Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25.7%	74.3%	0
25.7%	0%	74.3%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.9s (44.5%)

Results

1.1s	6184×	body	256	valid
524.0ms	1024×	body	1024	valid
283.0ms	1025×	body	512	valid
10.0ms	23×	body	2048	valid

preprocess71.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

497×	`associate-l_binary64`
451×	`distribute-rgt-neg-in_binary64`
426×	`distribute-lft-neg-in_binary64`
409×	`associate-r_binary64`
357×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	32	26
2	76	26
3	262	26
4	1173	20
5	4317	20
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 eps eps))
(*.f64 x (+.f64 eps (+.f64 x eps)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify27.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

569×	`distribute-rgt-in_binary64`
517×	`cancel-sign-sub-inv_binary64`
510×	`fma-neg_binary64`
459×	`distribute-lft-in_binary64`
430×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	49	13
3	166	13
4	657	8
5	2742	8

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))
(fma.f64 x (neg.f64 x) (pow.f64 (+.f64 x eps) 2))
(*.f64 eps (fma.f64 2 x eps))

eval1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(*.f64 eps (fma.f64 2 x eps))

Compiler

Compiled 8 to 5 computations (37.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 eps (fma.f64 2 x eps))
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))

Compiler

Compiled 15 to 8 computations (46.7% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite43.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`pow1_binary64`
531×	`add-sqr-sqrt_binary64`
507×	`add-log-exp_binary64`
507×	`log1p-expm1-u_binary64`
507×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	120	8
2	1364	8

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 eps (fma.f64 2 x eps))

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

Outputs

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

simplify155.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

802×	`sqr-pow_binary64`
582×	`fma-def_binary64`
565×	`cube-prod_binary64`
560×	`fabs-mul_binary64`
541×	`pow-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	267
1	18	231
2	37	213
3	75	177
4	165	177
5	456	177
6	1500	177
7	2751	177
8	3106	177
9	3328	177
10	3550	177
11	3856	177
12	4278	177
13	4790	177
14	5357	177
15	6055	177
16	6905	177
17	7296	177
18	7584	177
19	7860	177
20	7932	177
21	7968	177

Stop Event

1×	node limit

Counts

37 → 18

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))

Outputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))

eval4.0ms (0.1%)

Compiler: Compiled 142 to 87 computations (38.7% saved)

prune5.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	14	4	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	5	19

Error

0.0b

Counts

19 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
▶	26.4b	(cbrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3))
▶	16.5b	(*.f64 eps eps)
▶	21.6b	(.f64 2 (.f64 eps x))

Compiler

Compiled 42 to 28 computations (33.3% saved)

localize36.0ms (0.8%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(.f64 2 (.f64 eps x))
✓	0.0b	(.f64 2 (.f64 eps x))

Compiler

Compiled 13 to 6 computations (53.8% saved)

series4.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

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

rewrite53.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

554×	`pow1_binary64`
509×	`add-log-exp_binary64`
509×	`log1p-expm1-u_binary64`
509×	`expm1-log1p-u_binary64`
499×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1392	7

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))

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

Outputs

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

simplify98.0ms (2.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

11 → 11

Calls

Call 1

Inputs

Outputs

localize3.0ms (0.1%)

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

localize19.0ms (0.4%)

Local error

Found 6 expressions with local error:

New	Error	Program
	26.4b	(cbrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3))
	0.1b	(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3)
	0.0b	(*.f64 eps (fma.f64 2 x eps))
	0.0b	(*.f64 eps (fma.f64 2 x eps))
✓	0.1b	(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3)
✓	26.4b	(cbrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3))

Compiler

Compiled 33 to 20 computations (39.4% saved)

series11.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3)
2.0ms	eps	@	-inf	(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3)
2.0ms	eps	@	-inf	(cbrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3))
1.0ms	eps	@	0	(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3)
1.0ms	x	@	-inf	(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3)

rewrite72.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

717×	`pow1_binary64`
671×	`add-log-exp_binary64`
670×	`log1p-expm1-u_binary64`
670×	`expm1-log1p-u_binary64`
654×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	190	19
2	1922	19

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3))
(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3)

Outputs

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

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

simplify123.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-def_binary64`
599×	`fma-neg_binary64`
431×	`associate-+l+_binary64`
369×	`associate-l_binary64`
326×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	922
1	271	874
2	931	829
3	3207	787
4	7169	787

