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)

sample2.1s (31.1%)

Results

1.3s	6197×	body	256	valid
459.0ms	968×	body	1024	valid
367.0ms	1067×	body	512	valid
10.0ms	24×	body	2048	valid

preprocess137.0ms (2%)

Algorithm

2×	egg-herbie

Rules

498×	`associate-l_binary64`
451×	`distribute-rgt-neg-in_binary64`
426×	`distribute-lft-neg-in_binary64`
409×	`associate-r_binary64`
366×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	32	26
2	76	26
3	270	26
4	1173	20
5	4509	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 eps (+.f64 x x)))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 eps eps))
(*.f64 x (+.f64 x (+.f64 eps eps)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

563×	`distribute-rgt-in_binary64`
513×	`cancel-sign-sub-inv_binary64`
510×	`fma-neg_binary64`
463×	`distribute-lft-in_binary64`
412×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	49	13
3	161	13
4	636	8
5	2828	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

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

Click to see full alt table

Status	Error	Program
▶	10.7b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
▶	0.0b	(*.f64 eps (fma.f64 2 x eps))

Compiler

Compiled 19 to 13 computations (31.6% saved)

localize21.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	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))

rewrite193.0ms (2.8%)

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

simplify155.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
582×	`fma-def_binary64`
555×	`cube-prod_binary64`
536×	`fabs-mul_binary64`
471×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	267
1	18	231
2	37	213
3	75	177
4	166	177
5	467	177
6	1590	177
7	2841	177
8	3196	177
9	3418	177
10	3640	177
11	3957	177
12	4377	177
13	4892	177
14	5466	177
15	6166	177
16	7020	177
17	7411	177
18	7705	177
19	7979	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 (.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))
(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))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.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 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))
(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))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.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 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))
(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))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.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 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))
(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))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.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 (.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))
(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))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.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 (.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))
(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))
(fma.f64 2 (.f64 eps x) (.f64 eps eps))
(.f64 eps (+.f64 (.f64 2 x) eps))
(*.f64 eps (fma.f64 2 x eps))

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x eps) 2)
✓	2.6b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Compiler

Compiled 25 to 13 computations (48% saved)

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite126.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

963×	`pow1_binary64`
899×	`add-log-exp_binary64`
898×	`log1p-expm1-u_binary64`
898×	`expm1-log1p-u_binary64`
95×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	186	20
2	2533	20

Stop Event

1×	node limit

Counts

2 → 65

Calls

Call 1

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

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

Outputs

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

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

simplify316.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

947×	`sqr-pow_binary64`
620×	`fma-def_binary64`
551×	`fabs-mul_binary64`
539×	`cube-prod_binary64`
380×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	567
1	28	486
2	65	435
3	158	393
4	425	393
5	1568	393
6	2850	393
7	3122	393
8	3308	393
9	3552	393
10	3853	393
11	4244	393
12	4751	393
13	5331	393
14	6077	393
15	6625	393
16	6955	393
17	7285	393
18	7373	393
19	7401	393

Stop Event

1×	node limit

Counts

113 → 77

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

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

eval24.0ms (0.4%)

Compiler: Compiled 1363 to 639 computations (53.1% saved)

prune19.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	91	6	97

Error

0.0b

Counts

97 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	10.7b	(+.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x (neg.f64 x)))
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
▶	25.6b	(.f64 eps (.f64 2 x))
▶	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
▶	12.5b	(*.f64 eps eps)
▶	10.7b	(*.f64 (+.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x))

Compiler

Compiled 104 to 63 computations (39.4% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 25 to 13 computations (48% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite54.0ms (0.8%)

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	2324	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 (pow.f64 (cbrt.f64 eps) 2) (*.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 expm1.f64 (log1p.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))))))) (#(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 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)) (pow.f64 (cbrt.f64 eps) 2) (*.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))))))

simplify157.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
582×	`fma-def_binary64`
555×	`cube-prod_binary64`
536×	`fabs-mul_binary64`
477×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	267
1	18	231
2	37	213
3	75	177
4	167	177
5	468	177
6	1576	177
7	2822	177
8	3177	177
9	3399	177
10	3621	177
11	3939	177
12	4363	177
13	4878	177
14	5452	177
15	6148	177
16	7002	177
17	7395	177
18	7687	177
19	7963	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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 eps (.f64 2 x)))
(*.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 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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))

localize3.0ms (0%)

