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 (76.1%)

Results

742.0ms	5437×	body	128	valid
486.0ms	1120×	body	512	valid
461.0ms	1018×	body	1024	valid
155.0ms	656×	body	256	valid
13.0ms	25×	body	2048	valid

Compiler

Compiled 52 to 38 computations (26.9% saved)

preprocess44.0ms (1.8%)

Algorithm

2×	egg-herbie

Rules

497×	`associate-l_binary64`
409×	`associate-r_binary64`
202×	`fma-neg_binary64`
186×	`cancel-sign-sub-inv_binary64`
176×	`distribute-rgt-in_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 11 to 8 computations (27.3% saved)

simplify22.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

517×	`cancel-sign-sub-inv_binary64`
510×	`fma-neg_binary64`
430×	`fma-def_binary64`
372×	`unswap-sqr_binary64`
269×	`associate-l_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))

prune14.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.9b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
▶	0.0b	(*.f64 eps (fma.f64 2 x eps))

Compiler

Compiled 55 to 37 computations (32.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.2%)

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	x	@	0	(*.f64 eps (fma.f64 2 x eps))
1.0ms	eps	@	inf	(*.f64 eps (fma.f64 2 x eps))
1.0ms	x	@	inf	(*.f64 eps (fma.f64 2 x eps))

rewrite61.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`pow1_binary64`
507×	`add-log-exp_binary64`
507×	`log1p-expm1-u_binary64`
507×	`expm1-log1p-u_binary64`
497×	`add-exp-log_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 → 15

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 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 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 log1p.f64 (expm1.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 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 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 log1p.f64 (expm1.f64 (*.f64 eps (fma.f64 2 x eps))))))))

simplify66.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary64`
461×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
294×	`*-commutative_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

Stop Event

1×	node limit

Counts

39 → 20

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))

prune14.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	19	3	22

Error

Counts

22 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
▶	0.0b	(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
	14.9b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Compiler

Compiled 216 to 140 computations (35.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series13.0ms (0.5%)

Counts

2 → 6

Calls

12 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
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))

rewrite44.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

820×	`log1p-expm1-u_binary64`
820×	`expm1-log1p-u_binary64`
88×	`add-sqr-sqrt_binary64`
86×	`pow1_binary64`
85×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	175	18
2	2290	18

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

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

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

Outputs

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

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

simplify56.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

625×	`sqr-pow_binary64`
447×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
285×	`cube-prod_binary64`
277×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
1	16	33
2	30	33
3	56	33
4	124	33
5	358	33
6	1252	33
7	2130	33
8	2294	33
9	2507	33
10	2727	33
11	3020	33
12	3420	33
13	3908	33
14	4469	33

Stop Event

1×	node limit

Counts

57 → 55

Calls

Call 1

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

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

prune34.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	56	2	58

Error

Counts

58 → 2

Alt Table

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

Compiler

Compiled 826 to 525 computations (36.4% saved)

localize19.0ms (0.8%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite36.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`pow1_binary64`
605×	`add-log-exp_binary64`
605×	`log1p-expm1-u_binary64`
605×	`expm1-log1p-u_binary64`
70×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	141	10
2	1641	10

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify71.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary64`
461×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
294×	`*-commutative_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

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))

prune14.0ms (0.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	28	2	30

Error

Counts

30 → 2

Alt Table

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

Compiler

Compiled 337 to 208 computations (38.3% saved)

regimes20.0ms (0.8%)

Accuracy

Total 0.0b remaining (67.2%)

Threshold costs 0.0b (67.2%)

Counts

9 → 1

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	9	11

Stop Event

1×

saturated

Calls

Call 1

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

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

end41.0ms (1.7%)

Stop Event

1×

done

Compiler

Compiled 38 to 23 computations (39.5% saved)

Details

analyze1.0ms (0%)

sample1.9s (76.1%)

preprocess44.0ms (1.8%)

simplify22.0ms (0.9%)

prune14.0ms (0.6%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite61.0ms (2.5%)

simplify66.0ms (2.7%)

prune14.0ms (0.6%)

localize5.0ms (0.2%)

series13.0ms (0.5%)

rewrite44.0ms (1.8%)

simplify56.0ms (2.3%)

prune34.0ms (1.4%)

localize19.0ms (0.8%)

series3.0ms (0.1%)

rewrite36.0ms (1.5%)

simplify71.0ms (2.9%)

prune14.0ms (0.6%)

regimes20.0ms (0.8%)

simplify2.0ms (0.1%)

end41.0ms (1.7%)

Profiling