/.f64 1 eps) (pow.f64 1 1/3))) (+.f64 (.f64 (pow.f64 (.f64 eps 1) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 eps 4)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))))))) (.f64 1/9 (.f64 (/.f64 1 eps) (pow.f64 1 1/3))))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 1/3 (pow.f64 1 1/3)) (.f64 2/3 (pow.f64 1 1/3))) (pow.f64 x 2)) (.f64 -1 (*.f64 eps (pow.f64 1 1/3))))))
(fma.f64 (fma.f64 -2/27 (/.f64 1 (.f64 (.f64 eps eps) (pow.f64 (cbrt.f64 -1) 6))) (fma.f64 5/81 (/.f64 1 (.f64 (.f64 eps eps) (pow.f64 (cbrt.f64 -1) 6))) (fma.f64 (cbrt.f64 eps) (.f64 (cbrt.f64 -1) (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 7))) (/.f64 1 (pow.f64 (cbrt.f64 -1) 7))) 4/81)) (.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 eps eps))) (/.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 4))) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))) -1/9) (pow.f64 (cbrt.f64 -1) 2))))))) (pow.f64 x 6) (fma.f64 (fma.f64 -2/9 (/.f64 1 eps) (fma.f64 (cbrt.f64 eps) (.f64 (cbrt.f64 -1) (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 4))) (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))) -1/9)) (.f64 (/.f64 1 eps) 1/9))) (pow.f64 x 4) (+.f64 (neg.f64 eps) (*.f64 x x))))
(fma.f64 (+.f64 (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 eps eps))) (/.f64 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 4))) (.f64 -1 (cbrt.f64 -1))) (/.f64 (pow.f64 (cbrt.f64 -1) 2) -1/9))) (.f64 (cbrt.f64 eps) (.f64 (cbrt.f64 -1) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 7))) 4/81) (pow.f64 (cbrt.f64 -1) 7))))) (.f64 (/.f64 1 (.f64 eps eps)) -1/81)) (pow.f64 x 6) (-.f64 (fma.f64 (+.f64 (/.f64 -2/9 eps) (fma.f64 (.f64 (cbrt.f64 eps) (cbrt.f64 -1)) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 4))) -1/9) (.f64 -1 (cbrt.f64 -1))) (/.f64 1/9 eps))) (pow.f64 x 4) (.f64 x x)) eps))
(fma.f64 (+.f64 (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 eps eps))) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 4))) -1/9) 1)) (.f64 (cbrt.f64 eps) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 7))) (.f64 4/81 (cbrt.f64 -1))) (pow.f64 (cbrt.f64 -1) 7)))) (/.f64 -1/81 (.f64 eps eps))) (pow.f64 x 6) (-.f64 (fma.f64 (+.f64 (.f64 (cbrt.f64 -1) (.f64 (.f64 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 eps 4))) (cbrt.f64 -1)) 1/9) (cbrt.f64 eps))) (.f64 (/.f64 1 eps) -1/9)) (pow.f64 x 4) (.f64 x x)) eps))
(*.f64 (pow.f64 1 1/3) (pow.f64 x 2))
(*.f64 x x)
(+.f64 (.f64 eps (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -1/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)))) (.f64 (pow.f64 1 1/3) (pow.f64 x 2)))
(fma.f64 eps (.f64 (.f64 (pow.f64 (pow.f64 x 8) 1/18) (pow.f64 (pow.f64 x 8) 1/18)) -1) (*.f64 x x))
(fma.f64 x x (.f64 (.f64 (pow.f64 (pow.f64 x 8) 1/18) (pow.f64 (pow.f64 x 8) 1/18)) (neg.f64 eps)))
(fma.f64 eps (neg.f64 (.f64 (pow.f64 (pow.f64 x 8) 1/18) (pow.f64 (pow.f64 x 8) 1/18))) (.f64 x x))
(+.f64 (.f64 eps (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -1/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)))) (+.f64 (.f64 (pow.f64 1 1/3) (pow.f64 x 2)) (.f64 (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (+.f64 (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)))) (+.f64 (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)) (*.f64 2/9 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)))) (pow.f64 eps 2))))
(+.f64 (fma.f64 eps (.f64 (.f64 (pow.f64 (pow.f64 x 8) 1/18) (pow.f64 (pow.f64 x 8) 1/18)) -1) (.f64 x x)) (.f64 (.f64 eps eps) (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18)) -1/9) (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) 1/9))))
(fma.f64 eps (.f64 -1 (.f64 (pow.f64 (pow.f64 x 8) 1/18) (pow.f64 (pow.f64 x 8) 1/18))) (fma.f64 x x (.f64 (.f64 eps eps) (fma.f64 (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) 1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18)) (.f64 -1/9 (cbrt.f64 (*.f64 x x))))))))
(fma.f64 eps (neg.f64 (.f64 (pow.f64 (pow.f64 x 8) 1/18) (pow.f64 (pow.f64 x 8) 1/18))) (fma.f64 (.f64 eps eps) (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) -1/9)) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)))) (.f64 x x)))