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

localize8.0ms (0.1%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x))
✓	0.0b	(+.f64 (+.f64 x eps) x)
✓	5.9b	(-.f64 (+.f64 x eps) x)

Compiler

Compiled 28 to 6 computations (78.6% saved)

series8.0ms (0.1%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	inf	(*.f64 (+.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x))
1.0ms	x	@	-inf	(*.f64 (+.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x))
0.0ms	eps	@	-inf	(*.f64 (+.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x))
0.0ms	x	@	inf	(*.f64 (+.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x))
0.0ms	eps	@	0	(*.f64 (+.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x))

rewrite122.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`unpow-prod-down_binary64`
494×	`fma-def_binary64`
421×	`log-prod_binary64`
345×	`pow-prod-down_binary64`
233×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	30
1	166	27
2	2658	27

Stop Event

1×	node limit

Counts

3 → 305

Calls

Call 1

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

Outputs

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simplify198.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
582×	`fma-def_binary64`
555×	`cube-prod_binary64`
534×	`fabs-mul_binary64`
475×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	396
1	23	360
2	41	306
3	69	306
4	156	306
5	459	306
6	1565	306
7	2821	306
8	3176	306
9	3399	306
10	3621	306
11	3937	306
12	4361	306
13	4872	306
14	5446	306
15	6142	306
16	6992	306
17	7385	306
18	7675	306
19	7955	306

Stop Event

1×	node limit

Counts

377 → 316

Calls

Call 1

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

localize21.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (+.f64 x eps) 2)
✓	2.6b	(+.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x (neg.f64 x)))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite75.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

943×	`pow1_binary64`
880×	`add-log-exp_binary64`
878×	`log1p-expm1-u_binary64`
878×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	207	10
2	3018	10

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

Outputs

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

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

680×	`distribute-rgt-neg-in_binary64`
574×	`distribute-lft-neg-in_binary64`
500×	`associate-l_binary64`
372×	`unswap-sqr_binary64`
370×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	261
1	44	221
2	116	204
3	335	170
4	1197	170
5	5138	170

Stop Event

1×	node limit

Counts

62 → 48

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 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 2))
(+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))

Outputs
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(.f64 (.f64 2 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 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(.f64 (.f64 2 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 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 2))
(.f64 0 (.f64 x x))
0
(+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2)))
(.f64 (.f64 2 eps) x)
(.f64 eps (.f64 x 2))
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.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 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 (*.f64 2 eps) x))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))

eval321.0ms (4.7%)

Compiler: Compiled 8043 to 2662 computations (66.9% saved)

prune183.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	440	4	444
Fresh	0	0	0
Picked	1	0	1
Done	2	3	5
Total	443	7	450

Error

Counts

450 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	10.7b	(.f64 (+.f64 (.f64 2 x) eps) (-.f64 (+.f64 x eps) x))
▶	10.7b	(+.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (neg.f64 x)))
	36.7b	0
▶	0.0b	(*.f64 (+.f64 (+.f64 x eps) x) eps)
✓	25.6b	(.f64 eps (.f64 2 x))
✓	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
✓	12.5b	(*.f64 eps eps)

Compiler

Compiled 62 to 38 computations (38.7% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (+.f64 (.f64 2 x) eps) (-.f64 (+.f64 x eps) x))
	5.9b	(-.f64 (+.f64 x eps) x)

Compiler

Compiled 32 to 14 computations (56.3% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite120.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`fma-def_binary64`
529×	`log-prod_binary64`
465×	`pow-prod-down_binary64`
295×	`pow2_binary64`
293×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	212	14
2	3274	13

