Details

analyze19.0ms (0.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	12.8%	87.2%	0%	0%	0%	0
0%	0%	12.8%	87.2%	0%	0%	0%	1
0%	0%	12.8%	87.2%	0%	0%	0%	2
50%	6.4%	6.4%	87.2%	0%	0%	0%	3
57.1%	6.4%	4.8%	87.2%	0%	1.6%	0%	4
69.2%	7.2%	3.2%	87.2%	0%	2.4%	0%	5
75%	7.2%	2.4%	87.2%	0%	3.2%	0%	6
82.6%	7.6%	1.6%	87.2%	0%	3.6%	0%	7
86.4%	7.6%	1.2%	87.2%	0%	4%	0%	8
90.7%	7.8%	0.8%	87.2%	0%	4.2%	0%	9
92.6%	7.8%	0.6%	87.2%	0%	4.4%	0%	10
95%	7.9%	0.4%	87.2%	0%	4.5%	0%	11
96.3%	8%	0.3%	87.2%	0%	4.5%	0%	12

Compiler

Compiled 25 to 17 computations (32% saved)

sample1.5s (27.4%)

Results

840.0ms	5910×	body	256	valid
441.0ms	1202×	body	1024	valid
218.0ms	1101×	body	512	valid
17.0ms	178×	body	256	invalid
14.0ms	43×	body	2048	valid

Bogosity

preprocess59.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

1276×	`rational_best-simplify-61`
1266×	`rational_best-simplify-65`
864×	`rational_best-simplify-3`
774×	`rational_best-simplify-62`
514×	`rational_best-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	93	46
2	511	46
3	3437	46
0	2	2

Stop Event

1×	saturated
1×	node limit

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)))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

790×	`rational_best-simplify-113`
684×	`rational_best-simplify-96`
664×	`rational_best-simplify-117`
640×	`rational_best-simplify-61`
638×	`rational_best-simplify-65`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	53	23
2	269	23
3	1757	23

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

24.5b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	24.5b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	3.9b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 26 to 6 computations (76.9% saved)

series6.0ms (0.1%)

Counts

3 → 56

Calls

18 calls:

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

rewrite63.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

790×	`rational_best-simplify-113`
684×	`rational_best-simplify-96`
664×	`rational_best-simplify-117`
638×	`rational_best-simplify-65`
632×	`rational_best-simplify-61`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	53
1	53	53
2	269	53
3	1757	53

Stop Event

1×	node limit

Counts

3 → 70

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0)))) (#(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 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 0 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(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 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (-.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 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))) (+.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 1 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (-.f64 1 (.f64 1 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))) (-.f64 4 (.f64 -2 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))) (.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))) (-.f64 (.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1)) (.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))))))) (#(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 neg.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 x 0) (/.f64 (.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) x) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 x) 0) (/.f64 (.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) x) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0) (/.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 (neg.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0)) 0) (-.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 (.f64 x x) eps) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 eps) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 eps) (+.f64 (.f64 x x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 eps) (+.f64 0 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 x x) eps) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 eps (.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (-.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 (-.f64 eps (.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))) (+.f64 (-.f64 eps (.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))) (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x)))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))) (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x))))) (+.f64 (+.f64 (-.f64 eps (.f64 x x)) 1) (+.f64 (-.f64 eps (.f64 x x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 1 (-.f64 (.f64 x x) eps)) (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) (-.f64 1 (.f64 1 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x)))) (.f64 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))) (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))))) (-.f64 4 (.f64 -2 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (+.f64 (-.f64 eps (.f64 x x)) 1) (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x))))) (.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))) (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))))) (-.f64 (.f64 (+.f64 (-.f64 eps (.f64 x x)) 1) (+.f64 (-.f64 eps (.f64 x x)) 1)) (.f64 (+.f64 (-.f64 eps (.f64 x x)) 1) (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (.f64 x x) eps) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 eps (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (.f64 x x) eps) 0) (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps)) (+.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 eps 0) (/.f64 (.f64 eps (-.f64 (.f64 x x) eps)) eps) (-.f64 (.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (.f64 x x) 0) (.f64 (/.f64 x x) (/.f64 (.f64 x (-.f64 (.f64 x x) eps)) x)) (-.f64 (.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (neg.f64 eps) (.f64 x x)) 0) (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps)) (+.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 eps) 0) (/.f64 (.f64 eps (-.f64 (.f64 x x) eps)) eps) (-.f64 (.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (.f64 x (neg.f64 x)) 0) (.f64 (/.f64 x x) (/.f64 (.f64 x (-.f64 (.f64 x x) eps)) x)) (-.f64 (.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 eps (.f64 x x)) 0) (/.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 (neg.f64 (.f64 (-.f64 eps (.f64 x x)) 0)) 0) (-.f64 (*.f64 x x) eps))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (-.f64 (.f64 x x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 eps (.f64 x x))) (sqrt.f64 -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 -1) (sqrt.f64 (-.f64 eps (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0)))) (#(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 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 x 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 0 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(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 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.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 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (+.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (+.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 -1 (-.f64 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(#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0) (/.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0) (/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 x 0) (/.f64 (*.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0) (/.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 x) 0) (/.f64 (*.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 0) (/.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0) (/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 (neg.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 0)) 0) (-.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 (*.f64 x x) eps) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 eps) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 eps) (+.f64 (*.f64 x x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 eps) (+.f64 0 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) eps) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 eps (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.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 (-.f64 eps (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 eps (*.f64 x x)) (-.f64 eps (*.f64 x x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 eps (*.f64 x x)) (-.f64 -1 (-.f64 eps (*.f64 x x)))) (+.f64 (-.f64 eps (*.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 eps (*.f64 x x)) (-.f64 eps (*.f64 x x))) (+.f64 (-.f64 eps (*.f64 x x)) (-.f64 eps (*.f64 x x)))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 eps (*.f64 x x)) (-.f64 -1 (-.f64 eps (*.f64 x x)))) (*.f64 (-.f64 eps (*.f64 x x)) (-.f64 -1 (-.f64 eps (*.f64 x x))))) (+.f64 (+.f64 (-.f64 eps (*.f64 x x)) 1) (+.f64 (-.f64 eps (*.f64 x x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1 (-.f64 (*.f64 x x) eps)) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (-.f64 1 (*.f64 1 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 -2 (+.f64 (-.f64 eps (*.f64 x x)) (-.f64 eps (*.f64 x x)))) (*.f64 (+.f64 (-.f64 eps (*.f64 x x)) (-.f64 eps (*.f64 x x))) (+.f64 (-.f64 eps (*.f64 x x)) (-.f64 eps (*.f64 x x))))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 eps (*.f64 x x)) (-.f64 eps (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 (-.f64 eps (*.f64 x x)) 1) (*.f64 (-.f64 eps (*.f64 x x)) (-.f64 -1 (-.f64 eps (*.f64 x x))))) (*.f64 (*.f64 (-.f64 eps (*.f64 x x)) (-.f64 -1 (-.f64 eps (*.f64 x x)))) (*.f64 (-.f64 eps (*.f64 x x)) (-.f64 -1 (-.f64 eps (*.f64 x x)))))) (-.f64 (*.f64 (+.f64 (-.f64 eps (*.f64 x x)) 1) (+.f64 (-.f64 eps (*.f64 x x)) 1)) (*.f64 (+.f64 (-.f64 eps (*.f64 x x)) 1) (*.f64 (-.f64 eps (*.f64 x x)) (-.f64 -1 (-.f64 eps (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 x x) eps) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 eps (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (*.f64 x x) eps) 0) (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (+.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 eps 0) (/.f64 (*.f64 eps (-.f64 (*.f64 x x) eps)) eps) (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 x x) 0) (*.f64 (/.f64 x x) (/.f64 (*.f64 x (-.f64 (*.f64 x x) eps)) x)) (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (neg.f64 eps) (*.f64 x x)) 0) (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (+.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 eps) 0) (/.f64 (*.f64 eps (-.f64 (*.f64 x x) eps)) eps) (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 x (neg.f64 x)) 0) (*.f64 (/.f64 x x) (/.f64 (*.f64 x (-.f64 (*.f64 x x) eps)) x)) (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 eps (*.f64 x x)) 0) (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 (neg.f64 (*.f64 (-.f64 eps (*.f64 x x)) 0)) 0) (-.f64 (*.f64 x x) eps))))))

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

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

512×	`rational_best-simplify-124`
506×	`rational_best-simplify-126`
496×	`rational_best-simplify-127`
492×	`rational_best-simplify-62`
452×	`rational_best-simplify-61`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	291	3708
1	1356	3616

