Details

analyze28.0ms (0.7%)

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)

sample1.8s (43.6%)

Results

583.0ms	4927×	body	64	valid
528.0ms	1100×	body	1024	valid
406.0ms	1134×	body	512	valid
175.0ms	648×	body	256	valid
79.0ms	407×	body	128	valid
22.0ms	40×	body	2048	valid
16.0ms	157×	body	64	invalid

preprocess24.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 10 to 6 computations (40% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

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

23.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	23.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	3.2b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series12.0ms (0.3%)

Counts

2 → 40

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	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	x	@	0	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms	eps	@	-inf	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

rewrite58.0ms (1.4%)

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	19
1	162	19
2	2412	19

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

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

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

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

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

681×	`unswap-sqr_binary64`
521×	`associate-/l/_binary64`
362×	`distribute-rgt-in_binary64`
332×	`distribute-lft-in_binary64`
263×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	77	567
1	223	539
2	667	531
3	2775	518
4	4554	514

Stop Event

1×	node limit

Counts

115 → 105

Calls

Call 1

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

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

prune124.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	5	106

Error

Counts

106 → 5

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	23.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	40.6b	(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
	0.4b	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 1 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
	23.6b	(-.f64 x (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) eps)) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))

Compiler

Compiled 1914 to 790 computations (58.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series12.0ms (0.3%)

Counts

2 → 32

Calls

12 calls:

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

rewrite76.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 194

Calls

Call 1

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

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

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

simplify55.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
716×	`fma-neg_binary64`
416×	`times-frac_binary64`
333×	`associate-+l+_binary64`
318×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	854
1	372	822
2	1263	747
3	6400	725

Stop Event

1×	node limit

Counts

226 → 228

Calls

Call 1

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

Outputs
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(fma.f64 -1 (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 eps (/.f64 (neg.f64 eps) x)))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (*.f64 1 x))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) x)
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
(fma.f64 -1 (.f64 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/2) (.f64 x x)) (fma.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
(-.f64 (-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 eps (/.f64 (neg.f64 eps) x))) (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (.f64 -1/2 (*.f64 x x))))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps))) (.f64 x x) (.f64 1 x)))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 x (*.f64 x (/.f64 -1/2 (sqrt.f64 (neg.f64 eps)))) x))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 4))) (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (sqrt.f64 (neg.f64 eps))))) (pow.f64 x 3))) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))))
(fma.f64 -1 (.f64 (fma.f64 -1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 4)) (neg.f64 (/.f64 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/2) (sqrt.f64 (neg.f64 eps))))) (pow.f64 x 3)) (fma.f64 -1 (.f64 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/2) (.f64 x x)) (fma.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (/.f64 eps (sqrt.f64 (neg.f64 eps))))))
(-.f64 (-.f64 (-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 eps (/.f64 (neg.f64 eps) x))) (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (.f64 -1/2 (.f64 x x)))) (.f64 (-.f64 (/.f64 (/.f64 (*.f64 eps -1/2) (neg.f64 eps)) (neg.f64 eps)) (/.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 (sqrt.f64 (neg.f64 eps)) -1/2))) (pow.f64 x 3)))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (fma.f64 -1 (/.f64 1/2 eps) (/.f64 1/2 eps)) (pow.f64 x 3) (fma.f64 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps))) (.f64 x x) (.f64 1 x))))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (*.f64 x x) (fma.f64 x 0 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps)))) x))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 eps 1/2) 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 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 eps 1/2) x))
(fma.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) (/.f64 eps (/.f64 x 1/2)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3)))))
(*.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 (/.f64 -1/2 x) eps))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -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 (fma.f64 1/16 (pow.f64 eps 4) (pow.f64 (.f64 (.f64 eps eps) -1/8) 2)) (.f64 eps (pow.f64 x 5))) (.f64 -1/4 (/.f64 eps (/.f64 (pow.f64 x 5) (.f64 (.f64 eps eps) -1/8)))))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -2 (/.f64 (fma.f64 1/16 (pow.f64 eps 4) (.f64 (pow.f64 eps 4) 1/64)) (.f64 eps (pow.f64 x 5))) (/.f64 (.f64 -1/4 (*.f64 (pow.f64 eps 3) -1/8)) (pow.f64 x 5)))))))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -2 (/.f64 (.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 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 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 eps 1/2) x))
(fma.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) (/.f64 eps (/.f64 x 1/2)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3)))))
(sqrt.f64 (neg.f64 eps))
(+.f64 (sqrt.f64 (neg.f64 eps)) x)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (sqrt.f64 (neg.f64 eps)) x))
(fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) x))
(+.f64 x (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 eps))))
(+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) x))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) x)))
(fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) x)))
(+.f64 (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) x) (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 eps))))
(+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) (fma.f64 (/.f64 1/8 eps) (/.f64 (pow.f64 x 4) (sqrt.f64 (neg.f64 eps))) x)))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(fma.f64 -1/2 (/.f64 eps x) (*.f64 x 2))
(fma.f64 x 2 (*.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 -1/2 x) eps))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -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) (pow.f64 x 3)) -1/8))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (.f64 x 2))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 eps 1/2) x)
(/.f64 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 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 eps 1/2) x))
(fma.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) (/.f64 eps (/.f64 x 1/2)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3)))))
(*.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 (/.f64 -1/2 x) eps))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -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) (pow.f64 x 3)) -1/8))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (.f64 x 2))))