Stop Event

1×	node limit

Counts

104 → 89

Calls

Call 1

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

Outputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(.f64 -1 (.f64 (pow.f64 eps 2) (cbrt.f64 -1)))
(neg.f64 (.f64 (.f64 eps eps) (cbrt.f64 -1)))
(.f64 (.f64 eps eps) (neg.f64 (cbrt.f64 -1)))
(.f64 eps (neg.f64 (.f64 eps (cbrt.f64 -1))))
(+.f64 (.f64 -2 (.f64 eps (.f64 (cbrt.f64 -1) x))) (.f64 -1 (*.f64 (pow.f64 eps 2) (cbrt.f64 -1))))
(fma.f64 -2 (.f64 eps (.f64 x (cbrt.f64 -1))) (neg.f64 (.f64 (.f64 eps eps) (cbrt.f64 -1))))
(fma.f64 -2 (.f64 x (.f64 eps (cbrt.f64 -1))) (.f64 (.f64 eps eps) (neg.f64 (cbrt.f64 -1))))
(.f64 (.f64 eps (cbrt.f64 -1)) (-.f64 (*.f64 x -2) eps))
(.f64 eps (.f64 (cbrt.f64 -1) (-.f64 (*.f64 x -2) eps)))
(.f64 (.f64 eps (cbrt.f64 -1)) (fma.f64 x -2 (neg.f64 eps)))
(+.f64 (.f64 -2 (.f64 eps (.f64 (cbrt.f64 -1) x))) (.f64 -1 (*.f64 (pow.f64 eps 2) (cbrt.f64 -1))))
(fma.f64 -2 (.f64 eps (.f64 x (cbrt.f64 -1))) (neg.f64 (.f64 (.f64 eps eps) (cbrt.f64 -1))))
(fma.f64 -2 (.f64 x (.f64 eps (cbrt.f64 -1))) (.f64 (.f64 eps eps) (neg.f64 (cbrt.f64 -1))))
(.f64 (.f64 eps (cbrt.f64 -1)) (-.f64 (*.f64 x -2) eps))
(.f64 eps (.f64 (cbrt.f64 -1) (-.f64 (*.f64 x -2) eps)))
(.f64 (.f64 eps (cbrt.f64 -1)) (fma.f64 x -2 (neg.f64 eps)))
(+.f64 (.f64 -2 (.f64 eps (.f64 (cbrt.f64 -1) x))) (.f64 -1 (*.f64 (pow.f64 eps 2) (cbrt.f64 -1))))
(fma.f64 -2 (.f64 eps (.f64 x (cbrt.f64 -1))) (neg.f64 (.f64 (.f64 eps eps) (cbrt.f64 -1))))
(fma.f64 -2 (.f64 x (.f64 eps (cbrt.f64 -1))) (.f64 (.f64 eps eps) (neg.f64 (cbrt.f64 -1))))
(.f64 (.f64 eps (cbrt.f64 -1)) (-.f64 (*.f64 x -2) eps))
(.f64 eps (.f64 (cbrt.f64 -1) (-.f64 (*.f64 x -2) eps)))
(.f64 (.f64 eps (cbrt.f64 -1)) (fma.f64 x -2 (neg.f64 eps)))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)))
(.f64 (.f64 8 (pow.f64 eps 3)) (pow.f64 x 3))
(.f64 (pow.f64 eps 3) (.f64 8 (pow.f64 x 3)))
(+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (pow.f64 eps 4) (+.f64 (.f64 4 (pow.f64 x 2)) (*.f64 8 (pow.f64 x 2)))))
(fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (pow.f64 eps 4) (.f64 (.f64 x x) 12)))
(fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (.f64 (.f64 (pow.f64 eps 4) 12) x) x))
(.f64 (.f64 x x) (+.f64 (.f64 x (.f64 8 (pow.f64 eps 3))) (*.f64 (pow.f64 eps 4) 12)))
(.f64 x (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (*.f64 eps 12)))))
(+.f64 (.f64 (pow.f64 eps 5) (+.f64 (.f64 2 x) (.f64 4 x))) (+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (pow.f64 eps 4) (+.f64 (.f64 4 (pow.f64 x 2)) (.f64 8 (pow.f64 x 2))))))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (pow.f64 eps 4) (.f64 (*.f64 x x) 12))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (.f64 (*.f64 (pow.f64 eps 4) 12) x) x)))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 8 (pow.f64 eps 3))) (.f64 (pow.f64 eps 4) 12))))
(.f64 x (+.f64 (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (.f64 eps 12)))) (.f64 (pow.f64 eps 5) 6)))
(+.f64 (.f64 (pow.f64 eps 5) (+.f64 (.f64 2 x) (.f64 4 x))) (+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (+.f64 (pow.f64 eps 6) (.f64 (pow.f64 eps 4) (+.f64 (.f64 4 (pow.f64 x 2)) (.f64 8 (pow.f64 x 2)))))))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (+.f64 (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (pow.f64 eps 6)) (.f64 (pow.f64 eps 4) (.f64 (*.f64 x x) 12))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 (.f64 8 (pow.f64 eps 3)) (pow.f64 x 3) (fma.f64 (.f64 x x) (.f64 (pow.f64 eps 4) 12) (pow.f64 eps 6))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 x (.f64 x (.f64 (pow.f64 eps 4) 12)) (fma.f64 (pow.f64 x 3) (.f64 8 (pow.f64 eps 3)) (pow.f64 eps 6))))
(+.f64 (pow.f64 eps 6) (.f64 x (+.f64 (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (.f64 eps 12)))) (.f64 (pow.f64 eps 5) 6))))
(pow.f64 eps 6)
(+.f64 (.f64 (pow.f64 eps 5) (+.f64 (.f64 2 x) (*.f64 4 x))) (pow.f64 eps 6))
(fma.f64 (pow.f64 eps 5) (*.f64 x 6) (pow.f64 eps 6))
(fma.f64 x (*.f64 (pow.f64 eps 5) 6) (pow.f64 eps 6))
(+.f64 (.f64 (pow.f64 eps 5) (+.f64 (.f64 2 x) (.f64 4 x))) (+.f64 (pow.f64 eps 6) (.f64 (pow.f64 eps 4) (+.f64 (.f64 4 (pow.f64 x 2)) (.f64 8 (pow.f64 x 2))))))