Stop Event

1×	node limit

Counts

126 → 146

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) x))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 4) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 x 6))))) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 -1 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(*.f64 -1 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(*.f64 -1 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(*.f64 (sqrt.f64 eps) (sqrt.f64 -1))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 5))) (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)))))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(*.f64 -1 x)
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 -1 x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 -1 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1 x))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0)
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 x 0))
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 0 x))
(+.f64 0 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 1)
(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) -1)
(.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(/.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 1)
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) -1)
(/.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) -2)
(/.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1))
(/.f64 (+.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) 2)
(/.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) -4)
(/.f64 (+.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))) (+.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1)))
(/.f64 (-.f64 (.f64 1 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (-.f64 1 (.f64 1 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))) (-.f64 4 (.f64 -2 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (-.f64 (.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))) (.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))) (-.f64 (.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1) (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1)) (.f64 (+.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 1) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))))
(pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 1)
(neg.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (!=.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(if (!=.f64 x 0) (/.f64 (.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (neg.f64 x) 0) (/.f64 (.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0) (/.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(if (!=.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(if (!=.f64 0 0) (/.f64 (neg.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0)) 0) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (*.f64 x x) (neg.f64 eps))
(+.f64 (-.f64 (*.f64 x x) eps) 0)
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (neg.f64 eps) (+.f64 (*.f64 x x) 0))
(+.f64 (neg.f64 eps) (+.f64 0 (*.f64 x x)))
(+.f64 0 (-.f64 (*.f64 x x) eps))
(.f64 (-.f64 (.f64 x x) eps) 1)
(.f64 (-.f64 eps (.f64 x x)) -1)
(.f64 -1 (-.f64 eps (.f64 x x)))
(/.f64 (-.f64 (*.f64 x x) eps) 1)
(/.f64 (-.f64 eps (*.f64 x x)) -1)
(/.f64 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))) -2)
(/.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))) (+.f64 (-.f64 eps (.f64 x x)) 1))
(/.f64 (+.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)) 2)
(/.f64 (+.f64 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))) (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x)))) -4)
(/.f64 (+.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))) (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x))))) (+.f64 (+.f64 (-.f64 eps (.f64 x x)) 1) (+.f64 (-.f64 eps (.f64 x x)) 1)))
(/.f64 (-.f64 (.f64 1 (-.f64 (.f64 x x) eps)) (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) (-.f64 1 (.f64 1 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x)))) (.f64 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))) (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))))) (-.f64 4 (.f64 -2 (+.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (+.f64 (-.f64 eps (.f64 x x)) 1) (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x))))) (.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))) (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))))) (-.f64 (.f64 (+.f64 (-.f64 eps (.f64 x x)) 1) (+.f64 (-.f64 eps (.f64 x x)) 1)) (.f64 (+.f64 (-.f64 eps (.f64 x x)) 1) (.f64 (-.f64 eps (.f64 x x)) (-.f64 -1 (-.f64 eps (.f64 x x)))))))
(pow.f64 (-.f64 (*.f64 x x) eps) 1)
(neg.f64 (-.f64 eps (*.f64 x x)))
(if (!=.f64 (+.f64 (.f64 x x) eps) 0) (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps)) (+.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps))
(if (!=.f64 eps 0) (/.f64 (.f64 eps (-.f64 (.f64 x x) eps)) eps) (-.f64 (*.f64 x x) eps))
(if (!=.f64 (.f64 x x) 0) (.f64 (/.f64 x x) (/.f64 (.f64 x (-.f64 (.f64 x x) eps)) x)) (-.f64 (*.f64 x x) eps))
(if (!=.f64 (-.f64 (neg.f64 eps) (.f64 x x)) 0) (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps)) (+.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps))
(if (!=.f64 (neg.f64 eps) 0) (/.f64 (.f64 eps (-.f64 (.f64 x x) eps)) eps) (-.f64 (*.f64 x x) eps))
(if (!=.f64 (.f64 x (neg.f64 x)) 0) (.f64 (/.f64 x x) (/.f64 (.f64 x (-.f64 (.f64 x x) eps)) x)) (-.f64 (*.f64 x x) eps))
(if (!=.f64 (-.f64 eps (.f64 x x)) 0) (/.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))
(if (!=.f64 0 0) (/.f64 (neg.f64 (.f64 (-.f64 eps (.f64 x x)) 0)) 0) (-.f64 (*.f64 x x) eps))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0)
(+.f64 0 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 1)
(.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) -1)
(.f64 -1 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))
(.f64 (sqrt.f64 (-.f64 eps (.f64 x x))) (sqrt.f64 -1))
(.f64 (sqrt.f64 -1) (sqrt.f64 (-.f64 eps (.f64 x x))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) -1)
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 1)
(neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))

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

eval95.0ms (1.7%)

Compiler: Compiled 3180 to 1445 computations (54.6% saved)

prune59.0ms (1.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	135	11	146
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	135	12	147

Error

0.3b

Counts

147 → 12

Alt Table

Click to see full alt table

Status	Error	Program
	40.5b	(if (!=.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	24.6b	(if (!=.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
	59.4b	(-.f64 x (-.f64 x (*.f64 1/2 (/.f64 eps x))))
✓	24.5b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	27.4b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
	61.3b	(-.f64 x x)
	49.0b	(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
	47.9b	(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
▶	38.4b	(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
▶	61.8b	(*.f64 x 2)
▶	35.3b	(*.f64 1/2 (/.f64 eps x))
▶	27.2b	(neg.f64 (sqrt.f64 (neg.f64 eps)))

Compiler

Compiled 448 to 258 computations (42.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.3b	(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.3b	(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps)))
	3.9b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 111 to 14 computations (87.4% saved)

series7.0ms (0.1%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	inf	(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	x	@	-inf	(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	eps	@	-inf	(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	x	@	inf	(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
0.0ms	eps	@	0	(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

rewrite85.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

858×	`rational_best-simplify-96`
830×	`rational_best-simplify-61`
822×	`rational_best-simplify-65`
820×	`rational_best-simplify-111`
650×	`rational_best-simplify-110`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	112
1	63	112
2	345	112
3	2312	112

Stop Event

1×	node limit

Counts

2 → 24

Calls

Call 1

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

Inputs

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

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (sqrt.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 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (.f64 (sqrt.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 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 x (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))) (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.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 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0) (*.f64 (sqrt.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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 0) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 0) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 0) (/.f64 (*.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) 0) (/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0) (/.f64 (*.f64 x (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))))

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1068×	`rational_best-simplify-1`
760×	`rational_best-simplify-52`
712×	`rational_best-simplify-53`
674×	`rational_best-simplify-21`
660×	`rational_best-simplify-20`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	3684
1	1010	3536
2	5920	3372

Stop Event

1×	node limit

Counts

56 → 113

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) x))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 4) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 x 6))))) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) eps))
(+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) eps)) (.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 -1) x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) eps)) (.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 -1) x))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 eps)))) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) eps)) (.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 -1) x)))))
(*.f64 1/2 eps)
(+.f64 (.f64 1/2 eps) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 1/2 eps) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)))))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 6))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 1/2 eps) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (+.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 6))) (.f64 -1/16 (/.f64 (pow.f64 eps 4) (pow.f64 x 6))))))))))
(*.f64 -2 (pow.f64 x 2))
(+.f64 (.f64 -2 (pow.f64 x 2)) (.f64 -1 (+.f64 (.f64 -1/2 eps) (.f64 -1 eps))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (pow.f64 eps 2)) (+.f64 (.f64 -1/4 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2)))) (pow.f64 x 2))) (+.f64 (.f64 -2 (pow.f64 x 2)) (.f64 -1 (+.f64 (.f64 -1/2 eps) (.f64 -1 eps)))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (pow.f64 eps 2)) (+.f64 (.f64 -1/4 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2)))) (pow.f64 x 2))) (+.f64 (.f64 -2 (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/16 (pow.f64 eps 3)) (+.f64 (.f64 -1/8 (pow.f64 eps 3)) (.f64 1/8 (pow.f64 eps 3)))) (pow.f64 x 4))) (.f64 -1 (+.f64 (.f64 -1/2 eps) (.f64 -1 eps))))))
(*.f64 1/2 eps)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (.f64 1/2 eps))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (*.f64 1/2 eps)))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (+.f64 (.f64 1/2 eps) (.f64 (pow.f64 eps 4) (-.f64 (.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2))) (*.f64 5/64 (/.f64 1 (pow.f64 x 6))))))))
(if (!=.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 0)
(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0))
(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 0))
(+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))
(+.f64 0 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(+.f64 (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(+.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 0)
(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0))
(-.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps))))
(-.f64 0 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 x)))
(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 1)
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) -1)
(/.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)))) -2)
(neg.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(if (!=.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(if (!=.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(if (!=.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 x (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))) (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))