Stop Event

1×	node limit

Counts

1 → 74

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) (fma.f64 (neg.f64 x) x (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (+.f64 x eps) 2) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (fma.f64 2 x eps)) (*.f64 (-.f64 eps x) (fma.f64 2 x eps)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 x eps) (fma.f64 2 x eps)) (*.f64 (neg.f64 x) (fma.f64 2 x eps)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 x x) (+.f64 x (-.f64 eps x))) (*.f64 eps (+.f64 x (-.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps (+.f64 x (-.f64 eps x))) (*.f64 (+.f64 x x) (+.f64 x (-.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 2 x eps) x) (*.f64 (fma.f64 2 x eps) (-.f64 eps x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 2 x eps) (+.f64 x eps)) (*.f64 (fma.f64 2 x eps) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x x)) (*.f64 (+.f64 x (-.f64 eps x)) eps))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 x (-.f64 eps x)) eps) (*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 eps 3)) (-.f64 (pow.f64 (+.f64 x eps) 3) (pow.f64 x 3))) (*.f64 (fma.f64 eps (-.f64 eps (+.f64 x x)) (pow.f64 (+.f64 x x) 2)) (fma.f64 x (fma.f64 2 x eps) (pow.f64 (+.f64 x eps) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x x) 2) (*.f64 eps eps)) (-.f64 (pow.f64 (+.f64 x eps) 3) (pow.f64 x 3))) (*.f64 (-.f64 (+.f64 x x) eps) (fma.f64 x (fma.f64 2 x eps) (pow.f64 (+.f64 x eps) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 eps 3)) (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) (fma.f64 8 (pow.f64 x 3) (pow.f64 eps 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x x) 2) (*.f64 eps eps)) (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) (*.f64 (-.f64 (+.f64 x x) eps) (fma.f64 2 x eps)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 3) (pow.f64 x 3)) (fma.f64 8 (pow.f64 x 3) (pow.f64 eps 3))) (*.f64 (fma.f64 x (fma.f64 2 x eps) (pow.f64 (+.f64 x eps) 2)) (fma.f64 eps (-.f64 eps (+.f64 x x)) (pow.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) (fma.f64 8 (pow.f64 x 3) (pow.f64 eps 3))) (*.f64 (fma.f64 2 x eps) (fma.f64 eps (-.f64 eps (+.f64 x x)) (pow.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 3) (pow.f64 x 3)) (-.f64 (pow.f64 (+.f64 x x) 2) (*.f64 eps eps))) (*.f64 (fma.f64 x (fma.f64 2 x eps) (pow.f64 (+.f64 x eps) 2)) (-.f64 (+.f64 x x) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) (-.f64 (pow.f64 (+.f64 x x) 2) (*.f64 eps eps))) (-.f64 (pow.f64 (+.f64 x x) 2) (*.f64 eps eps)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 x eps) 2) 2) (pow.f64 (*.f64 x x) 2)) (+.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x eps) 6) (pow.f64 x 6)) (+.f64 (pow.f64 (pow.f64 (+.f64 x eps) 2) 2) (+.f64 (pow.f64 (*.f64 x x) 2) (pow.f64 (*.f64 x (+.f64 x eps)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 eps 3)) (+.f64 x (-.f64 eps x))) (fma.f64 eps (-.f64 eps (+.f64 x x)) (pow.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x x) 2) (*.f64 eps eps)) (+.f64 x (-.f64 eps x))) (-.f64 (+.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 3) (pow.f64 x 3)) (fma.f64 2 x eps)) (fma.f64 x (fma.f64 2 x eps) (pow.f64 (+.f64 x eps) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 2 x eps) (-.f64 (pow.f64 (+.f64 x eps) 3) (pow.f64 x 3))) (fma.f64 x (fma.f64 2 x eps) (pow.f64 (+.f64 x eps) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x (-.f64 eps x)) (fma.f64 8 (pow.f64 x 3) (pow.f64 eps 3))) (fma.f64 eps (-.f64 eps (+.f64 x x)) (pow.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x (-.f64 eps x)) (-.f64 (pow.f64 (+.f64 x x) 2) (*.f64 eps eps))) (-.f64 (+.f64 x x) eps))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 2 x eps) (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) (fma.f64 2 x eps))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) (fma.f64 2 x eps)) (fma.f64 2 x eps))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (pow.f64 (+.f64 x eps) 2)) (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (fma.f64 2 x eps) (*.f64 (-.f64 eps x) (fma.f64 2 x eps)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x x) (+.f64 x (-.f64 eps x)) (*.f64 eps (+.f64 x (-.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 eps (+.f64 x (-.f64 eps x)) (*.f64 (+.f64 x x) (+.f64 x (-.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 2 x eps) x (*.f64 (fma.f64 2 x eps) (-.f64 eps x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 2 x eps) (+.f64 x eps) (*.f64 (fma.f64 2 x eps) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 2 x eps) (+.f64 x (-.f64 eps x)) (fma.f64 (neg.f64 x) x (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x eps) (fma.f64 2 x eps) (*.f64 (neg.f64 x) (fma.f64 2 x eps)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x eps) (+.f64 x eps) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x eps) (+.f64 x eps) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (-.f64 eps x)) (+.f64 x x) (*.f64 (+.f64 x (-.f64 eps x)) eps))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (-.f64 eps x)) eps (*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x)) (fma.f64 (neg.f64 x) x (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (+.f64 x eps) 2) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (+.f64 x eps) 2) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) 2) (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) (fma.f64 (neg.f64 x) x (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 x eps) 2)) (*.f64 (cbrt.f64 (+.f64 x eps)) (+.f64 x eps)) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 x eps) 2)) (*.f64 (cbrt.f64 (+.f64 x eps)) (+.f64 x eps)) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) (sqrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))) (fma.f64 (neg.f64 x) x (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x eps)) (*.f64 (sqrt.f64 (+.f64 x eps)) (+.f64 x eps)) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x eps)) (*.f64 (sqrt.f64 (+.f64 x eps)) (+.f64 x eps)) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x eps) 2)) 2) (cbrt.f64 (pow.f64 (+.f64 x eps) 2)) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x eps) 2)) 2) (cbrt.f64 (pow.f64 (+.f64 x eps) 2)) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x eps) 3/2) (sqrt.f64 (+.f64 x eps)) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x eps) 3/2) (sqrt.f64 (+.f64 x eps)) (*.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 x eps) (cbrt.f64 (pow.f64 (+.f64 x eps) 2))) (cbrt.f64 (+.f64 x eps)) (neg.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 x eps) (cbrt.f64 (pow.f64 (+.f64 x eps) 2))) (cbrt.f64 (+.f64 x eps)) (*.f64 (neg.f64 x) x))))))