(+.f64 (fma.f64 (pow.f64 eps 5) (.f64 x 6) (pow.f64 eps 6)) (.f64 (pow.f64 eps 4) (.f64 (.f64 x x) 12)))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (fma.f64 (.f64 x x) (*.f64 (pow.f64 eps 4) 12) (pow.f64 eps 6)))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 (.f64 (pow.f64 eps 4) (*.f64 x x)) 12 (pow.f64 eps 6)))
(+.f64 (pow.f64 eps 6) (.f64 x (fma.f64 x (.f64 (pow.f64 eps 4) 12) (*.f64 (pow.f64 eps 5) 6))))
(+.f64 (.f64 (pow.f64 eps 5) (+.f64 (.f64 2 x) (.f64 4 x))) (+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (+.f64 (pow.f64 eps 6) (.f64 (pow.f64 eps 4) (+.f64 (.f64 4 (pow.f64 x 2)) (.f64 8 (pow.f64 x 2)))))))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (+.f64 (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (pow.f64 eps 6)) (.f64 (pow.f64 eps 4) (.f64 (*.f64 x x) 12))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 (.f64 8 (pow.f64 eps 3)) (pow.f64 x 3) (fma.f64 (.f64 x x) (.f64 (pow.f64 eps 4) 12) (pow.f64 eps 6))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 x (.f64 x (.f64 (pow.f64 eps 4) 12)) (fma.f64 (pow.f64 x 3) (.f64 8 (pow.f64 eps 3)) (pow.f64 eps 6))))
(+.f64 (pow.f64 eps 6) (.f64 x (+.f64 (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (.f64 eps 12)))) (.f64 (pow.f64 eps 5) 6))))
(pow.f64 eps 6)
(+.f64 (pow.f64 eps 6) (.f64 -1 (.f64 (pow.f64 eps 5) (+.f64 (.f64 -2 x) (.f64 -4 x)))))
(fma.f64 (pow.f64 eps 5) (*.f64 x 6) (pow.f64 eps 6))
(fma.f64 x (*.f64 (pow.f64 eps 5) 6) (pow.f64 eps 6))
(+.f64 (pow.f64 eps 6) (+.f64 (.f64 -1 (.f64 (pow.f64 eps 5) (+.f64 (.f64 -2 x) (.f64 -4 x)))) (.f64 (pow.f64 eps 4) (+.f64 (.f64 4 (pow.f64 x 2)) (*.f64 8 (pow.f64 x 2))))))
(+.f64 (fma.f64 (pow.f64 eps 5) (.f64 x 6) (pow.f64 eps 6)) (.f64 (pow.f64 eps 4) (.f64 (.f64 x x) 12)))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (fma.f64 (.f64 x x) (*.f64 (pow.f64 eps 4) 12) (pow.f64 eps 6)))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 (.f64 (pow.f64 eps 4) (*.f64 x x)) 12 (pow.f64 eps 6)))
(+.f64 (pow.f64 eps 6) (.f64 x (fma.f64 x (.f64 (pow.f64 eps 4) 12) (*.f64 (pow.f64 eps 5) 6))))
(+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (+.f64 (pow.f64 eps 6) (+.f64 (.f64 -1 (.f64 (pow.f64 eps 5) (+.f64 (.f64 -2 x) (.f64 -4 x)))) (.f64 (pow.f64 eps 4) (+.f64 (.f64 4 (pow.f64 x 2)) (*.f64 8 (pow.f64 x 2)))))))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (+.f64 (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (pow.f64 eps 6)) (.f64 (pow.f64 eps 4) (.f64 (*.f64 x x) 12))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 (.f64 8 (pow.f64 eps 3)) (pow.f64 x 3) (fma.f64 (.f64 x x) (.f64 (pow.f64 eps 4) 12) (pow.f64 eps 6))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 x (.f64 x (.f64 (pow.f64 eps 4) 12)) (fma.f64 (pow.f64 x 3) (.f64 8 (pow.f64 eps 3)) (pow.f64 eps 6))))
(+.f64 (pow.f64 eps 6) (.f64 x (+.f64 (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (.f64 eps 12)))) (.f64 (pow.f64 eps 5) 6))))
(pow.f64 eps 6)
(+.f64 (.f64 (+.f64 (.f64 2 (pow.f64 eps 5)) (*.f64 4 (pow.f64 eps 5))) x) (pow.f64 eps 6))
(fma.f64 (pow.f64 eps 5) (*.f64 x 6) (pow.f64 eps 6))
(fma.f64 x (*.f64 (pow.f64 eps 5) 6) (pow.f64 eps 6))
(+.f64 (.f64 (+.f64 (.f64 4 (pow.f64 eps 4)) (.f64 8 (pow.f64 eps 4))) (pow.f64 x 2)) (+.f64 (.f64 (+.f64 (.f64 2 (pow.f64 eps 5)) (.f64 4 (pow.f64 eps 5))) x) (pow.f64 eps 6)))
(+.f64 (fma.f64 (pow.f64 eps 5) (.f64 x 6) (pow.f64 eps 6)) (.f64 (pow.f64 eps 4) (.f64 (.f64 x x) 12)))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (fma.f64 (.f64 x x) (*.f64 (pow.f64 eps 4) 12) (pow.f64 eps 6)))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 (.f64 (pow.f64 eps 4) (*.f64 x x)) 12 (pow.f64 eps 6)))
(+.f64 (pow.f64 eps 6) (.f64 x (fma.f64 x (.f64 (pow.f64 eps 4) 12) (*.f64 (pow.f64 eps 5) 6))))
(+.f64 (.f64 (+.f64 (.f64 4 (pow.f64 eps 4)) (.f64 8 (pow.f64 eps 4))) (pow.f64 x 2)) (+.f64 (.f64 (+.f64 (.f64 2 (pow.f64 eps 5)) (.f64 4 (pow.f64 eps 5))) x) (+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (pow.f64 eps 6))))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (+.f64 (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (pow.f64 eps 6)) (.f64 (pow.f64 eps 4) (.f64 (*.f64 x x) 12))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 (.f64 8 (pow.f64 eps 3)) (pow.f64 x 3) (fma.f64 (.f64 x x) (.f64 (pow.f64 eps 4) 12) (pow.f64 eps 6))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 x (.f64 x (.f64 (pow.f64 eps 4) 12)) (fma.f64 (pow.f64 x 3) (.f64 8 (pow.f64 eps 3)) (pow.f64 eps 6))))