Outputs
(.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(.f64 -1 (sqrt.f64 (.f64 -1 eps)))
(neg.f64 (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) x)
(+.f64 (.f64 -1 (sqrt.f64 (.f64 -1 eps))) x)
(+.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) x))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 -1 (sqrt.f64 (.f64 -1 eps))) x))
(+.f64 (+.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) x) (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) x)))
(+.f64 (.f64 -1 (sqrt.f64 (.f64 -1 eps))) (+.f64 x (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))))))
(+.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (+.f64 (+.f64 x (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))))
(+.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))))
(*.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 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (*.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 (.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(+.f64 (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))) (.f64 1/2 (/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.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)))))
(+.f64 (.f64 x 2) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) (*.f64 -1/2 (/.f64 eps x))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 x 2) (*.f64 (/.f64 (pow.f64 eps 2) (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))))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) (+.f64 (.f64 x 2) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16))))
(+.f64 (+.f64 (.f64 x 2) (.f64 -1/2 (/.f64 eps x))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (*.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 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))) (.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 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))) (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 4) (-.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 (/.f64 1 (pow.f64 x 6)) -1/16))) x))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16)) (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 4) (-.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 (/.f64 1 (pow.f64 x 6)) -1/16))) x))))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) eps))
(.f64 -1 (.f64 eps 1))
(neg.f64 eps)
(+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) eps)) (.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 -1) x)))
(+.f64 (.f64 -1 (.f64 eps 1)) (.f64 (sqrt.f64 -1) (.f64 (sqrt.f64 eps) x)))
(+.f64 (*.f64 x (sqrt.f64 (neg.f64 eps))) (neg.f64 eps))
(-.f64 (*.f64 x (sqrt.f64 (neg.f64 eps))) eps)
(+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) eps)) (.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 -1) x))))
(+.f64 (.f64 -1 (.f64 eps 1)) (+.f64 (.f64 (sqrt.f64 -1) (.f64 (sqrt.f64 eps) x)) (*.f64 -1 (pow.f64 x 2))))
(+.f64 (*.f64 x (sqrt.f64 (neg.f64 eps))) (+.f64 (neg.f64 (pow.f64 x 2)) (neg.f64 eps)))
(-.f64 (-.f64 (*.f64 x (sqrt.f64 (neg.f64 eps))) eps) (pow.f64 x 2))
(+.f64 (.f64 1/2 (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 eps)))) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) eps)) (.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 -1) x)))))
(+.f64 (+.f64 (.f64 -1 (.f64 eps 1)) (.f64 (sqrt.f64 -1) (.f64 (sqrt.f64 eps) x))) (+.f64 (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 -1)) (.f64 1/2 (sqrt.f64 (/.f64 1 eps)))) (*.f64 -1 (pow.f64 x 2))))
(+.f64 (.f64 x (sqrt.f64 (neg.f64 eps))) (+.f64 (+.f64 (neg.f64 (pow.f64 x 2)) (neg.f64 eps)) (.f64 (sqrt.f64 (/.f64 1 eps)) (*.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 -1))))))
(+.f64 (-.f64 (-.f64 (.f64 x (sqrt.f64 (neg.f64 eps))) eps) (pow.f64 x 2)) (.f64 (sqrt.f64 (/.f64 1 eps)) (*.f64 1/2 (/.f64 (pow.f64 x 3) (sqrt.f64 -1)))))
(*.f64 1/2 eps)
(*.f64 eps 1/2)
(+.f64 (.f64 1/2 eps) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)))))
(+.f64 (.f64 eps 1/2) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 1/2 eps) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)))))))
(+.f64 (+.f64 (.f64 eps 1/2) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (*.f64 -1/8 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)))))
(+.f64 (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)))) (+.f64 (+.f64 (.f64 eps 1/2) (.f64 -1/8 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)))) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)))))
(+.f64 (.f64 eps 1/2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (-.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (-.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)) 1/4) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2)))))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 6))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 1/2 eps) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (+.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 6))) (.f64 -1/16 (/.f64 (pow.f64 eps 4) (pow.f64 x 6))))))))))
(+.f64 (+.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 6))) (.f64 -1/16 (/.f64 (pow.f64 eps 4) (pow.f64 x 6)))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (.f64 eps 1/2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (.f64 -1/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 6)))))
(+.f64 (+.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 6))) (.f64 -1/16 (/.f64 (pow.f64 eps 4) (pow.f64 x 6)))))) (+.f64 (.f64 eps 1/2) (.f64 -1/8 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (.f64 -1/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 6)))))
(*.f64 -2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) -2)
(+.f64 (.f64 -2 (pow.f64 x 2)) (.f64 -1 (+.f64 (.f64 -1/2 eps) (.f64 -1 eps))))
(+.f64 (.f64 (pow.f64 x 2) -2) (.f64 -1 (+.f64 (.f64 eps -1/2) (.f64 -1 eps))))
(+.f64 (.f64 (pow.f64 x 2) -2) (neg.f64 (+.f64 (.f64 eps -1/2) (neg.f64 eps))))
(+.f64 (.f64 (pow.f64 x 2) -2) (-.f64 eps (.f64 eps -1/2)))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (pow.f64 eps 2)) (+.f64 (.f64 -1/4 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2)))) (pow.f64 x 2))) (+.f64 (.f64 -2 (pow.f64 x 2)) (.f64 -1 (+.f64 (.f64 -1/2 eps) (.f64 -1 eps)))))
(+.f64 (.f64 (pow.f64 x 2) -2) (+.f64 (.f64 -1 (+.f64 (.f64 eps -1/2) (.f64 -1 eps))) (.f64 -1 (/.f64 (+.f64 (.f64 (pow.f64 eps 2) -1/8) (+.f64 (.f64 (pow.f64 eps 2) 1/4) (.f64 (pow.f64 eps 2) -1/4))) (pow.f64 x 2)))))
(+.f64 (neg.f64 (+.f64 (.f64 eps -1/2) (neg.f64 eps))) (+.f64 (.f64 (pow.f64 x 2) -2) (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 eps 2) -1/8) (-.f64 (.f64 (pow.f64 eps 2) -1/4) (*.f64 (pow.f64 eps 2) -1/4))) (pow.f64 x 2)))))
(+.f64 (-.f64 eps (.f64 eps -1/2)) (-.f64 (.f64 (pow.f64 x 2) -2) (/.f64 (+.f64 (*.f64 (pow.f64 eps 2) -1/8) 0) (pow.f64 x 2))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (pow.f64 eps 2)) (+.f64 (.f64 -1/4 (pow.f64 eps 2)) (.f64 -1/8 (pow.f64 eps 2)))) (pow.f64 x 2))) (+.f64 (.f64 -2 (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/16 (pow.f64 eps 3)) (+.f64 (.f64 -1/8 (pow.f64 eps 3)) (.f64 1/8 (pow.f64 eps 3)))) (pow.f64 x 4))) (.f64 -1 (+.f64 (.f64 -1/2 eps) (.f64 -1 eps))))))
(+.f64 (.f64 (pow.f64 x 2) -2) (+.f64 (+.f64 (.f64 -1 (+.f64 (.f64 eps -1/2) (.f64 -1 eps))) (.f64 -1 (/.f64 (+.f64 (.f64 (pow.f64 eps 3) -1/16) (+.f64 (.f64 (pow.f64 eps 3) -1/8) (.f64 1/8 (pow.f64 eps 3)))) (pow.f64 x 4)))) (.f64 -1 (/.f64 (+.f64 (.f64 (pow.f64 eps 2) -1/8) (+.f64 (.f64 (pow.f64 eps 2) 1/4) (.f64 (pow.f64 eps 2) -1/4))) (pow.f64 x 2)))))
(+.f64 (.f64 (pow.f64 x 2) -2) (+.f64 (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 eps 2) -1/8) (-.f64 (.f64 (pow.f64 eps 2) -1/4) (.f64 (pow.f64 eps 2) -1/4))) (pow.f64 x 2))) (+.f64 (neg.f64 (+.f64 (.f64 eps -1/2) (neg.f64 eps))) (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 eps 3) -1/16) (+.f64 (.f64 (pow.f64 eps 3) -1/8) (.f64 1/8 (pow.f64 eps 3)))) (pow.f64 x 4))))))
(-.f64 (-.f64 (.f64 (pow.f64 x 2) -2) (-.f64 (/.f64 (.f64 (pow.f64 eps 3) -1/16) (pow.f64 x 4)) (-.f64 eps (.f64 eps -1/2)))) (/.f64 (+.f64 (.f64 (pow.f64 eps 2) -1/8) 0) (pow.f64 x 2)))
(*.f64 1/2 eps)
(*.f64 eps 1/2)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (.f64 1/2 eps))
(+.f64 (.f64 eps 1/2) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (*.f64 1/2 eps)))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (+.f64 (.f64 eps 1/2) (*.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)))))
(+.f64 (.f64 eps 1/2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (*.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)))))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (+.f64 (.f64 1/2 eps) (.f64 (pow.f64 eps 4) (-.f64 (.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2))) (*.f64 5/64 (/.f64 1 (pow.f64 x 6))))))))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (+.f64 (.f64 (pow.f64 eps 4) (-.f64 (.f64 1/2 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 x 6))))) (.f64 (/.f64 1 (pow.f64 x 6)) 5/64))) (+.f64 (.f64 eps 1/2) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))))))
(+.f64 (.f64 eps 1/2) (+.f64 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (.f64 (pow.f64 eps 4) (+.f64 (.f64 1/2 (-.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 (/.f64 1 (pow.f64 x 6)) -1/16))) (.f64 (/.f64 1 (pow.f64 x 6)) -5/64)))) (*.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4)))))
(+.f64 (.f64 eps 1/2) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 4))) (-.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 2))) (.f64 (pow.f64 eps 4) (+.f64 (.f64 (/.f64 1 (pow.f64 x 6)) 5/64) (.f64 (-.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (*.f64 (/.f64 1 (pow.f64 x 6)) -1/16)) -1/2))))))
(if (!=.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 0)
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 0))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 0 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 0)
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 0 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 x)))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) 1)
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) -1)
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)))) -2)
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(neg.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) 0) (/.f64 (.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(if (!=.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 x (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))) (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))

localize3.0ms (0%)

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

localize5.0ms (0.1%)

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

localize5.0ms (0.1%)

Compiler: Compiled 12 to 5 computations (58.3% saved)

localize21.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
✓	0.2b	(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
✓	30.0b	(/.f64 (pow.f64 eps 2) (pow.f64 x 3))

Compiler

Compiled 53 to 35 computations (34% saved)

series7.0ms (0.1%)