prune445.0ms (10.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	273	5	278

Error

Counts

278 → 5

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	23.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
	23.6b	(-.f64 x (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) eps)) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
	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 6816 to 1873 computations (72.5% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series6.0ms (0.1%)

Counts

2 → 32

Calls

12 calls:

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

rewrite70.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

593×	`fma-def_binary64`
479×	`log-prod_binary64`
284×	`fma-neg_binary64`
247×	`pow2_binary64`
168×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	275	18
2	4111	18

Stop Event

1×	node limit

Counts

2 → 197

Calls

Call 1

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

Outputs

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

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
716×	`fma-neg_binary64`
416×	`times-frac_binary64`
333×	`associate-+l+_binary64`
318×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	854
1	372	822
2	1263	747
3	6400	725

Stop Event

1×	node limit

Counts

229 → 231

Calls

Call 1

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

Outputs
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(fma.f64 -1 (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 eps (/.f64 (neg.f64 eps) x)))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (*.f64 1 x))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) x)
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
(fma.f64 -1 (.f64 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/2) (.f64 x x)) (fma.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
(-.f64 (-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 eps (/.f64 (neg.f64 eps) x))) (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (.f64 -1/2 (*.f64 x x))))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps))) (.f64 x x) (.f64 1 x)))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 x (*.f64 x (/.f64 -1/2 (sqrt.f64 (neg.f64 eps)))) x))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 4))) (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (sqrt.f64 (neg.f64 eps))))) (pow.f64 x 3))) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))))
(fma.f64 -1 (.f64 (fma.f64 -1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 4)) (neg.f64 (/.f64 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/2) (sqrt.f64 (neg.f64 eps))))) (pow.f64 x 3)) (fma.f64 -1 (.f64 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/2) (.f64 x x)) (fma.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (/.f64 eps (sqrt.f64 (neg.f64 eps))))))
(-.f64 (-.f64 (-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (/.f64 eps (/.f64 (neg.f64 eps) x))) (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (.f64 -1/2 (.f64 x x)))) (.f64 (-.f64 (/.f64 (/.f64 (*.f64 eps -1/2) (neg.f64 eps)) (neg.f64 eps)) (/.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 (sqrt.f64 (neg.f64 eps)) -1/2))) (pow.f64 x 3)))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (fma.f64 -1 (/.f64 1/2 eps) (/.f64 1/2 eps)) (pow.f64 x 3) (fma.f64 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps))) (.f64 x x) (.f64 1 x))))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (*.f64 x x) (fma.f64 x 0 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps)))) x))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 eps 1/2) 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 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 eps 1/2) x))
(fma.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) (/.f64 eps (/.f64 x 1/2)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3)))))
(*.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 (/.f64 -1/2 x) eps))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -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 (fma.f64 1/16 (pow.f64 eps 4) (pow.f64 (.f64 (.f64 eps eps) -1/8) 2)) (.f64 eps (pow.f64 x 5))) (.f64 -1/4 (/.f64 eps (/.f64 (pow.f64 x 5) (.f64 (.f64 eps eps) -1/8)))))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -2 (/.f64 (fma.f64 1/16 (pow.f64 eps 4) (.f64 (pow.f64 eps 4) 1/64)) (.f64 eps (pow.f64 x 5))) (/.f64 (.f64 -1/4 (*.f64 (pow.f64 eps 3) -1/8)) (pow.f64 x 5)))))))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -2 (/.f64 (.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 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 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 eps 1/2) x))
(fma.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) (/.f64 eps (/.f64 x 1/2)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3)))))
(sqrt.f64 (neg.f64 eps))
(+.f64 (sqrt.f64 (neg.f64 eps)) x)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (sqrt.f64 (neg.f64 eps)) x))
(fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) x))
(+.f64 x (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 eps))))
(+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) x))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 (neg.f64 eps)))) (+.f64 (sqrt.f64 (neg.f64 eps)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) x)))
(fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) x)))
(+.f64 (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) x) (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 eps))))
(+.f64 (sqrt.f64 (neg.f64 eps)) (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) x) (fma.f64 (/.f64 1/8 eps) (/.f64 (pow.f64 x 4) (sqrt.f64 (neg.f64 eps))) x)))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(fma.f64 -1/2 (/.f64 eps x) (*.f64 x 2))
(fma.f64 x 2 (*.f64 -1/2 (/.f64 eps x)))
(fma.f64 x 2 (*.f64 (/.f64 -1/2 x) eps))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -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) (pow.f64 x 3)) -1/8))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (.f64 x 2))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 eps 1/2) x)
(/.f64 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 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 (.f64 eps 1/2) x))
(fma.f64 1/8 (/.f64 (*.f64 eps eps) (pow.f64 x 3)) (/.f64 eps (/.f64 x 1/2)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) (.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3)))))
(*.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 (/.f64 -1/2 x) eps))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -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) (pow.f64 x 3)) -1/8))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (.f64 x 2))))

prune143.0ms (3.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	231	5	236

Error

Counts

236 → 5

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	23.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
	23.6b	(-.f64 x (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) eps)) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
▶	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 5315 to 1551 computations (70.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series34.0ms (0.8%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
26.0ms	eps	@	inf	(/.f64 1 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
2.0ms	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	eps	@	inf	(.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (/.f64 1 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))

rewrite118.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

789×	`fma-def_binary64`
561×	`log-prod_binary64`
314×	`fma-neg_binary64`
228×	`egg-rr`
206×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	296	27
2	4313	25

Stop Event

1×	node limit

Counts

2 → 256

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

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

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

505×	`times-frac_binary64`
459×	`associate-+l+_binary64`
393×	`associate-/l*_binary64`
362×	`associate-/r*_binary64`
353×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	982
1	483	893
2	1668	809
3	6988	783