(+.f64 (pow.f64 eps 6) (.f64 x (+.f64 (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (.f64 eps 12)))) (.f64 (pow.f64 eps 5) 6))))
(.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)))
(.f64 (.f64 8 (pow.f64 eps 3)) (pow.f64 x 3))
(.f64 (pow.f64 eps 3) (.f64 8 (pow.f64 x 3)))
(+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (+.f64 (.f64 8 (pow.f64 eps 4)) (*.f64 4 (pow.f64 eps 4))) (pow.f64 x 2)))
(fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (pow.f64 eps 4) (.f64 (.f64 x x) 12)))
(fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (.f64 (.f64 (pow.f64 eps 4) 12) x) x))
(.f64 (.f64 x x) (+.f64 (.f64 x (.f64 8 (pow.f64 eps 3))) (*.f64 (pow.f64 eps 4) 12)))
(.f64 x (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (*.f64 eps 12)))))
(+.f64 (.f64 (+.f64 (.f64 2 (pow.f64 eps 5)) (.f64 4 (pow.f64 eps 5))) x) (+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (+.f64 (.f64 8 (pow.f64 eps 4)) (.f64 4 (pow.f64 eps 4))) (pow.f64 x 2))))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (pow.f64 eps 4) (.f64 (*.f64 x x) 12))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (.f64 (*.f64 (pow.f64 eps 4) 12) x) x)))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 8 (pow.f64 eps 3))) (.f64 (pow.f64 eps 4) 12))))
(.f64 x (+.f64 (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (.f64 eps 12)))) (.f64 (pow.f64 eps 5) 6)))
(+.f64 (.f64 (+.f64 (.f64 2 (pow.f64 eps 5)) (.f64 4 (pow.f64 eps 5))) x) (+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (+.f64 (pow.f64 eps 6) (.f64 (+.f64 (.f64 8 (pow.f64 eps 4)) (.f64 4 (pow.f64 eps 4))) (pow.f64 x 2)))))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (+.f64 (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (pow.f64 eps 6)) (.f64 (pow.f64 eps 4) (.f64 (*.f64 x x) 12))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 (.f64 8 (pow.f64 eps 3)) (pow.f64 x 3) (fma.f64 (.f64 x x) (.f64 (pow.f64 eps 4) 12) (pow.f64 eps 6))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 x (.f64 x (.f64 (pow.f64 eps 4) 12)) (fma.f64 (pow.f64 x 3) (.f64 8 (pow.f64 eps 3)) (pow.f64 eps 6))))
(+.f64 (pow.f64 eps 6) (.f64 x (+.f64 (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (.f64 eps 12)))) (.f64 (pow.f64 eps 5) 6))))
(.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)))
(.f64 (.f64 8 (pow.f64 eps 3)) (pow.f64 x 3))
(.f64 (pow.f64 eps 3) (.f64 8 (pow.f64 x 3)))
(+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (+.f64 (.f64 8 (pow.f64 eps 4)) (*.f64 4 (pow.f64 eps 4))) (pow.f64 x 2)))
(fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (pow.f64 eps 4) (.f64 (.f64 x x) 12)))
(fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (.f64 (.f64 (pow.f64 eps 4) 12) x) x))
(.f64 (.f64 x x) (+.f64 (.f64 x (.f64 8 (pow.f64 eps 3))) (*.f64 (pow.f64 eps 4) 12)))
(.f64 x (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (*.f64 eps 12)))))
(+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -2 (pow.f64 eps 5)) (.f64 -4 (pow.f64 eps 5))) x)) (.f64 (+.f64 (.f64 8 (pow.f64 eps 4)) (*.f64 4 (pow.f64 eps 4))) (pow.f64 x 2))))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (pow.f64 eps 4) (.f64 (*.f64 x x) 12))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (.f64 (.f64 (*.f64 (pow.f64 eps 4) 12) x) x)))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 8 (pow.f64 eps 3))) (.f64 (pow.f64 eps 4) 12))))
(.f64 x (+.f64 (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (.f64 eps 12)))) (.f64 (pow.f64 eps 5) 6)))
(+.f64 (.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3))) (+.f64 (pow.f64 eps 6) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -2 (pow.f64 eps 5)) (.f64 -4 (pow.f64 eps 5))) x)) (.f64 (+.f64 (.f64 8 (pow.f64 eps 4)) (*.f64 4 (pow.f64 eps 4))) (pow.f64 x 2)))))
(fma.f64 (pow.f64 eps 5) (.f64 x 6) (+.f64 (fma.f64 8 (.f64 (pow.f64 eps 3) (pow.f64 x 3)) (pow.f64 eps 6)) (.f64 (pow.f64 eps 4) (.f64 (*.f64 x x) 12))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 (.f64 8 (pow.f64 eps 3)) (pow.f64 x 3) (fma.f64 (.f64 x x) (.f64 (pow.f64 eps 4) 12) (pow.f64 eps 6))))
(fma.f64 x (.f64 (pow.f64 eps 5) 6) (fma.f64 x (.f64 x (.f64 (pow.f64 eps 4) 12)) (fma.f64 (pow.f64 x 3) (.f64 8 (pow.f64 eps 3)) (pow.f64 eps 6))))
(+.f64 (pow.f64 eps 6) (.f64 x (+.f64 (.f64 x (.f64 (pow.f64 eps 3) (+.f64 (.f64 x 8) (.f64 eps 12)))) (.f64 (pow.f64 eps 5) 6))))