Counts

3 → 24

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(/.f64 (pow.f64 eps 2) (pow.f64 x 3))
1.0ms	eps	@	0	(/.f64 (pow.f64 eps 2) (pow.f64 x 3))
1.0ms	x	@	0	(/.f64 (pow.f64 eps 2) (pow.f64 x 3))
0.0ms	eps	@	inf	(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
0.0ms	eps	@	inf	(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))

rewrite84.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`rational_best-simplify-124`
510×	`rational_best-simplify-126`
504×	`rational_best-simplify-113`
480×	`rational_best-simplify-61`
466×	`rational_best-simplify-65`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	87
1	39	87
2	212	87
3	1338	87

Stop Event

1×	node limit

Counts

3 → 22

Calls

Call 1

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

Outputs

()

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 (/.f64 eps x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 1/2 (/.f64 eps x)) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))) (*.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (-.f64 1 (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 (/.f64 eps x) -1/2)) 0) (/.f64 (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) (*.f64 1/8 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8))) (*.f64 1/2 (*.f64 (*.f64 (/.f64 eps x) -1/2) (/.f64 eps x)))) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 (/.f64 eps x) -1/2))) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 (/.f64 eps x) -1/2) 0) (/.f64 (*.f64 (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))) (*.f64 (/.f64 eps x) -1/2)) (*.f64 (/.f64 eps x) -1/2)) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) 0) (/.f64 (*.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x)))) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8)) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (*.f64 1/2 (/.f64 eps x)) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) (/.f64 (-.f64 (*.f64 1/2 (*.f64 (/.f64 eps x) (*.f64 1/2 (/.f64 eps x)))) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) (*.f64 1/8 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8)))) (+.f64 (*.f64 1/2 (/.f64 eps x)) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 1/2 (/.f64 eps x)) 0) (/.f64 (*.f64 (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))) (*.f64 (/.f64 eps x) -1/2)) (*.f64 (/.f64 eps x) -1/2)) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) 0) (/.f64 (*.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x)))) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8)) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) 0) (/.f64 (-.f64 0 (*.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (+.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0)) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) (/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) (*.f64 (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (+.f64 (*.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) (+.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))))))

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Rules

906×	`rational_best-simplify-113`
698×	`rational_best-simplify-61`
696×	`rational_best-simplify-65`
692×	`rational_best-simplify-96`
612×	`rational_best-simplify-111`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	1762
1	405	1762
2	2681	1762

Stop Event

1×	node limit

Counts

46 → 26

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(-.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) 0)
(-.f64 0 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(/.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) -1)
(neg.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(-.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 (/.f64 eps x) -1/2))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(-.f64 0 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))
(.f64 -1 (+.f64 (.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))
(.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) -1)
(/.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))) 1)
(/.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) -1)
(/.f64 (+.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) -2)
(/.f64 (-.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))) (.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (-.f64 1 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x)))))
(neg.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))
(if (!=.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 (/.f64 eps x) -1/2)) 0) (/.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) (.f64 1/8 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8))) (.f64 1/2 (.f64 (.f64 (/.f64 eps x) -1/2) (/.f64 eps x)))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 (/.f64 eps x) -1/2))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(if (!=.f64 (.f64 (/.f64 eps x) -1/2) 0) (/.f64 (.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))) (.f64 (/.f64 eps x) -1/2)) (.f64 (/.f64 eps x) -1/2)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(if (!=.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) 0) (/.f64 (.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x)))) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(if (!=.f64 (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) (/.f64 (-.f64 (.f64 1/2 (.f64 (/.f64 eps x) (.f64 1/2 (/.f64 eps x)))) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) (.f64 1/8 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8)))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(if (!=.f64 (.f64 1/2 (/.f64 eps x)) 0) (/.f64 (.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))) (.f64 (/.f64 eps x) -1/2)) (.f64 (/.f64 eps x) -1/2)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(if (!=.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) 0) (/.f64 (.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x)))) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(if (!=.f64 (+.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) 0) (/.f64 (-.f64 0 (.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (+.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))
(if (!=.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) (/.f64 (-.f64 (.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) (.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))

Outputs
(*.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 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(-.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) 0)
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(-.f64 0 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(/.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) -1)
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(neg.f64 (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(-.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 (/.f64 eps x) -1/2))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 0 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(.f64 -1 (+.f64 (.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (*.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) -1)
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(/.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))) 1)
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(/.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) -1)
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(/.f64 (+.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) -2)
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(/.f64 (-.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))) (.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (-.f64 1 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x)))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(neg.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(if (!=.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 (/.f64 eps x) -1/2)) 0) (/.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) (.f64 1/8 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8))) (.f64 1/2 (.f64 (.f64 (/.f64 eps x) -1/2) (/.f64 eps x)))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 (/.f64 eps x) -1/2))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(if (!=.f64 (.f64 (/.f64 eps x) -1/2) 0) (/.f64 (.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))) (.f64 (/.f64 eps x) -1/2)) (.f64 (/.f64 eps x) -1/2)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(if (!=.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) 0) (/.f64 (.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x)))) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(if (!=.f64 (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) (/.f64 (-.f64 (.f64 1/2 (.f64 (/.f64 eps x) (.f64 1/2 (/.f64 eps x)))) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) (.f64 1/8 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8)))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(if (!=.f64 (.f64 1/2 (/.f64 eps x)) 0) (/.f64 (.f64 (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))) (.f64 (/.f64 eps x) -1/2)) (.f64 (/.f64 eps x) -1/2)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(if (!=.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) 0) (/.f64 (.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x)))) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(if (!=.f64 (+.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) 0) (/.f64 (-.f64 0 (.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (+.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0)) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (*.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))
(if (!=.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) (/.f64 (-.f64 (.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) 0) (.f64 (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 1/2 (/.f64 eps x))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))

eval219.0ms (3.9%)

Compiler: Compiled 23465 to 6482 computations (72.4% saved)

prune96.0ms (1.7%)

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	458	2	460
Fresh	0	6	6
Picked	0	1	1
Done	1	4	5
Total	459	13	472

Error

0.3b

Counts

472 → 13

Alt Table

Click to see full alt table

Status	Error	Program
▶	40.5b	(if (!=.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	30.7b	(if (!=.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (/.f64 (.f64 eps 1/2) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
▶	24.6b	(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	59.4b	(-.f64 x (-.f64 x (*.f64 1/2 (/.f64 eps x))))
✓	24.5b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	27.4b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
▶	61.3b	(-.f64 x x)
▶	49.0b	(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
	47.9b	(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
✓	38.4b	(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
✓	61.8b	(*.f64 x 2)
✓	35.3b	(*.f64 1/2 (/.f64 eps x))
✓	27.2b	(neg.f64 (sqrt.f64 (neg.f64 eps)))

Compiler

Compiled 465 to 259 computations (44.3% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
	0.3b	(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	0.3b	(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps)))
	3.9b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 110 to 16 computations (85.5% saved)

localize3.0ms (0%)

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 5 computations (64.3% saved)

series2.0ms (0%)

Counts

1 → 13

Calls

6 calls:

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

rewrite89.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

906×	`rational_best-simplify-1`
656×	`rational_best-simplify-18`
426×	`rational_best-simplify-124`
418×	`rational_best-simplify-126`
418×	`rational_best-simplify-127`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	36	15
2	172	15
3	1051	15
4	7575	15

Stop Event

1×	node limit

Counts

1 → 28

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (neg.f64 (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x)))) (+.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 -2 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (*.f64 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x)))) (*.f64 (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))))) (-.f64 (*.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))) (*.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) 0) (/.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 eps eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 (*.f64 (sqrt.f64 (neg.f64 eps)) (-.f64 x (sqrt.f64 (neg.f64 eps)))) (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 x 0) (/.f64 (*.f64 x (-.f64 x (sqrt.f64 (neg.f64 eps)))) x) (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) 0) (/.f64 (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 x) 0) (/.f64 (*.f64 x (-.f64 x (sqrt.f64 (neg.f64 eps)))) x) (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) 0) (/.f64 (*.f64 (sqrt.f64 (neg.f64 eps)) (-.f64 x (sqrt.f64 (neg.f64 eps)))) (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (neg.f64 x) (sqrt.f64 (neg.f64 eps))) 0) (/.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 eps eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 x (sqrt.f64 (neg.f64 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 -1 0) (-.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))))))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

884×	`rational_best-simplify-61`
830×	`rational_best-simplify-96`
826×	`rational_best-simplify-65`
692×	`rational_best-simplify-3`
574×	`rational_best-simplify-110`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	707
1	414	707
2	2614	707

Stop Event

1×	node limit

Counts

41 → 33

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
x
(+.f64 x (neg.f64 (sqrt.f64 (neg.f64 eps))))
(+.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 0)
(+.f64 0 (-.f64 x (sqrt.f64 (neg.f64 eps))))
(+.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) x)
(*.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 1)
(*.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))
(*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) -1)
(*.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 1)
(/.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) -1)
(/.f64 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) -2)
(/.f64 (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))))
(/.f64 (+.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps)))) 2)
(/.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x))) -4)
(/.f64 (+.f64 (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x)))) (+.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))))
(/.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (.f64 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)))))
(/.f64 (-.f64 (.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x)))) (.f64 (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))))) (-.f64 (.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))) (.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))))))
(pow.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 1)
(neg.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x))
(if (!=.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 eps eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 (*.f64 (sqrt.f64 (neg.f64 eps)) (-.f64 x (sqrt.f64 (neg.f64 eps)))) (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 x 0) (/.f64 (*.f64 x (-.f64 x (sqrt.f64 (neg.f64 eps)))) x) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 0 0) 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) 0) (/.f64 (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 (neg.f64 x) 0) (/.f64 (*.f64 x (-.f64 x (sqrt.f64 (neg.f64 eps)))) x) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) 0) (/.f64 (*.f64 (sqrt.f64 (neg.f64 eps)) (-.f64 x (sqrt.f64 (neg.f64 eps)))) (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 (-.f64 (neg.f64 x) (sqrt.f64 (neg.f64 eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 eps eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 -1 0) (-.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))