simplify325.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
582×	`fma-def_binary64`
555×	`cube-prod_binary64`
536×	`fabs-mul_binary64`
477×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	267
1	18	231
2	37	213
3	75	177
4	167	177
5	468	177
6	1576	177
7	2822	177
8	3177	177
9	3399	177
10	3621	177
11	3939	177
12	4363	177
13	4878	177
14	5452	177
15	6148	177
16	7002	177
17	7395	177
18	7687	177
19	7963	177

Stop Event

1×	node limit

Counts

98 → 80

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

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 19 to 5 computations (73.7% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`pow1_binary64`
810×	`add-log-exp_binary64`
810×	`log1p-expm1-u_binary64`
810×	`expm1-log1p-u_binary64`
793×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	139	10
2	2146	10

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify182.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
582×	`fma-def_binary64`
555×	`cube-prod_binary64`
536×	`fabs-mul_binary64`
477×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	267
1	18	231
2	37	213
3	75	177
4	167	177
5	468	177
6	1576	177
7	2822	177
8	3177	177
9	3399	177
10	3621	177
11	3939	177
12	4363	177
13	4878	177
14	5452	177
15	6148	177
16	7002	177
17	7395	177
18	7687	177
19	7963	177

Stop Event

1×	node limit

Counts

45 → 27

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

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x eps) (+.f64 x eps))
✓	2.6b	(+.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (neg.f64 x)))

Compiler

Compiled 32 to 7 computations (78.1% saved)

series3.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite170.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

944×	`pow1_binary64`
884×	`add-log-exp_binary64`
883×	`log1p-expm1-u_binary64`
883×	`expm1-log1p-u_binary64`
103×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	190	17
2	3121	17

Stop Event

1×	node limit

Counts

2 → 65

Calls

Call 1

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

Outputs

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

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

simplify197.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

680×	`distribute-rgt-neg-in_binary64`
574×	`distribute-lft-neg-in_binary64`
493×	`associate-l_binary64`
372×	`unswap-sqr_binary64`
360×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	561
1	47	476
2	124	426
3	351	386
4	1222	386
5	5164	386

Stop Event

1×	node limit

Counts

113 → 80

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 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 2))
(+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))