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
✓	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))

Compiler

Compiled 25 to 13 computations (48% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite69.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

890×	`pow1_binary64`
828×	`add-log-exp_binary64`
827×	`log1p-expm1-u_binary64`
827×	`expm1-log1p-u_binary64`
809×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	174	8
2	2321	8

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

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

Outputs

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

simplify154.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

802×	`sqr-pow_binary64`
582×	`fma-def_binary64`
565×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
541×	`pow-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	267
1	18	231
2	37	213
3	75	177
4	168	177
5	466	177
6	1519	177
7	2765	177
8	3120	177
9	3342	177
10	3564	177
11	3868	177
12	4290	177
13	4800	177
14	5367	177
15	6061	177
16	6911	177
17	7302	177
18	7590	177
19	7868	177
20	7940	177
21	7974	177

Stop Event

1×	node limit

Counts

64 → 45

Calls

Call 1

Inputs
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))

Outputs
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 x 2))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 x 2))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 x 2))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))

eval171.0ms (4%)

Compiler: Compiled 2370 to 1607 computations (32.2% saved)

prune34.0ms (0.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	0	0	0
Picked	0	1	1
Done	2	2	4
Total	163	5	168

Error

Counts

168 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(fma.f64 eps (.f64 2 x) (.f64 eps eps))
✓	21.6b	(.f64 2 (.f64 eps x))
▶	0.0b	(.f64 eps (+.f64 eps (.f64 2 x)))
✓	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
✓	16.5b	(*.f64 eps eps)

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(.f64 eps (+.f64 eps (.f64 2 x)))
✓	0.0b	(.f64 eps (+.f64 eps (.f64 2 x)))

Compiler

Compiled 20 to 12 computations (40% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite81.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

818×	`pow1_binary64`
764×	`add-log-exp_binary64`
763×	`log1p-expm1-u_binary64`
763×	`expm1-log1p-u_binary64`
748×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	153	8
2	2084	8

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(.f64 eps (+.f64 eps (.f64 2 x)))

Outputs

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

simplify153.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

802×	`sqr-pow_binary64`
582×	`fma-def_binary64`
565×	`cube-prod_binary64`
560×	`fabs-mul_binary64`
541×	`pow-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	267
1	18	231
2	37	213
3	75	177
4	165	177
5	456	177
6	1500	177
7	2751	177
8	3106	177
9	3328	177
10	3550	177
11	3856	177
12	4278	177
13	4790	177
14	5357	177
15	6055	177
16	6905	177
17	7296	177
18	7584	177
19	7860	177
20	7932	177
21	7968	177

Stop Event

1×	node limit

Counts

47 → 28

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))

Outputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))

localize12.0ms (0.3%)

Compiler: Compiled 19 to 9 computations (52.6% saved)

eval7.0ms (0.2%)

Compiler: Compiled 339 to 200 computations (41% saved)

prune6.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	28	5	33

Error

Counts

33 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
▶	9.8b	(/.f64 (.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x)))) (+.f64 eps (*.f64 -2 x)))
✓	21.6b	(.f64 2 (.f64 eps x))
✓	0.0b	(.f64 eps (+.f64 eps (.f64 2 x)))
✓	16.5b	(*.f64 eps eps)

Compiler

Compiled 51 to 33 computations (35.3% saved)

localize35.0ms (0.8%)

Local error

Found 8 expressions with local error:

New	Error	Program
	9.8b	(/.f64 (.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x)))) (+.f64 eps (*.f64 -2 x)))
	0.1b	(.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x))))
	0.0b	(.f64 4 (.f64 x x))
	0.0b	(-.f64 (.f64 eps eps) (.f64 4 (*.f64 x x)))
✓	0.0b	(-.f64 (.f64 eps eps) (.f64 4 (*.f64 x x)))
✓	0.0b	(.f64 4 (.f64 x x))
✓	0.1b	(.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x))))
✓	9.8b	(/.f64 (.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x)))) (+.f64 eps (*.f64 -2 x)))