Outputs
(.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(neg.f64 (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
x
(+.f64 x (neg.f64 (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 0)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 0 (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(+.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) x)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 1)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) -1)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 1)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) -1)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) -2)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (+.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps)))) 2)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x))) -4)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (+.f64 (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x)))) (+.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (.f64 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 (sqrt.f64 (neg.f64 eps)) x)))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 (-.f64 (.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x)))) (.f64 (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))) (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))))) (-.f64 (.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))) (.f64 (-.f64 1 (-.f64 x (sqrt.f64 (neg.f64 eps)))) (.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 -1 (-.f64 (sqrt.f64 (neg.f64 eps)) x))))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(pow.f64 (-.f64 x (sqrt.f64 (neg.f64 eps))) 1)
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(neg.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(if (!=.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 eps eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 (*.f64 (sqrt.f64 (neg.f64 eps)) (-.f64 x (sqrt.f64 (neg.f64 eps)))) (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(if (!=.f64 x 0) (/.f64 (*.f64 x (-.f64 x (sqrt.f64 (neg.f64 eps)))) x) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(if (!=.f64 0 0) 1 (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(if (!=.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) 0) (/.f64 (*.f64 (-.f64 (sqrt.f64 (neg.f64 eps)) x) (-.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 (sqrt.f64 (neg.f64 eps)) x)) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(if (!=.f64 (neg.f64 x) 0) (/.f64 (*.f64 x (-.f64 x (sqrt.f64 (neg.f64 eps)))) x) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(if (!=.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) 0) (/.f64 (*.f64 (sqrt.f64 (neg.f64 eps)) (-.f64 x (sqrt.f64 (neg.f64 eps)))) (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(if (!=.f64 (-.f64 (neg.f64 x) (sqrt.f64 (neg.f64 eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 eps eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(if (!=.f64 -1 0) (-.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	3.8b	(-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))))
	3.9b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	21.3b	(sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 153 to 17 computations (88.9% saved)

series11.0ms (0.2%)

Counts

3 → 64

Calls

18 calls:

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

rewrite73.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1136×	`rational_best-simplify-96`
1028×	`rational_best-simplify-61`
990×	`rational_best-simplify-65`
858×	`rational_best-simplify-3`
628×	`rational_best-simplify-62`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	157
1	73	157
2	454	157
3	3043	157

Stop Event

1×	node limit

Counts

3 → 41

Calls

Call 1

Inputs

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

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.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 (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 eps (*.f64 x x))) (sqrt.f64 (-.f64 eps (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fabs.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (fabs.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)))) (+.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x))) (+.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)))) (-.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x))))) (+.f64 (+.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) 1) (+.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) 0) (/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) 0) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (/.f64 0 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 x x) 0) (/.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))) (*.f64 x x)) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 x x)) 0) (/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (*.f64 x (neg.f64 x)) 0) (/.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))) (*.f64 x x)) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) 0) (/.f64 (*.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x))) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) 0) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (/.f64 0 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 (neg.f64 (*.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) 0)) 0) (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))))))))

((#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))))

simplify94.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1114×	`rational_best-simplify-3`
884×	`rational_best-simplify-1`
684×	`rational_best-simplify-53`
558×	`rational_best-simplify-21`
550×	`rational_best-simplify-20`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3837
1	872	3685
2	5258	3567

Stop Event

1×	node limit

Counts

105 → 94

Calls

Call 1

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

Outputs
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (neg.f64 eps) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) eps)
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(*.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps))
(*.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1)))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (.f64 -1 (/.f64 x 1)))
(+.f64 (*.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (neg.f64 (/.f64 x 1)))
(-.f64 (*.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (/.f64 x 1))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2)))))
(+.f64 (.f64 -1 (/.f64 x 1)) (+.f64 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))) (.f64 (/.f64 1 (sqrt.f64 -1)) (.f64 1/2 (sqrt.f64 (/.f64 1 eps))))) (.f64 -1 (pow.f64 x 2))) (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1)))))
(+.f64 (neg.f64 (/.f64 x 1)) (+.f64 (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (neg.f64 (.f64 (pow.f64 x 2) (+.f64 (neg.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))) (.f64 (/.f64 1 (sqrt.f64 -1)) (*.f64 (sqrt.f64 (/.f64 1 eps)) 1/2)))))))
(+.f64 (-.f64 (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (/.f64 x 1)) (.f64 (pow.f64 x 2) (-.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1))) (.f64 (/.f64 1 (sqrt.f64 -1)) (*.f64 (sqrt.f64 (/.f64 1 eps)) 1/2)))))
(+.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 4) eps))) (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (sqrt.f64 -1))))) (pow.f64 x 3)) (+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (*.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2))))))
(+.f64 (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (+.f64 (+.f64 (.f64 -1 (/.f64 x 1)) (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))) (.f64 (/.f64 1 (sqrt.f64 -1)) (.f64 1/2 (sqrt.f64 (/.f64 1 eps))))) (.f64 -1 (pow.f64 x 2)))) (.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 eps 1))) (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))) (.f64 (/.f64 1 (sqrt.f64 -1)) (*.f64 1/2 (sqrt.f64 (/.f64 1 eps))))) (sqrt.f64 -1))))) (pow.f64 x 3))))
(+.f64 (neg.f64 (/.f64 x 1)) (+.f64 (+.f64 (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (neg.f64 (.f64 (pow.f64 x 2) (+.f64 (neg.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))) (.f64 (/.f64 1 (sqrt.f64 -1)) (.f64 (sqrt.f64 (/.f64 1 eps)) 1/2)))))) (.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 eps 1))) (neg.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (+.f64 (neg.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))) (.f64 (/.f64 1 (sqrt.f64 -1)) (.f64 (sqrt.f64 (/.f64 1 eps)) 1/2))) (sqrt.f64 -1))))) (pow.f64 x 3))))
(+.f64 (-.f64 (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (/.f64 x 1)) (+.f64 (.f64 (pow.f64 x 2) (-.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1))) (.f64 (/.f64 1 (sqrt.f64 -1)) (.f64 (sqrt.f64 (/.f64 1 eps)) 1/2)))) (.f64 (+.f64 (.f64 1/2 (/.f64 1 eps)) (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (.f64 (sqrt.f64 (/.f64 1 eps)) 1/2)) (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))) (sqrt.f64 -1)))) (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 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (*.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 (+.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 -1 (/.f64 (+.f64 (.f64 -1/32 (pow.f64 eps 4)) (.f64 (pow.f64 eps 4) -1/128)) (pow.f64 x 7)))))
(+.f64 (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))) (neg.f64 (/.f64 (+.f64 (.f64 -1/32 (pow.f64 eps 4)) (*.f64 (pow.f64 eps 4) -1/128)) (pow.f64 x 7))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (-.f64 (.f64 1/2 (/.f64 eps x)) (/.f64 (+.f64 (.f64 -1/32 (pow.f64 eps 4)) (*.f64 (pow.f64 eps 4) -1/128)) (pow.f64 x 7)))))
(*.f64 2 x)
(*.f64 x 2)
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(if (!=.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

localize85.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	18.3b	(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
✓	30.0b	(/.f64 (pow.f64 eps 2) (pow.f64 x 3))
✓	35.8b	(/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
✓	36.2b	(/.f64 (pow.f64 eps 3) (pow.f64 x 5))

Compiler

Compiled 222 to 168 computations (24.3% saved)

series9.0ms (0.2%)

Counts

4 → 48

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
1.0ms	x	@	0	(/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
1.0ms	eps	@	0	(/.f64 (pow.f64 eps 3) (pow.f64 x 5))
1.0ms	x	@	0	(/.f64 (pow.f64 eps 3) (pow.f64 x 5))
1.0ms	eps	@	inf	(/.f64 (pow.f64 eps 3) (pow.f64 x 5))

rewrite81.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1208×	`rational_best-simplify-61`
1148×	`rational_best-simplify-65`
936×	`rational_best-simplify-3`
790×	`rational_best-simplify-62`
586×	`rational_best-simplify-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	208
1	100	208
2	543	172
3	3468	172

Stop Event

1×	node limit

Counts

4 → 34

Calls

Call 1

Inputs
(/.f64 (pow.f64 eps 3) (pow.f64 x 5))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (pow.f64 eps 2) (pow.f64 x 3))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 eps 2) 2)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))

Outputs
()
()
()
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simplify171.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1120×	`rational_best-simplify-1`
930×	`rational_best-simplify-53`
598×	`rational_best-simplify-21`
596×	`rational_best-simplify-18`
588×	`rational_best-simplify-52`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	171	8148
1	950	7968
2	6217	7968