(+.f64 (.f64 eps (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -1/3 (pow.f64 (.f64 1 (pow.f64 x 8)) 1/9)))) (+.f64 (.f64 (pow.f64 1 1/3) (pow.f64 x 2)) (+.f64 (.f64 (pow.f64 eps 3) (+.f64 (.f64 -1/3 (.f64 (+.f64 (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9))) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/9))) (+.f64 (.f64 2/27 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3))) (+.f64 (.f64 -1/3 (.f64 (+.f64 (.f64 -1/27 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)) (.f64 2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)))) (pow.f64 1 1/3))) (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (+.f64 (.f64 2/27 (.f64 (pow.f64 1 1/9) (/.f64 1 (pow.f64 x 2)))) (.f64 -2/3 (.f64 (+.f64 (.f64 -1/27 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)) (.f64 2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3)))) (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3))))))))) (.f64 (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (+.f64 (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)) (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/9)))) (+.f64 (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)) (.f64 2/9 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)))) (pow.f64 eps 2)))))
(+.f64 (fma.f64 eps (.f64 (.f64 (pow.f64 (pow.f64 x 8) 1/18) (pow.f64 (pow.f64 x 8) 1/18)) -1) (.f64 x x)) (fma.f64 (pow.f64 eps 3) (fma.f64 -1/3 (.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18)) -1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/18))) (+.f64 (.f64 2/27 (cbrt.f64 (/.f64 1 (pow.f64 x 4)))) (fma.f64 -1/3 (.f64 1 (fma.f64 -1/27 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (.f64 2/9 (cbrt.f64 (/.f64 1 (pow.f64 x 4)))))) (.f64 (cbrt.f64 (.f64 x x)) (fma.f64 2/27 (/.f64 1 (.f64 x x)) (.f64 -2/3 (.f64 (fma.f64 -1/27 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (.f64 2/9 (cbrt.f64 (/.f64 1 (pow.f64 x 4))))) (cbrt.f64 (/.f64 1 (.f64 x x)))))))))) (.f64 (.f64 eps eps) (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18)) -1/9) (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) 1/9)))))
(fma.f64 eps (.f64 -1 (.f64 (pow.f64 (pow.f64 x 8) 1/18) (pow.f64 (pow.f64 x 8) 1/18))) (fma.f64 x x (fma.f64 (.f64 eps eps) (fma.f64 (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) 1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18)) (.f64 -1/9 (cbrt.f64 (.f64 x x))))) (.f64 (pow.f64 eps 3) (fma.f64 -1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18)) (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/18)))) (fma.f64 2/27 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (fma.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) 5/27) (.f64 (cbrt.f64 (.f64 x x)) (fma.f64 -2/3 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) 5/27) (cbrt.f64 (/.f64 1 (.f64 x x)))) (/.f64 2/27 (.f64 x x)))))))))))
(fma.f64 eps (neg.f64 (.f64 (pow.f64 (pow.f64 x 8) 1/18) (pow.f64 (pow.f64 x 8) 1/18))) (fma.f64 x x (.f64 (.f64 eps eps) (+.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) -1/9)) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)))) (.f64 (fma.f64 -1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 8)) 1/18) -1/9)) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/18))) (fma.f64 2/27 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (fma.f64 (cbrt.f64 (.f64 x x)) (fma.f64 -2/3 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) 5/27) (cbrt.f64 (/.f64 1 (.f64 x x)))) (/.f64 2/27 (.f64 x x))) (.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) 5/27))))) eps)))))
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(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 (pow.f64 eps 4) 1/16)) (.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 -2 (/.f64 (fma.f64 (pow.f64 eps 4) 1/16 (.f64 (pow.f64 eps 4) 1/64)) (*.f64 eps (pow.f64 x 5)))))))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (fma.f64 (.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -1/4 (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) -1/8)) (.f64 -2 (/.f64 (/.f64 (*.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 5)) 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 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(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 (pow.f64 x 3)) eps) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 (pow.f64 eps 3) 1/16) (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))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 -1 (/.f64 (.f64 (pow.f64 eps 4) -5/128) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 (pow.f64 eps 3) 1/16) (pow.f64 x 5)))))