Compiler

Compiled 62 to 28 computations (54.8% saved)

series10.0ms (0.2%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(/.f64 (.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x)))) (+.f64 eps (*.f64 -2 x)))
1.0ms	x	@	inf	(/.f64 (.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x)))) (+.f64 eps (*.f64 -2 x)))
1.0ms	x	@	0	(/.f64 (.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x)))) (+.f64 eps (*.f64 -2 x)))
1.0ms	eps	@	-inf	(/.f64 (.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x)))) (+.f64 eps (*.f64 -2 x)))
1.0ms	eps	@	inf	(/.f64 (.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x)))) (+.f64 eps (*.f64 -2 x)))

rewrite122.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

793×	`fma-def_binary64`
732×	`log-prod_binary64`
325×	`fma-neg_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	302	34
2	4467	34

Stop Event

1×	node limit

Counts

4 → 362

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 eps (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 eps (fma.f64 x -2 eps)))) (cbrt.f64 (exp.f64 (.f64 eps (fma.f64 x -2 eps)))))) (log.f64 (cbrt.f64 (exp.f64 (.f64 eps (fma.f64 x -2 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 eps (fma.f64 x -2 eps))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 eps (fma.f64 x -2 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 eps (fma.f64 x -2 eps)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 eps (fma.f64 x -2 eps))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x -2 eps) 2) (.f64 eps (/.f64 1 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2)) (/.f64 1 (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 eps (fma.f64 x -2 eps)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 eps (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2))) 2) (.f64 (cbrt.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2))) (/.f64 1 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 eps (fma.f64 x -2 eps))) (pow.f64 (cbrt.f64 (.f64 eps (fma.f64 x -2 eps))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 eps (fma.f64 x -2 eps))) 2) (cbrt.f64 (.f64 eps (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 eps)) (.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 eps)) (/.f64 1 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 eps (fma.f64 x -2 eps))) (sqrt.f64 (.f64 eps (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 eps (neg.f64 (pow.f64 (fma.f64 x -2 eps) 2))) (/.f64 1 (neg.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (fma.f64 x -2 eps)) (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 eps 1) (fma.f64 x -2 eps))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (fma.f64 x -2 eps) 2) 1) (/.f64 eps (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 eps (fma.f64 x -2 eps)) (pow.f64 (fma.f64 x -2 eps) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2))) 2) 1) (/.f64 (cbrt.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2))) (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 eps)) 1) (/.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 eps)) (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 eps (cbrt.f64 (pow.f64 (fma.f64 x -2 eps) 2))) (/.f64 (pow.f64 (fma.f64 x -2 eps) 2) (cbrt.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (fma.f64 x -2 eps) 2) (cbrt.f64 (pow.f64 (fma.f64 x -2 eps) 2))) (/.f64 eps (cbrt.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 x -2 eps) 2))) (/.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2)) (cbrt.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2))) 2) (cbrt.f64 (pow.f64 (fma.f64 x -2 eps) 2))) (cbrt.f64 (.f64 eps (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 eps)) (cbrt.f64 (pow.f64 (fma.f64 x -2 eps) 2))) (/.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 eps)) (cbrt.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 eps (sqrt.f64 (fma.f64 x -2 eps))) (/.f64 (pow.f64 (fma.f64 x -2 eps) 2) (sqrt.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (fma.f64 x -2 eps) 2) (sqrt.f64 (fma.f64 x -2 eps))) (/.f64 eps (sqrt.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (fma.f64 x -2 eps))) (/.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2)) (sqrt.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2))) 2) (sqrt.f64 (fma.f64 x -2 eps))) (/.f64 (cbrt.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2))) (sqrt.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2)) (fma.f64 (pow.f64 x 3) -8 (pow.f64 eps 3))) (fma.f64 (.f64 x -2) (-.f64 (.f64 x -2) eps) (.f64 eps eps)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2)) (pow.f64 (fma.f64 x -2 eps) 2)) (fma.f64 x -2 eps))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 eps (fma.f64 x -2 eps)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 eps (fma.f64 x -2 eps)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 eps (fma.f64 x -2 eps))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 eps (fma.f64 x -2 eps))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1 (fma.f64 x -2 eps)) eps) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2)) (neg.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 eps (fma.f64 x -2 eps)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 eps (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 eps (fma.f64 x -2 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 eps (fma.f64 x -2 eps)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2)) 3) (pow.f64 (fma.f64 x -2 eps) 3)))))) (#(struct:change 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x -2 eps) (sqrt.f64 (fma.f64 x -2 eps))) (sqrt.f64 (fma.f64 x -2 eps)) (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 (fma.f64 x -2 eps))) (sqrt.f64 (fma.f64 x -2 eps)) (fma.f64 (.f64 (.f64 x x) -4) 1 (.f64 4 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 (fma.f64 x -2 eps))) (sqrt.f64 (fma.f64 x -2 eps)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (.f64 x -2)) 2)) (cbrt.f64 (.f64 (pow.f64 x 4) 16)) (.f64 4 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 (fma.f64 x -2 eps))) (sqrt.f64 (fma.f64 x -2 eps)) (fma.f64 (neg.f64 x) (.f64 4 x) (.f64 4 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 (fma.f64 x -2 eps))) (sqrt.f64 (fma.f64 x -2 eps)) (.f64 (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 (fma.f64 x -2 eps))) (sqrt.f64 (fma.f64 x -2 eps)) (+.f64 (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x))) (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 eps (sqrt.f64 eps)) (sqrt.f64 eps) (.f64 (.f64 x x) -4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 eps (sqrt.f64 eps)) (sqrt.f64 eps) (.f64 (.f64 (.f64 x x) -4) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 eps (sqrt.f64 eps)) (sqrt.f64 eps) (fma.f64 (.f64 x x) -4 (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 eps (sqrt.f64 eps)) (sqrt.f64 eps) (neg.f64 (-.f64 (.f64 4 (.f64 x x)) (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (.f64 (.f64 x x) -4)) (cbrt.f64 (.f64 (.f64 x x) -4))) (cbrt.f64 (.f64 (.f64 x x) -4)) (.f64 eps eps))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x)))) (cbrt.f64 (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x))))) (cbrt.f64 (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x)))) (pow.f64 (fma.f64 x -2 eps) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (.f64 x x) -4)) (sqrt.f64 (.f64 (.f64 x x) -4)) (.f64 eps eps))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 (sqrt.f64 (.f64 (.f64 x x) -4)) (.f64 x -2)) (hypot.f64 (sqrt.f64 (.f64 (.f64 x x) -4)) (.f64 x -2)) (pow.f64 (fma.f64 x -2 eps) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (.f64 x -2)) (.f64 x -2) (.f64 eps eps))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (.f64 4 (.f64 x x)) (.f64 eps eps))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 eps 1) (fma.f64 x -2 eps) (.f64 (.f64 x -2) (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (fma.f64 x -2 eps) 2) 1) (/.f64 eps (fma.f64 x -2 eps)) (.f64 (.f64 x -2) (fma.f64 x -2 eps)))))) (#(struct:change 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x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 x -2 eps) 2))) (/.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2)) (cbrt.f64 (fma.f64 x -2 eps))) (.f64 (.f64 x -2) (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 eps (pow.f64 (fma.f64 x -2 eps) 2))) 2) (cbrt.f64 (pow.f64 (fma.f64 x -2 eps) 2))) (cbrt.f64 (.f64 eps (fma.f64 x -2 eps))) (.f64 (.f64 x -2) (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 eps)) (cbrt.f64 (pow.f64 (fma.f64 x -2 eps) 2))) (/.f64 (.f64 (fma.f64 x -2 eps) (sqrt.f64 eps)) (cbrt.f64 (fma.f64 x -2 eps))) (.f64 (.f64 x -2) (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 eps (sqrt.f64 (fma.f64 x -2 eps))) (/.f64 (pow.f64 (fma.f64 x -2 eps) 2) (sqrt.f64 (fma.f64 x -2 eps))) (.f64 (.f64 x -2) (fma.f64 x -2 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 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fma.f64 (.f64 eps (pow.f64 (cbrt.f64 eps) 2)) (cbrt.f64 eps) (.f64 (.f64 (.f64 x x) -4) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 eps (pow.f64 (cbrt.f64 eps) 2)) (cbrt.f64 eps) (fma.f64 (.f64 x x) -4 (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 eps (pow.f64 (cbrt.f64 eps) 2)) (cbrt.f64 eps) (neg.f64 (-.f64 (.f64 4 (.f64 x x)) (fma.f64 (.f64 x x) -4 (.f64 4 (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (fma.f64 x -2 eps))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (fma.f64 x -2 eps))) 1))))))