Stop Event

1×	node limit

Counts

288 → 303

Calls

Call 1

Inputs
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 4))) (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (sqrt.f64 (neg.f64 eps))))) (pow.f64 x 3))) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/32 (pow.f64 eps 4)) (.f64 -1/128 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 -2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (.f64 eps (pow.f64 x 5)))) (.f64 -1/4 (/.f64 (.f64 eps (+.f64 (.f64 -1/4 (pow.f64 eps 2)) (*.f64 1/8 (pow.f64 eps 2)))) (pow.f64 x 5)))))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(/.f64 1 (sqrt.f64 (neg.f64 eps)))
(+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (*.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (*.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))))))
(/.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 eps (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(fma.f64 -1 (/.f64 (*.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (*.f64 (/.f64 eps (neg.f64 eps)) x))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (*.f64 1 x))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) x)
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
(fma.f64 -1 (.f64 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/2) (.f64 x x)) (fma.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
(-.f64 (-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (.f64 (/.f64 eps (neg.f64 eps)) x)) (.f64 x (.f64 x (/.f64 (.f64 eps -1/2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps))) (.f64 x x) (.f64 1 x)))
(+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps))) (*.f64 x x) x))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 4))) (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (sqrt.f64 (neg.f64 eps))))) (pow.f64 x 3))) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (.f64 -1 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)))) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))))
(fma.f64 -1 (.f64 (fma.f64 -1/2 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 4)) (neg.f64 (/.f64 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/2) (sqrt.f64 (neg.f64 eps))))) (pow.f64 x 3)) (fma.f64 -1 (.f64 (.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) -1/2) (.f64 x x)) (fma.f64 -1 (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)) (/.f64 eps (sqrt.f64 (neg.f64 eps))))))
(-.f64 (-.f64 (-.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (.f64 (/.f64 eps (neg.f64 eps)) x)) (.f64 x (.f64 x (/.f64 (.f64 eps -1/2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))))) (.f64 (-.f64 (.f64 -1/2 (/.f64 (/.f64 eps (neg.f64 eps)) (neg.f64 eps))) (/.f64 (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 (sqrt.f64 (neg.f64 eps)) -1/2))) (pow.f64 x 3)))
(fma.f64 (+.f64 (neg.f64 (/.f64 1/2 eps)) (/.f64 1/2 eps)) (pow.f64 x 3) (+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps))) (.f64 x x) (.f64 1 x))))
(fma.f64 0 (pow.f64 x 3) (+.f64 (/.f64 eps (sqrt.f64 (neg.f64 eps))) (fma.f64 (/.f64 -1/2 (sqrt.f64 (neg.f64 eps))) (*.f64 x x) x)))
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/8 (/.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)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/32 (pow.f64 eps 4)) (.f64 -1/128 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 -1 (/.f64 (.f64 (pow.f64 eps 4) -5/128) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/8 (/.f64 eps (/.f64 (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 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(*.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 (/.f64 -1/2 x) eps))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (*.f64 (/.f64 eps (/.f64 (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 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -1/4 (/.f64 (.f64 (pow.f64 eps 3) -1/8) (pow.f64 x 5)) (.f64 -2 (/.f64 (fma.f64 1/16 (pow.f64 eps 4) (.f64 (pow.f64 eps 4) 1/64)) (*.f64 eps (pow.f64 x 5)))))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (.f64 eps (pow.f64 x 5))) (/.f64 (*.f64 (pow.f64 eps 3) 1/32) (pow.f64 x 5)))))))