Stop Event

1×	node limit

Counts

82 → 84

Calls

Call 1

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

Outputs
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 5/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))
(/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7))
(*.f64 1/2 (/.f64 eps x))
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(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128) (.f64 1/2 (/.f64 eps x)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128))))
(+.f64 (-.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) -5/128)) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(*.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128)
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))
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(-.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) -5/128))
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(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (-.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) -5/128)))
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(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128) (.f64 1/2 (/.f64 eps x)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128))))
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(*.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))
(*.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128)
(+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) -5/128))
(+.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 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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (-.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) -5/128)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128) (.f64 1/2 (/.f64 eps x)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) 5/128))))
(+.f64 (-.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)) -5/128)) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (*.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7)))
(.f64 (/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (*.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7)) 1/2)
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 (/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7)) 1/2))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 (/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7)) -1/2))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (*.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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 (/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (*.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7)) 1/2)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (-.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 (/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (*.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7)) -1/2)))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/64 (pow.f64 eps 4)) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/8 (/.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))))))
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(-.f64 (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))) (.f64 (/.f64 (+.f64 (.f64 (pow.f64 eps 4) 1/64) (.f64 (pow.f64 eps 4) 1/16)) (pow.f64 x 7)) -1/2))
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(*.f64 1/2 (/.f64 eps x))
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(*.f64 1/2 (/.f64 eps x))
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(if (!=.f64 (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) 0) (/.f64 (-.f64 (.f64 (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))) (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (.f64 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16) (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8))))) (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (-.f64 (.f64 1/2 (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (+.f64 (.f64 1/2 (/.f64 eps x)) (-.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16)))))
(-.f64 (.f64 1/2 (/.f64 (.f64 5/64 (pow.f64 eps 4)) (pow.f64 x 7))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) (+.f64 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16) (*.f64 (/.f64 eps x) -1/2))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 (*.f64 5/64 (pow.f64 eps 4)) (pow.f64 x 7))))))
(if (!=.f64 (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) 1/16)) 0) (/.f64 (-.f64 (.f64 (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) 1/16)) (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) 1/16))) (.f64 (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) 1/16)) (+.f64 (.f64 (/.f64 eps x) -1/2) (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8)))) (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) 1/16))) (+.f64 (.f64 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7)) 1/2) (+.f64 (.f64 1/2 (/.f64 eps x)) (-.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) 1/8) (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16)))))
(-.f64 (.f64 1/2 (/.f64 (.f64 5/64 (pow.f64 eps 4)) (pow.f64 x 7))) (+.f64 (.f64 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)) -1/8) (+.f64 (.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16) (*.f64 (/.f64 eps x) -1/2))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 1/2 (/.f64 (*.f64 5/64 (pow.f64 eps 4)) (pow.f64 x 7))))))

eval427.0ms (7.6%)

Compiler: Compiled 35314 to 12893 computations (63.5% saved)

prune136.0ms (2.4%)

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	666	3	669
Fresh	2	1	3
Picked	1	0	1
Done	3	6	9
Total	672	10	682

Error

0.0b

Counts

682 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.3b	(if (!=.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	30.7b	(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 (.f64 eps 1/2) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	59.4b	(-.f64 x (-.f64 x (*.f64 1/2 (/.f64 eps x))))
✓	24.5b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	27.4b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	61.3b	(-.f64 x x)
✓	38.4b	(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
✓	35.3b	(*.f64 1/2 (/.f64 eps x))
✓	27.2b	(neg.f64 (sqrt.f64 (neg.f64 eps)))
	61.8b	x

Compiler

Compiled 123 to 71 computations (42.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 1/2 (/.f64 eps x)))
✓	3.6b	(-.f64 x (-.f64 x (*.f64 1/2 (/.f64 eps x))))

Compiler

Compiled 29 to 13 computations (55.2% saved)

series37.0ms (0.7%)

Counts

2 → 48

Calls

12 calls:

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

rewrite78.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

904×	`rational_best-simplify-111`
830×	`rational_best-simplify-61`
830×	`rational_best-simplify-96`
800×	`rational_best-simplify-65`
568×	`rational_best-simplify-110`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	44
1	61	44
2	338	44
3	2282	44

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1066×	`rational_best-simplify-61`
1018×	`rational_best-simplify-65`
746×	`rational_best-simplify-62`
718×	`rational_best-simplify-3`
600×	`rational_best-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	139	1554
1	557	1554
2	4152	1554

Stop Event

1×	node limit

Counts

102 → 59

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 -1/2 (/.f64 eps x))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
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x
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x
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x
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(/.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 -1 (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 1))
(/.f64 (+.f64 (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 (.f64 1/2 (/.f64 eps x)) x)) (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 (.f64 1/2 (/.f64 eps x)) x))) -4)
(/.f64 (+.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 -1 (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 -1 (-.f64 (.f64 1/2 (/.f64 eps x)) x)))) (+.f64 (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 1) (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 1)))
(pow.f64 (+.f64 x (*.f64 (/.f64 eps x) -1/2)) 1)
(neg.f64 (-.f64 (*.f64 1/2 (/.f64 eps x)) x))
(if (!=.f64 (+.f64 x (.f64 1/2 (/.f64 eps x))) 0) (/.f64 (-.f64 (.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/2 (/.f64 eps x))) (.f64 x x)) (-.f64 (.f64 (/.f64 eps x) -1/2) x)) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(if (!=.f64 (.f64 1/2 (/.f64 eps x)) 0) (/.f64 (.f64 1/2 (.f64 (/.f64 eps x) (+.f64 x (.f64 (/.f64 eps x) -1/2)))) (.f64 1/2 (/.f64 eps x))) (+.f64 x (.f64 (/.f64 eps x) -1/2)))
(if (!=.f64 x 0) (/.f64 (.f64 x (+.f64 x (.f64 (/.f64 eps x) -1/2))) x) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(if (!=.f64 (-.f64 (.f64 (/.f64 eps x) -1/2) x) 0) (/.f64 (-.f64 (.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/2 (/.f64 eps x))) (.f64 x x)) (-.f64 (.f64 (/.f64 eps x) -1/2) x)) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(if (!=.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 0) (/.f64 (.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) (+.f64 x (.f64 (/.f64 eps x) -1/2))) (+.f64 x (.f64 (/.f64 eps x) -1/2))) (+.f64 x (.f64 (/.f64 eps x) -1/2)))
(if (!=.f64 (neg.f64 x) 0) (/.f64 (.f64 x (+.f64 x (.f64 (/.f64 eps x) -1/2))) x) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(if (!=.f64 (.f64 (/.f64 eps x) -1/2) 0) (/.f64 (.f64 1/2 (.f64 (/.f64 eps x) (+.f64 x (.f64 (/.f64 eps x) -1/2)))) (.f64 1/2 (/.f64 eps x))) (+.f64 x (.f64 (/.f64 eps x) -1/2)))
(if (!=.f64 0 0) (/.f64 (neg.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 0)) 0) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(if (!=.f64 -1 0) (+.f64 x (.f64 (/.f64 eps x) -1/2)) (+.f64 x (.f64 (/.f64 eps x) -1/2)))

Outputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 -1/2 (/.f64 eps x))
(*.f64 (/.f64 eps x) -1/2)
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(*.f64 -1/2 (/.f64 eps x))
(*.f64 (/.f64 eps x) -1/2)
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(*.f64 -1/2 (/.f64 eps x))
(*.f64 (/.f64 eps x) -1/2)
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (*.f64 1/2 (/.f64 eps x)) (-.f64 x x))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)) 0)
(*.f64 1/2 (/.f64 eps x))
(+.f64 (-.f64 (*.f64 1/2 (/.f64 eps x)) x) x)
(*.f64 1/2 (/.f64 eps x))
(+.f64 0 (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (+.f64 x (*.f64 1/2 (/.f64 eps x))) (neg.f64 x))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (neg.f64 x) (+.f64 x (*.f64 1/2 (/.f64 eps x))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (-.f64 x x) (*.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(.f64 (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x)) 1)
(*.f64 1/2 (/.f64 eps x))
(.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) -1)
(*.f64 1/2 (/.f64 eps x))
(.f64 -1 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)) 1)
(*.f64 1/2 (/.f64 eps x))
(/.f64 (-.f64 (+.f64 x (*.f64 (/.f64 eps x) -1/2)) x) -1)
(*.f64 1/2 (/.f64 eps x))
(/.f64 (+.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x)) -2)
(*.f64 1/2 (/.f64 eps x))
(/.f64 (.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) (-.f64 -1 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x))) (+.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) 1))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (+.f64 (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x)) (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x))) 2)
(*.f64 1/2 (/.f64 eps x))
(/.f64 (+.f64 (+.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x)) (+.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x))) -4)
(*.f64 1/2 (/.f64 eps x))
(/.f64 (+.f64 (.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) (-.f64 -1 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x))) (.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) (-.f64 -1 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x)))) (+.f64 (+.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) 1) (+.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) 1)))
(*.f64 1/2 (/.f64 eps x))
(pow.f64 (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)) 1)
(*.f64 1/2 (/.f64 eps x))
(neg.f64 (-.f64 (+.f64 x (*.f64 (/.f64 eps x) -1/2)) x))
(*.f64 1/2 (/.f64 eps x))
(if (!=.f64 (+.f64 x (+.f64 x (.f64 (/.f64 eps x) -1/2))) 0) (/.f64 (+.f64 (.f64 x x) (.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (+.f64 x (+.f64 x (.f64 (/.f64 eps x) -1/2)))) (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(if (!=.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) 0) (/.f64 (.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (+.f64 x (.f64 (/.f64 eps x) -1/2))) (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(if (!=.f64 x 0) (/.f64 (.f64 x (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x))) x) (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(if (!=.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 0) (/.f64 (.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (+.f64 x (.f64 (/.f64 eps x) -1/2))) (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(if (!=.f64 (-.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) x) 0) (/.f64 (+.f64 (.f64 x x) (.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (+.f64 x (+.f64 x (.f64 (/.f64 eps x) -1/2)))) (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(if (!=.f64 (neg.f64 x) 0) (/.f64 (.f64 x (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x))) x) (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(if (!=.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) 0) (/.f64 (.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x)) (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(if (!=.f64 0 0) (/.f64 (neg.f64 (.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) 0)) 0) (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (+.f64 x (*.f64 (/.f64 eps x) -1/2)) 0)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 (*.f64 (/.f64 eps x) -1/2) x)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(+.f64 0 (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) 1)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) -1)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(.f64 -1 (-.f64 (.f64 1/2 (/.f64 eps x)) x))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(.f64 1 (+.f64 x (.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(/.f64 (+.f64 x (*.f64 (/.f64 eps x) -1/2)) 1)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(/.f64 (-.f64 (*.f64 1/2 (/.f64 eps x)) x) -1)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(/.f64 (+.f64 x (+.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) (.f64 (/.f64 eps x) -1/2))) 2)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(/.f64 (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 (.f64 1/2 (/.f64 eps x)) x)) -2)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(/.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 -1 (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 1))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(/.f64 (+.f64 (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 (.f64 1/2 (/.f64 eps x)) x)) (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 (.f64 1/2 (/.f64 eps x)) x))) -4)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(/.f64 (+.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 -1 (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) (-.f64 -1 (-.f64 (.f64 1/2 (/.f64 eps x)) x)))) (+.f64 (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 1) (+.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 1)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(pow.f64 (+.f64 x (*.f64 (/.f64 eps x) -1/2)) 1)
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(neg.f64 (-.f64 (*.f64 1/2 (/.f64 eps x)) x))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(if (!=.f64 (+.f64 x (.f64 1/2 (/.f64 eps x))) 0) (/.f64 (-.f64 (.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/2 (/.f64 eps x))) (.f64 x x)) (-.f64 (.f64 (/.f64 eps x) -1/2) x)) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(if (!=.f64 (.f64 1/2 (/.f64 eps x)) 0) (/.f64 (.f64 1/2 (.f64 (/.f64 eps x) (+.f64 x (.f64 (/.f64 eps x) -1/2)))) (.f64 1/2 (/.f64 eps x))) (+.f64 x (.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(if (!=.f64 x 0) (/.f64 (.f64 x (+.f64 x (.f64 (/.f64 eps x) -1/2))) x) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(if (!=.f64 (-.f64 (.f64 (/.f64 eps x) -1/2) x) 0) (/.f64 (-.f64 (.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/2 (/.f64 eps x))) (.f64 x x)) (-.f64 (.f64 (/.f64 eps x) -1/2) x)) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(if (!=.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 0) (/.f64 (.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) (+.f64 x (.f64 (/.f64 eps x) -1/2))) (+.f64 x (.f64 (/.f64 eps x) -1/2))) (+.f64 x (.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(if (!=.f64 (neg.f64 x) 0) (/.f64 (.f64 x (+.f64 x (.f64 (/.f64 eps x) -1/2))) x) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(if (!=.f64 (.f64 (/.f64 eps x) -1/2) 0) (/.f64 (.f64 1/2 (.f64 (/.f64 eps x) (+.f64 x (.f64 (/.f64 eps x) -1/2)))) (.f64 1/2 (/.f64 eps x))) (+.f64 x (.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(if (!=.f64 0 0) (/.f64 (neg.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) 0)) 0) (+.f64 x (*.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))
(if (!=.f64 -1 0) (+.f64 x (.f64 (/.f64 eps x) -1/2)) (+.f64 x (.f64 (/.f64 eps x) -1/2)))
(+.f64 x (*.f64 (/.f64 eps x) -1/2))

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.3b	(/.f64 (.f64 eps 1/2) (sqrt.f64 (-.f64 (.f64 x x) eps)))
	3.9b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 75 to 23 computations (69.3% saved)

series7.0ms (0.1%)

Counts

1 → 16

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	(/.f64 (.f64 eps 1/2) (sqrt.f64 (-.f64 (.f64 x x) eps)))
1.0ms	x	@	0	(/.f64 (.f64 eps 1/2) (sqrt.f64 (-.f64 (.f64 x x) eps)))
1.0ms	eps	@	inf	(/.f64 (.f64 eps 1/2) (sqrt.f64 (-.f64 (.f64 x x) eps)))
1.0ms	eps	@	-inf	(/.f64 (.f64 eps 1/2) (sqrt.f64 (-.f64 (.f64 x x) eps)))
1.0ms	x	@	inf	(/.f64 (.f64 eps 1/2) (sqrt.f64 (-.f64 (.f64 x x) eps)))

rewrite47.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

908×	`rational_best-simplify-113`
594×	`rational_best-simplify-124`
556×	`rational_best-simplify-96`
544×	`rational_best-simplify-65`
544×	`rational_best-simplify-61`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	46	29
2	236	29
3	1542	29

Stop Event

1×	node limit

Counts

1 → 0

Calls

Call 1

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

Outputs
()

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

880×	`rational_best-simplify-65`
852×	`rational_best-simplify-61`
688×	`rational_best-simplify-113`
682×	`rational_best-simplify-96`
656×	`rational_best-simplify-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1652
1	435	1628
2	2467	1466

Stop Event

1×	node limit

Counts

16 → 45

Calls

Call 1

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

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

localize41.0ms (0.7%)

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)))
✓	0.3b	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	3.9b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 84 to 14 computations (83.3% saved)

series3.0ms (0%)

Counts

2 → 32

Calls

12 calls:

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

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`rational_best-simplify-113`
624×	`rational_best-simplify-96`
608×	`rational_best-simplify-117`
604×	`rational_best-simplify-61`
600×	`rational_best-simplify-65`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	52
1	46	52
2	256	52
3	1699	52

Stop Event

1×	node limit

Counts

2 → 17

Calls

Call 1

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

Outputs

()

((#(struct:change #<rule egg-rr> (2) ((x -.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (neg.f64 x) (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))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (neg.f64 x) (+.f64 x (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps))))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) (-.f64 1 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 0) (/.f64 (-.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (*.f64 x x)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 x) 0) (/.f64 (*.f64 x (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) 0) (/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0) (/.f64 (-.f64 (*.f64 x x) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 x 0) (/.f64 (*.f64 x (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0) (/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1012×	`rational_best-simplify-3`
966×	`rational_best-simplify-1`
688×	`rational_best-simplify-53`
596×	`rational_best-simplify-21`
590×	`rational_best-simplify-20`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	2513
1	877	2473
2	5043	2415

Stop Event

1×	node limit

Counts

49 → 80

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2)))))
(+.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 4) eps))) (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (sqrt.f64 -1))))) (pow.f64 x 3)) (+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (*.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/32 (pow.f64 eps 4)) (.f64 -1/128 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 -2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (.f64 eps (pow.f64 x 5)))) (.f64 -1/4 (/.f64 (.f64 eps (+.f64 (.f64 -1/4 (pow.f64 eps 2)) (*.f64 1/8 (pow.f64 eps 2)))) (pow.f64 x 5)))))))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 eps))
(+.f64 x (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(+.f64 x (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps))))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 x (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/16 (pow.f64 eps 4)) (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2)) (pow.f64 x 7))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(-.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 x))
(-.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0)
(-.f64 0 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 -1 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))) -1)
(/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 1)
(/.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) -1)
(/.f64 (-.f64 (neg.f64 x) (+.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps))))) -2)
(/.f64 (-.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (-.f64 1 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(neg.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) 0) (/.f64 (-.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) (.f64 x x)) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (neg.f64 x) 0) (/.f64 (.f64 x (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(if (!=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (-.f64 (.f64 x x) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 x 0) (/.f64 (.f64 x (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (!=.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (+.f64 x (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 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 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))))))
(*.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps))
(*.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1)))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (.f64 -1 (/.f64 x 1)))
(+.f64 (*.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (neg.f64 (/.f64 x 1)))
(-.f64 (*.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) x)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2)))))
(+.f64 (.f64 -1 (/.f64 x 1)) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1))))) (pow.f64 x 2))) (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1)))))
(+.f64 (+.f64 (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) (neg.f64 (/.f64 x 1))) (neg.f64 (.f64 (+.f64 (neg.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))) (.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1))))) (pow.f64 x 2))))
(+.f64 (-.f64 (.f64 (sqrt.f64 eps) (/.f64 1 (sqrt.f64 -1))) x) (.f64 (pow.f64 x 2) (-.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1))) (.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (sqrt.f64 -1)))))))
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(*.f64 2 x)
(*.f64 x 2)
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(*.f64 x 2)
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(-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 x))
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(-.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 0)
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(-.f64 0 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
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(.f64 -1 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))))
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(.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))) -1)
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(/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) 1)
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(if (!=.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) 0) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
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eval420.0ms (7.5%)

Compiler: Compiled 25753 to 10061 computations (60.9% saved)

prune179.0ms (3.2%)