localize3.0ms (0%)

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

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 13 to 6 computations (53.8% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite71.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`pow1_binary64`
652×	`add-log-exp_binary64`
652×	`log1p-expm1-u_binary64`
652×	`expm1-log1p-u_binary64`
639×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	134	7
2	1770	7

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

Inputs
(/.f64 1/2 (/.f64 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 eps x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 eps (/.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (/.f64 eps x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 1/2 (/.f64 eps x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/2 (/.f64 eps x))) (pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 eps x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 eps x))) 2) (cbrt.f64 (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 1/2 (/.f64 eps x))) (sqrt.f64 (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (/.f64 1 (/.f64 (neg.f64 x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 eps x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 x) eps)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (neg.f64 x)) (neg.f64 eps))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/2 x) 1) eps)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/2 x) (pow.f64 (cbrt.f64 eps) 2)) (cbrt.f64 eps))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/2 x) (sqrt.f64 eps)) (sqrt.f64 eps))))) (#(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 pow.f64 (*.f64 (/.f64 x eps) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (pow.f64 (/.f64 x eps) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (/.f64 eps 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 expm1.f64 (log1p.f64 (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.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 (0.1%)

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

50 → 26

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 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))

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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

3 → 54

Calls

18 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)))

rewrite98.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	311	33
2	4869	33

Stop Event

1×	node limit

Counts

3 → 183

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

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

766×	`associate-/l*_binary64`
603×	`associate-+l+_binary64`
566×	`fma-def_binary64`
454×	`associate-/r*_binary64`
335×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	828
1	133	828
2	369	828
3	1216	819
4	5726	819
5	6781	819
6	7244	819

Stop Event

1×	node limit

Counts

237 → 205

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

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)

series10.0ms (0.1%)

Counts

2 → 26

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 (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))))
1.0ms	x	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))

rewrite80.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

444×	`log-prod_binary64`
417×	`fma-def_binary64`
296×	`fma-neg_binary64`
287×	`pow-prod-down_binary64`
229×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	255	15
2	4012	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 expm1.f64 (log1p.f64 (/.f64 eps (+.f64 x (sqrt.f64 eps)))))))) (#(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 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 expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (sqrt.f64 eps))))))) (#(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))))) (#(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)))))