simplify195.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

804×	`sqr-pow_binary64`
727×	`cube-prod_binary64`
671×	`unswap-sqr_binary64`
629×	`fabs-mul_binary64`
407×	`unpow3_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	912
1	48	840
2	101	822
3	243	786
4	859	786
5	1479	786
6	2573	786
7	2776	786
8	2985	786
9	3237	786
10	3586	786
11	4046	786
12	4627	786
13	5349	786
14	6282	786
15	6827	786
16	7324	786
17	7768	786

Stop Event

1×	node limit

Counts

446 → 379

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 -4 (.f64 eps (pow.f64 x 2)))
(+.f64 (pow.f64 eps 3) (.f64 -4 (.f64 eps (pow.f64 x 2))))
(+.f64 (pow.f64 eps 3) (.f64 -4 (.f64 eps (pow.f64 x 2))))
(+.f64 (pow.f64 eps 3) (.f64 -4 (.f64 eps (pow.f64 x 2))))
(pow.f64 eps 3)
(+.f64 (.f64 -4 (.f64 eps (pow.f64 x 2))) (pow.f64 eps 3))
(+.f64 (.f64 -4 (.f64 eps (pow.f64 x 2))) (pow.f64 eps 3))
(+.f64 (.f64 -4 (.f64 eps (pow.f64 x 2))) (pow.f64 eps 3))
(pow.f64 eps 3)
(+.f64 (.f64 -4 (.f64 eps (pow.f64 x 2))) (pow.f64 eps 3))
(+.f64 (.f64 -4 (.f64 eps (pow.f64 x 2))) (pow.f64 eps 3))
(+.f64 (.f64 -4 (.f64 eps (pow.f64 x 2))) (pow.f64 eps 3))
(pow.f64 eps 3)
(+.f64 (.f64 -4 (.f64 eps (pow.f64 x 2))) (pow.f64 eps 3))
(+.f64 (.f64 -4 (.f64 eps (pow.f64 x 2))) (pow.f64 eps 3))
(+.f64 (.f64 -4 (.f64 eps (pow.f64 x 2))) (pow.f64 eps 3))
(.f64 -4 (.f64 eps (pow.f64 x 2)))
(+.f64 (pow.f64 eps 3) (.f64 -4 (.f64 eps (pow.f64 x 2))))
(+.f64 (pow.f64 eps 3) (.f64 -4 (.f64 eps (pow.f64 x 2))))
(+.f64 (pow.f64 eps 3) (.f64 -4 (.f64 eps (pow.f64 x 2))))
(.f64 -4 (.f64 eps (pow.f64 x 2)))
(+.f64 (pow.f64 eps 3) (.f64 -4 (.f64 eps (pow.f64 x 2))))
(+.f64 (pow.f64 eps 3) (.f64 -4 (.f64 eps (pow.f64 x 2))))
(+.f64 (pow.f64 eps 3) (.f64 -4 (.f64 eps (pow.f64 x 2))))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 -4 (pow.f64 x 2))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(*.f64 -4 (pow.f64 x 2))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(*.f64 -4 (pow.f64 x 2))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))

Outputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (*.f64 eps eps))
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(+.f64 (pow.f64 eps 2) (*.f64 -4 (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (.f64 -4 (*.f64 x x)))
(fma.f64 eps eps (.f64 x (.f64 x -4)))
(fma.f64 x (.f64 x -4) (.f64 eps eps))

eval191.0ms (4.4%)

Compiler: Compiled 10039 to 5943 computations (40.8% saved)

prune76.0ms (1.8%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	379	0	379
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	379	5	384

Error

Counts

384 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
✓	9.8b	(/.f64 (.f64 eps (-.f64 (.f64 eps eps) (.f64 4 (.f64 x x)))) (+.f64 eps (*.f64 -2 x)))
✓	21.6b	(.f64 2 (.f64 eps x))
✓	0.0b	(.f64 eps (+.f64 eps (.f64 2 x)))
✓	16.5b	(*.f64 eps eps)

Compiler

Compiled 51 to 33 computations (35.3% saved)

regimes132.0ms (3.1%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(.f64 eps (+.f64 eps (.f64 2 x)))

Calls

2 calls:

126.0ms	x
4.0ms	eps

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`eps`

Compiler

Compiled 49 to 27 computations (44.9% saved)

regimes22.0ms (0.5%)

Accuracy

Total -32.6b remaining (-753.7%)

Threshold costs -32.6b (-753.7%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	eps
9.0ms	x

Results

Error	Segments	Branch
4.3b	3	`x`
6.1b	3	`eps`

Compiler

Compiled 16 to 10 computations (37.5% saved)

bsearch122.0ms (2.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
59.0ms	1.098304022362111e-114	8.219798410752278e-114
62.0ms	-6.2773064417801106e-117	-3.919784321844409e-117

Compiler

Compiled 16 to 12 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	22	44

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 eps (+.f64 eps (*.f64 2 x)))

(if (<=.f64 x -4562589406156050944/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (*.f64 2 (*.f64 eps x)) (if (<=.f64 x 3045234277734415/2772669694120814859578414184143083703436437075375816575170479580614621307805625623039974406104139578097391210961403571828974157824) (*.f64 eps eps) (*.f64 2 (*.f64 eps x))))

(*.f64 eps eps)

Outputs
(.f64 eps (+.f64 eps (.f64 2 x)))
(if (<=.f64 x -4562589406156050944/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (.f64 2 (.f64 eps x)) (if (<=.f64 x 3045234277734415/2772669694120814859578414184143083703436437075375816575170479580614621307805625623039974406104139578097391210961403571828974157824) (.f64 eps eps) (.f64 2 (*.f64 eps x))))
(if (<=.f64 x -8911307433898537/1419606883389857208104148062281258856159455782592418086487285545274686109596480318996466895925319463985864300012238628776434768805888) (.f64 2 (.f64 eps x)) (if (<=.f64 x 3045234277734415/2772669694120814859578414184143083703436437075375816575170479580614621307805625623039974406104139578097391210961403571828974157824) (.f64 eps eps) (.f64 2 (*.f64 eps x))))
(*.f64 eps eps)

end46.0ms (1.1%)

Stop Event

1×

done

Compiler

Compiled 70 to 41 computations (41.4% saved)

Details

analyze1.0ms (0%)

sample1.9s (44.5%)

preprocess71.0ms (1.6%)

simplify27.0ms (0.6%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite43.0ms (1%)

simplify155.0ms (3.6%)

eval4.0ms (0.1%)

prune5.0ms (0.1%)

localize36.0ms (0.8%)

series4.0ms (0.1%)

rewrite53.0ms (1.2%)

simplify98.0ms (2.3%)

localize3.0ms (0.1%)

localize19.0ms (0.4%)

series11.0ms (0.2%)

rewrite72.0ms (1.7%)

simplify123.0ms (2.8%)

localize9.0ms (0.2%)

series2.0ms (0.1%)

rewrite69.0ms (1.6%)

simplify154.0ms (3.6%)

eval171.0ms (4%)

prune34.0ms (0.8%)

localize11.0ms (0.3%)

series3.0ms (0.1%)

rewrite81.0ms (1.9%)

simplify153.0ms (3.5%)

localize12.0ms (0.3%)

eval7.0ms (0.2%)

prune6.0ms (0.1%)

localize35.0ms (0.8%)

series10.0ms (0.2%)

rewrite122.0ms (2.8%)

simplify195.0ms (4.5%)

eval191.0ms (4.4%)

prune76.0ms (1.8%)

regimes132.0ms (3.1%)

regimes22.0ms (0.5%)

bsearch122.0ms (2.8%)

simplify3.0ms (0.1%)

end46.0ms (1.1%)

Profiling