Pruning

16 alts after pruning (9 fresh and 7 done)

	Pruned	Kept	Total
New	625	8	633
Fresh	0	1	1
Picked	1	0	1
Done	1	7	8
Total	627	16	643

Error

0.0b

Counts

643 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	59.7b	(if (!=.f64 (-.f64 (-.f64 (.f64 1/2 (/.f64 eps x)) x) x) 0) (/.f64 (+.f64 (.f64 x x) (.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) (-.f64 (.f64 1/2 (/.f64 eps x)) x))) (+.f64 x (+.f64 x (.f64 (/.f64 eps x) -1/2)))) (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)))
	35.3b	(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 (.f64 eps 1/2) (-.f64 x (.f64 1/2 (/.f64 eps x)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	0.3b	(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
	59.4b	(if (!=.f64 x 0) (/.f64 (.f64 x (+.f64 x (-.f64 (.f64 1/2 (/.f64 eps x)) x))) x) (+.f64 x (-.f64 (*.f64 1/2 (/.f64 eps x)) x)))
	59.7b	(/.f64 (.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) (-.f64 -1 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x))) (+.f64 (-.f64 (+.f64 x (.f64 (/.f64 eps x) -1/2)) x) 1))
	59.7b	(-.f64 x (if (!=.f64 (-.f64 (.f64 (/.f64 eps x) -1/2) x) 0) (/.f64 (-.f64 (.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/2 (/.f64 eps x))) (.f64 x x)) (-.f64 (.f64 (/.f64 eps x) -1/2) x)) (+.f64 x (*.f64 (/.f64 eps x) -1/2))))
	59.7b	(-.f64 x (if (!=.f64 (.f64 (/.f64 eps x) -1/2) 0) (/.f64 (.f64 1/2 (.f64 (/.f64 eps x) (+.f64 x (.f64 (/.f64 eps x) -1/2)))) (.f64 1/2 (/.f64 eps x))) (+.f64 x (.f64 (/.f64 eps x) -1/2))))
✓	59.4b	(-.f64 x (-.f64 x (*.f64 1/2 (/.f64 eps x))))
	60.6b	(-.f64 x (*.f64 (/.f64 eps x) -1/2))
✓	24.5b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	27.4b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	61.3b	(-.f64 x x)
✓	38.4b	(+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
✓	35.3b	(*.f64 1/2 (/.f64 eps x))
✓	27.2b	(neg.f64 (sqrt.f64 (neg.f64 eps)))
	61.8b	x

Compiler

Compiled 325 to 193 computations (40.6% saved)

regimes45.0ms (0.8%)

Counts

25 → 1

Calls

Call 1

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

Outputs
(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))

Calls

3 calls:

12.0ms	eps
12.0ms	x
11.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

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

Compiler

Compiled 583 to 233 computations (60% saved)

regimes105.0ms (1.9%)

Counts

15 → 2

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 (.f64 eps 1/2) (-.f64 x (.f64 1/2 (/.f64 eps x)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Calls

3 calls:

72.0ms	eps
15.0ms	x
13.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Error	Segments	Branch
5.3b	2	`x`
8.8b	4	`eps`
1.0b	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 275 to 135 computations (50.9% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.7448582974516274e-154	-2.757956379393094e-155

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes92.0ms (1.6%)

Counts

14 → 2

Calls

Call 1

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

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

Calls

3 calls:

41.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
27.0ms	eps
14.0ms	x

Results

Error	Segments	Branch
5.3b	2	`x`
8.8b	4	`eps`
1.0b	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 250 to 126 computations (49.6% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.7448582974516274e-154	-2.757956379393094e-155

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes44.0ms (0.8%)

Counts

13 → 2

Calls

Call 1

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

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

Calls

2 calls:

26.0ms	eps
13.0ms	x

Results

Error	Segments	Branch
6.2b	2	`x`
10.3b	4	`eps`

Compiler

Compiled 232 to 117 computations (49.6% saved)

bsearch9.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
9.0ms	6.595397259269318e-105	1.1166495478514317e-104

Results

5.0ms	52×	body	256	valid
2.0ms	12×	body	512	valid
2.0ms	7×	body	256	invalid

Compiler

Compiled 79 to 58 computations (26.6% saved)

regimes69.0ms (1.2%)

Counts

12 → 2

Calls

Call 1

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

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

Calls

2 calls:

51.0ms	eps
13.0ms	x

Results

Error	Segments	Branch
6.5b	2	`x`
10.3b	4	`eps`

Compiler

Compiled 227 to 116 computations (48.9% saved)

bsearch9.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
9.0ms	6.595397259269318e-105	1.1166495478514317e-104

Results

5.0ms	55×	body	256	valid
2.0ms	9×	body	512	valid
1.0ms	8×	body	256	invalid

Compiler

Compiled 75 to 58 computations (22.7% saved)

regimes53.0ms (0.9%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

2 calls:

43.0ms	eps
6.0ms	x

Results

Error	Segments	Branch
35.3b	1	`x`
35.3b	1	`eps`

Compiler

Compiled 223 to 113 computations (49.3% saved)

regimes8.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(-.f64 x x)

Calls

2 calls:

4.0ms	eps
3.0ms	x

Results

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

Compiler

Compiled 15 to 9 computations (40% saved)

regimes7.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(*.f64 x 2)

Outputs
x

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

Error	Segments	Branch
61.8b	1	`x`
61.8b	1	`eps`

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	354

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 (.f64 eps 1/2) (-.f64 x (.f64 1/2 (/.f64 eps x)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (*.f64 1/2 (/.f64 eps x)))
(if (<=.f64 x 7101187164738999/645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344) (-.f64 x (sqrt.f64 (neg.f64 eps))) (*.f64 1/2 (/.f64 eps x)))
(if (<=.f64 x 1710740544232577/161390617380431786853494948250188242145606612051826469551916209783790476376052574664352834580008614464743948248296718336) (neg.f64 (sqrt.f64 (neg.f64 eps))) (*.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(-.f64 x x)
x

Outputs
(if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (if (!=.f64 (sqrt.f64 (neg.f64 eps)) 0) (/.f64 (.f64 eps 1/2) (-.f64 x (.f64 1/2 (/.f64 eps x)))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (*.f64 1/2 (/.f64 eps x)))
(if (<=.f64 x 7101187164738999/645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344) (-.f64 x (sqrt.f64 (neg.f64 eps))) (*.f64 1/2 (/.f64 eps x)))
(if (<=.f64 x 1710740544232577/161390617380431786853494948250188242145606612051826469551916209783790476376052574664352834580008614464743948248296718336) (neg.f64 (sqrt.f64 (neg.f64 eps))) (*.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(-.f64 x x)
x

Compiler

Compiled 144 to 78 computations (45.8% saved)

soundness74.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1012×	`rational_best-simplify-3`
966×	`rational_best-simplify-1`
688×	`rational_best-simplify-53`
596×	`rational_best-simplify-21`
590×	`rational_best-simplify-20`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	2513
1	877	2473
2	5043	2415

Stop Event

1×	node limit

Compiler

Compiled 102 to 32 computations (68.6% saved)

end58.0ms (1%)

Compiler: Compiled 130 to 46 computations (64.6% saved)

Details

analyze19.0ms (0.3%)

sample1.5s (27.4%)

preprocess59.0ms (1.1%)

simplify43.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.1%)

series6.0ms (0.1%)

rewrite63.0ms (1.1%)

simplify63.0ms (1.1%)

eval95.0ms (1.7%)

prune59.0ms (1.1%)

localize15.0ms (0.3%)

series7.0ms (0.1%)

rewrite85.0ms (1.5%)

simplify88.0ms (1.6%)

localize3.0ms (0%)

localize5.0ms (0.1%)

localize5.0ms (0.1%)

localize21.0ms (0.4%)

series7.0ms (0.1%)

rewrite84.0ms (1.5%)

simplify59.0ms (1%)

eval219.0ms (3.9%)

prune96.0ms (1.7%)

localize20.0ms (0.4%)

localize3.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite89.0ms (1.6%)

simplify57.0ms (1%)

localize20.0ms (0.4%)

series11.0ms (0.2%)

rewrite73.0ms (1.3%)

simplify94.0ms (1.7%)

localize85.0ms (1.5%)

series9.0ms (0.2%)

rewrite81.0ms (1.4%)

simplify171.0ms (3%)

eval427.0ms (7.6%)

prune136.0ms (2.4%)

localize9.0ms (0.2%)

series37.0ms (0.7%)

rewrite78.0ms (1.4%)

simplify71.0ms (1.3%)

localize18.0ms (0.3%)

series7.0ms (0.1%)

rewrite47.0ms (0.8%)

simplify62.0ms (1.1%)

localize41.0ms (0.7%)

series3.0ms (0%)

rewrite53.0ms (0.9%)

simplify83.0ms (1.5%)

eval420.0ms (7.5%)

prune179.0ms (3.2%)

regimes45.0ms (0.8%)

regimes105.0ms (1.9%)

bsearch0.0ms (0%)

regimes92.0ms (1.6%)

bsearch0.0ms (0%)

regimes44.0ms (0.8%)

bsearch9.0ms (0.2%)

regimes69.0ms (1.2%)

bsearch9.0ms (0.2%)

regimes53.0ms (0.9%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

simplify7.0ms (0.1%)

soundness74.0ms (1.3%)

end58.0ms (1%)

Profiling