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-neg_binary64`
593×	`cancel-sign-sub-inv_binary64`
411×	`div-sub_binary64`
310×	`neg-sub0_binary64`
294×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	513
1	170	450
2	568	406
3	2491	387
4	6123	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)) (-.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x -1) (/.f64 x (sqrt.f64 -1)))) (/.f64 x -1)))
(+.f64 x (fma.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 x (/.f64 (neg.f64 (sqrt.f64 -1)) x)) (/.f64 (sqrt.f64 eps) (sqrt.f64 -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (fma.f64 (neg.f64 x) (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 x (sqrt.f64 -1))) x))
(+.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 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (-.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x -1) (/.f64 x (sqrt.f64 -1)))) (/.f64 x -1))) (/.f64 (pow.f64 x 3) (*.f64 1 eps)))
(+.f64 x (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 x (/.f64 (neg.f64 (sqrt.f64 -1)) x)) (/.f64 (sqrt.f64 eps) (sqrt.f64 -1))) (/.f64 (pow.f64 x 3) 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 (sqrt.f64 -1) (.f64 x x))))
(-.f64 (/.f64 eps x) (.f64 (/.f64 (pow.f64 eps 3/2) (.f64 x x)) (sqrt.f64 -1)))
(fma.f64 (/.f64 (sqrt.f64 -1) (*.f64 x x)) (neg.f64 (pow.f64 eps 3/2)) (/.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 (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 eps x) (-.f64 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1) (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x)))))
(-.f64 (fma.f64 (/.f64 -1 (pow.f64 x 3)) (.f64 eps eps) (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 3/2) (*.f64 x x)) (sqrt.f64 -1)))
(-.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 (sqrt.f64 -1) (.f64 x x)))) (-.f64 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1) (/.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 (/.f64 (pow.f64 eps 3/2) (*.f64 x x)) (sqrt.f64 -1)))
(-.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 (sqrt.f64 -1) (.f64 x x))))
(-.f64 (/.f64 eps x) (.f64 (/.f64 (pow.f64 eps 3/2) (.f64 x x)) (sqrt.f64 -1)))
(fma.f64 (/.f64 (sqrt.f64 -1) (*.f64 x x)) (neg.f64 (pow.f64 eps 3/2)) (/.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 (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 eps x) (-.f64 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1) (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x)))))
(-.f64 (fma.f64 (/.f64 -1 (pow.f64 x 3)) (.f64 eps eps) (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 3/2) (*.f64 x x)) (sqrt.f64 -1)))
(-.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 (sqrt.f64 -1) (.f64 x x)))) (-.f64 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1) (/.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 (/.f64 (pow.f64 eps 3/2) (*.f64 x x)) (sqrt.f64 -1)))
(-.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

eval432.0ms (6.1%)

Compiler: Compiled 18708 to 7068 computations (62.2% saved)

prune195.0ms (2.7%)

Pruning

19 alts after pruning (10 fresh and 9 done)

	Pruned	Kept	Total
New	734	7	741
Fresh	1	3	4
Picked	0	1	1
Done	2	8	10
Total	737	19	756

Error

Counts

756 → 19

Alt Table

Click to see full alt table

Status	Error	Program
▶	25.6b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	38.9b	(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
	59.0b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
✓	37.6b	(*.f64 1/2 (/.f64 eps x))
▶	60.9b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
▶	60.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
▶	60.5b	(*.f64 -2 x)
▶	37.7b	(*.f64 (/.f64 1/2 x) eps)
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	60.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
✓	36.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
✓	23.8b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
✓	0.8b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3))))
✓	22.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.4b	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 1 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
	41.6b	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x))))
	56.9b	(/.f64 eps x)
✓	37.6b	(/.f64 1/2 (/.f64 x eps))
	36.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x)))

Compiler

Compiled 394 to 236 computations (40.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 5 computations (64.3% saved)

series2.0ms (0%)

Counts

1 → 13

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(-.f64 x (sqrt.f64 (neg.f64 eps)))
0.0ms	eps	@	-inf	(-.f64 x (sqrt.f64 (neg.f64 eps)))
0.0ms	eps	@	0	(-.f64 x (sqrt.f64 (neg.f64 eps)))
0.0ms	x	@	0	(-.f64 x (sqrt.f64 (neg.f64 eps)))
0.0ms	x	@	-inf	(-.f64 x (sqrt.f64 (neg.f64 eps)))

rewrite54.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`pow1_binary64`
583×	`add-log-exp_binary64`
582×	`log1p-expm1-u_binary64`
582×	`expm1-log1p-u_binary64`
569×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	133	6
2	1911	6

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

101×	`fma-def_binary64`
56×	`fma-neg_binary64`
27×	`cancel-sign-sub-inv_binary64`
17×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	121
1	16	112
2	32	112
3	45	112
4	57	112
5	88	112
6	148	112
7	196	112
8	254	112
9	341	112
10	391	112
11	397	112

Stop Event

1×

saturated

Counts

48 → 40

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
x

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

localize3.0ms (0%)

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

localize97.0ms (1.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 13 to 8 computations (38.5% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite51.0ms (0.7%)

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

simplify13.0ms (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 → 22

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 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))

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.6b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)