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 1/2 x) eps)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/8 (/.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)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 -1 (/.f64 (.f64 (pow.f64 eps 4) -5/128) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/8 (/.f64 eps (/.f64 (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 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(/.f64 1 (sqrt.f64 (neg.f64 eps)))
(+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (*.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))))
(+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (neg.f64 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))))
(-.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (/.f64 x (neg.f64 eps)))
(-.f64 (/.f64 x eps) (/.f64 -1 (sqrt.f64 (neg.f64 eps))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))))
(fma.f64 1/2 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (neg.f64 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2)))))
(-.f64 (fma.f64 1/2 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (/.f64 x (neg.f64 eps)))
(+.f64 (/.f64 x eps) (fma.f64 1/2 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (/.f64 1 (sqrt.f64 (neg.f64 eps)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5))) (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (*.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))))))
(fma.f64 1/2 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (+.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (neg.f64 (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) 2))))))
(fma.f64 1/2 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (-.f64 (/.f64 1 (sqrt.f64 (neg.f64 eps))) (/.f64 x (neg.f64 eps)))))
(fma.f64 1/2 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (-.f64 (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (/.f64 1 (sqrt.f64 (neg.f64 eps)))) (/.f64 x (neg.f64 eps))))
(fma.f64 1/2 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 (neg.f64 eps)) 3)) (+.f64 (/.f64 x eps) (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 (neg.f64 eps)) 5)) (/.f64 1 (sqrt.f64 (neg.f64 eps))))))
(/.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 eps (/.f64 (pow.f64 x 5) eps)) (/.f64 1/2 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (fma.f64 1/16 (*.f64 (/.f64 eps (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 eps (/.f64 (pow.f64 x 5) eps)) (/.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 x (/.f64 eps 2))
(-.f64 (.f64 2 (/.f64 x eps)) (.f64 1/2 (/.f64 1 x)))
(-.f64 (*.f64 2 (/.f64 x eps)) (/.f64 1/2 x))
(fma.f64 2 (/.f64 x eps) (/.f64 -1/2 x))
(-.f64 (+.f64 (.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 (*.f64 -1/8 (/.f64 eps (pow.f64 x 3))) (fma.f64 2 (/.f64 x eps) (/.f64 -1/2 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 (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 (.f64 eps (.f64 eps -1/8)) (pow.f64 x 5)) (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 eps (.f64 eps (pow.f64 x 5)))) (+.f64 (+.f64 (fma.f64 -1/4 (.f64 (/.f64 eps (pow.f64 x 5)) (.f64 eps -1/8)) (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)))
(fma.f64 -2 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (.f64 eps (.f64 eps (pow.f64 x 5)))) (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps eps) 1/32) (pow.f64 x 5)) (fma.f64 2 (/.f64 x eps) (/.f64 (.f64 eps eps) (/.f64 (pow.f64 x 5) 1/16)))) (-.f64 (*.f64 -1/8 (/.f64 eps (pow.f64 x 3))) (/.f64 1/2 x))))
(+.f64 (+.f64 (/.f64 (.f64 (.f64 eps eps) 1/32) (pow.f64 x 5)) (+.f64 (fma.f64 2 (/.f64 x eps) (/.f64 (.f64 eps eps) (/.f64 (pow.f64 x 5) 1/16))) (.f64 -1/8 (/.f64 eps (pow.f64 x 3))))) (fma.f64 -2 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (.f64 eps (*.f64 eps (pow.f64 x 5)))) (/.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 eps (/.f64 (pow.f64 x 5) eps)) (/.f64 1/2 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (fma.f64 1/16 (*.f64 (/.f64 eps (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 eps (/.f64 (pow.f64 x 5) eps)) (/.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))))