Compiler

Compiled 30 to 17 computations (43.3% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite233.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`unpow-prod-down_binary64`
490×	`prod-diff_binary64`
417×	`log-prod_binary64`
410×	`fma-def_binary64`
234×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	203	7
2	2844	7

Stop Event

1×	node limit

Counts

1 → 119

Calls

Call 1

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

Outputs

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

simplify12.0ms (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

143 → 119

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 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))

localize22.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
✓	0.3b	(*.f64 eps (/.f64 -1/2 x))

Compiler

Compiled 47 to 15 computations (68.1% saved)

series36.0ms (0.5%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
32.0ms	x	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
1.0ms	x	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
0.0ms	x	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
0.0ms	eps	@	0	(*.f64 eps (/.f64 -1/2 x))
0.0ms	eps	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))

rewrite216.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

516×	`log-prod_binary64`
512×	`prod-diff_binary64`
263×	`fma-def_binary64`
255×	`pow2_binary64`
189×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	253	17
2	3748	17

Stop Event

1×	node limit

Counts

2 → 82

Calls

Call 1

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

Outputs

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

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

simplify183.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	8	264
1	12	264
2	16	264
3	20	264
4	21	264

Stop Event

1×

saturated

Counts

130 → 85

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))
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)

Outputs
(*.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))
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)
(*.f64 -2 x)
(*.f64 x -2)

eval148.0ms (2.1%)

Compiler: Compiled 3373 to 1815 computations (46.2% saved)

prune58.0ms (0.8%)

Pruning

24 alts after pruning (11 fresh and 13 done)

	Pruned	Kept	Total
New	259	7	266
Fresh	1	4	5
Picked	1	0	1
Done	0	13	13
Total	261	24	285

Error

Counts

285 → 24

Alt Table

Click to see full alt table

Status	Error	Program
✓	22.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	60.5b	(neg.f64 (/.f64 eps (*.f64 (/.f64 -1/2 x) (neg.f64 eps))))
✓	25.6b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	38.9b	(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
	59.0b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
✓	37.6b	(*.f64 1/2 (/.f64 eps x))
✓	60.9b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
	60.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 (*.f64 eps -1/2) x))
	60.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 1 (/.f64 x (*.f64 eps -1/2))))
	41.6b	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x))))
	60.9b	(*.f64 (/.f64 1 eps) (/.f64 eps (/.f64 -1/2 x)))
	56.9b	(/.f64 eps x)
	60.5b	(.f64 (neg.f64 eps) (/.f64 1 (.f64 (/.f64 -1/2 x) (neg.f64 eps))))
✓	60.5b	(*.f64 -2 x)
✓	37.7b	(*.f64 (/.f64 1/2 x) eps)
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	60.5b	(.f64 (/.f64 (.f64 x -2) eps) eps)
✓	36.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
✓	23.8b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
✓	0.8b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3))))
✓	0.4b	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 1 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
✓	37.6b	(/.f64 1/2 (/.f64 x eps))
	36.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x)))
	61.7b	x

Compiler

Compiled 317 to 192 computations (39.4% saved)

regimes84.0ms (1.2%)

Counts

29 → 1

Calls

Call 1

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

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

Calls

3 calls:

40.0ms	x
19.0ms	eps
16.0ms	(-.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)))`

Compiler

Compiled 328 to 127 computations (61.3% saved)

regimes247.0ms (3.5%)

Counts

25 → 2

Calls

Call 1

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

Calls

3 calls:

111.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
76.0ms	x
52.0ms	eps

Results

Error	Segments	Branch
5.8b	2	`x`
10.5b	2	`eps`
0.5b	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 246 to 105 computations (57.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.248262158298355e-152	-8.215063690446345e-153

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes271.0ms (3.8%)

Counts

23 → 2

Calls

Call 1

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

Calls

2 calls:

218.0ms	eps
41.0ms	x

Results

Error	Segments	Branch
6.8b	2	`x`
12.3b	2	`eps`

Compiler

Compiled 213 to 94 computations (55.9% saved)

bsearch59.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
59.0ms	1.0858610229481089e-111	2.718017346592238e-111

Compiler

Compiled 165 to 105 computations (36.4% saved)

regimes43.0ms (0.6%)

Counts

22 → 1

Calls

Call 1

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

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

Calls

2 calls:

22.0ms	x
14.0ms	eps

Results

Error	Segments	Branch
36.7b	1	`x`
36.7b	1	`eps`

Compiler

Compiled 208 to 92 computations (55.8% saved)

regimes90.0ms (1.3%)

Counts

20 → 1

Calls

Call 1

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

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

Calls

2 calls:

54.0ms	eps
31.0ms	x

Results

Error	Segments	Branch
37.6b	1	`x`
37.6b	1	`eps`

Compiler

Compiled 170 to 81 computations (52.4% saved)

regimes15.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	eps
5.0ms	x

Results

Error	Segments	Branch
37.6b	1	`x`
37.6b	1	`eps`

Compiler

Compiled 36 to 21 computations (41.7% saved)

regimes16.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

10.0ms	eps
5.0ms	x

Results

Error	Segments	Branch
37.7b	1	`x`
37.7b	1	`eps`

Compiler

Compiled 26 to 15 computations (42.3% saved)

regimes12.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(/.f64 eps x)

Calls

2 calls:

6.0ms	eps
5.0ms	x

Results

Error	Segments	Branch
56.9b	1	`x`
56.9b	1	`eps`

Compiler

Compiled 21 to 12 computations (42.9% saved)

regimes9.0ms (0.1%)

Accuracy

Total -1.7b remaining (-2.9%)

Threshold costs -1.7b (-2.9%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(*.f64 -2 x)

Outputs
(*.f64 -2 x)

Calls

2 calls:

5.0ms	eps
3.0ms	x

Results

Error	Segments	Branch
60.5b	1	`x`
60.5b	1	`eps`

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`*-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	36	184
1	58	184
2	73	184
3	82	184
4	86	184

Stop Event

1×	fuel
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))) -4717453031026927/471745303102692669030194322623533611364615152552055053547025787530703020299018606510765840647207345942683546878845480612471323078740599079070179281429087005456174415872) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))))
(if (<=.f64 x 186153360811334/169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920983350278405979725889536) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x)))
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(*.f64 (/.f64 1/2 x) eps)
(/.f64 eps x)
(*.f64 -2 x)
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))) -4717453031026927/471745303102692669030194322623533611364615152552055053547025787530703020299018606510765840647207345942683546878845480612471323078740599079070179281429087005456174415872) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -4717453031026927/471745303102692669030194322623533611364615152552055053547025787530703020299018606510765840647207345942683546878845480612471323078740599079070179281429087005456174415872) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 x 2))))
(if (<=.f64 x 186153360811334/169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920983350278405979725889536) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))))
(if (<=.f64 x 93076680405667/84615164005151820665845159428194693098035799419427996068435045795123941278247852265624218936283556460491675139202989862944768) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 x 2))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 x 2)))
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 eps x) 1/2)
(/.f64 1/2 (/.f64 x eps))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 eps (/.f64 1/2 x))
(/.f64 eps x)
(*.f64 -2 x)
(*.f64 x -2)
x

Compiler

Compiled 145 to 81 computations (44.1% saved)

soundness0.0ms (0%)

end76.0ms (1.1%)

Compiler: Compiled 127 to 48 computations (62.2% saved)

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	353	24
7	506	24
8	608	24
9	660	24
10	670	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	361	12
9	439	12
10	495	12
11	499	12

Iter	Nodes	Cost
0	9	121
1	16	112
2	32	112
3	45	112
4	57	112
5	88	112
6	148	112
7	196	112
8	254	112
9	341	112
10	391	112
11	397	112

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	353	24
7	506	24
8	608	24
9	660	24
10	670	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	361	12
9	439	12
10	495	12
11	499	12

Iter	Nodes	Cost
0	9	121
1	16	112
2	32	112
3	45	112
4	57	112
5	88	112
6	148	112
7	196	112
8	254	112
9	341	112
10	391	112
11	397	112

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	353	24
7	506	24
8	608	24
9	660	24
10	670	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	361	12
9	439	12
10	495	12
11	499	12

Iter	Nodes	Cost
0	9	121
1	16	112
2	32	112
3	45	112
4	57	112
5	88	112
6	148	112
7	196	112
8	254	112
9	341	112
10	391	112
11	397	112