prune878.0ms (21%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	413	0	413
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	413	5	418

Error

Counts

418 → 5

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	23.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
	23.6b	(-.f64 x (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) eps)) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
✓	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 11116 to 3337 computations (70% saved)

regimes17.0ms (0.4%)

Accuracy

Total -61.9b remaining (-19093.5%)

Threshold costs -61.9b (-19093.5%)

Counts

6 → 1

Calls

Call 1

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

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

Results

6.0ms	0.3b	`x`
5.0ms	0.3b	`eps`
4.0ms	0.3b	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 119 to 43 computations (63.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	22	27
2	30	27
3	35	27
4	37	27

Stop Event

1×

saturated

Calls

Call 1

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

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

end16.0ms (0.4%)

Stop Event

1×

fuel

Compiler

Compiled 40 to 20 computations (50% saved)

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

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

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

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

Details

analyze28.0ms (0.7%)

sample1.8s (43.6%)

preprocess24.0ms (0.6%)

simplify12.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series12.0ms (0.3%)

rewrite58.0ms (1.4%)

simplify73.0ms (1.7%)

prune124.0ms (3%)

localize8.0ms (0.2%)

series12.0ms (0.3%)

rewrite76.0ms (1.8%)

simplify55.0ms (1.3%)

prune445.0ms (10.6%)

localize9.0ms (0.2%)

series6.0ms (0.1%)

rewrite70.0ms (1.7%)

simplify57.0ms (1.4%)

prune143.0ms (3.4%)

localize9.0ms (0.2%)

series34.0ms (0.8%)

rewrite118.0ms (2.8%)

simplify66.0ms (1.6%)

prune878.0ms (21%)

regimes17.0ms (0.4%)

simplify2.0ms (0.1%)

end16.0ms (0.4%)

Profiling

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

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