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 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 2))
(.f64 0 (.f64 x x))
0
(+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (*.f64 eps x)) (pow.f64 x 2))))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.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 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 2 (.f64 eps x)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2))
(fma.f64 2 (.f64 eps x) (.f64 x x))
(.f64 x (+.f64 (.f64 eps 2) x))
(*.f64 x (fma.f64 eps 2 x))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2))
(fma.f64 2 (.f64 eps x) (.f64 x x))
(.f64 x (+.f64 (.f64 eps 2) x))
(*.f64 x (fma.f64 eps 2 x))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2))
(fma.f64 2 (.f64 eps x) (.f64 x x))
(.f64 x (+.f64 (.f64 eps 2) x))
(*.f64 x (fma.f64 eps 2 x))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(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 2 (.f64 eps x)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(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 2 (.f64 eps x)))
(.f64 eps (+.f64 eps (.f64 2 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (.f64 eps eps) (fma.f64 2 (.f64 eps x) (*.f64 x x)))
(fma.f64 eps eps (.f64 x (+.f64 (.f64 eps 2) x)))
(fma.f64 x (fma.f64 eps 2 x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 x (fma.f64 eps 2 x)))

eval152.0ms (2.2%)

Compiler: Compiled 7061 to 2848 computations (59.7% saved)

prune56.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	405	2	407
Fresh	0	1	1
Picked	1	0	1
Done	2	3	5
Total	408	6	414

Error

Counts

414 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	36.7b	0
✓	0.0b	(*.f64 (+.f64 (+.f64 x eps) x) eps)
▶	0.0b	(+.f64 (.f64 (+.f64 x eps) eps) (.f64 x eps))
✓	25.6b	(.f64 eps (.f64 2 x))
✓	12.5b	(*.f64 eps eps)
▶	0.0b	(.f64 (+.f64 (.f64 2 x) eps) eps)

Compiler

Compiled 44 to 28 computations (36.4% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series21.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
20.0ms	x	@	-inf	(.f64 (+.f64 (.f64 2 x) eps) eps)
0.0ms	eps	@	0	(.f64 (+.f64 (.f64 2 x) eps) eps)
0.0ms	x	@	0	(.f64 (+.f64 (.f64 2 x) eps) eps)
0.0ms	x	@	inf	(.f64 (+.f64 (.f64 2 x) eps) eps)
0.0ms	eps	@	-inf	(.f64 (+.f64 (.f64 2 x) eps) eps)

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

788×	`pow1_binary64`
733×	`add-log-exp_binary64`
732×	`log1p-expm1-u_binary64`
732×	`expm1-log1p-u_binary64`
718×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	151	8
2	2001	8

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

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

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

simplify158.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
582×	`fma-def_binary64`
555×	`cube-prod_binary64`
536×	`fabs-mul_binary64`
477×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	267
1	18	231
2	37	213
3	75	177
4	167	177
5	468	177
6	1576	177
7	2822	177
8	3177	177
9	3399	177
10	3621	177
11	3939	177
12	4363	177
13	4878	177
14	5452	177
15	6148	177
16	7002	177
17	7395	177
18	7687	177
19	7963	177

Stop Event

1×	node limit

Counts

43 → 25

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

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 24 to 6 computations (75% saved)

series4.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite58.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

974×	`pow1_binary64`
907×	`add-log-exp_binary64`
907×	`log1p-expm1-u_binary64`
907×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	161	17
2	2480	17

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

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

Outputs

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

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

simplify145.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1066×	`fma-def_binary64`
778×	`sqr-pow_binary64`
511×	`associate-l_binary64`
439×	`cube-prod_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	471
1	20	381
2	47	363
3	92	327
4	207	327
5	565	327
6	1875	327
7	3408	327
8	3946	327
9	4178	327
10	4402	327
11	4735	327
12	5171	327
13	5688	327
14	6266	327
15	6964	327
16	7829	327

Stop Event

1×	node limit

Counts

108 → 69

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

eval53.0ms (0.8%)

Compiler: Compiled 1223 to 440 computations (64% saved)

prune40.0ms (0.6%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	1	1
Picked	0	1	1
Done	0	4	4
Total	94	6	100

Error

Counts

100 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	36.7b	0
✓	0.0b	(*.f64 (+.f64 (+.f64 x eps) x) eps)
✓	0.0b	(+.f64 (.f64 (+.f64 x eps) eps) (.f64 x eps))
✓	25.6b	(.f64 eps (.f64 2 x))
✓	12.5b	(*.f64 eps eps)
✓	0.0b	(.f64 (+.f64 (.f64 2 x) eps) eps)

Compiler

Compiled 44 to 28 computations (36.4% saved)

regimes25.0ms (0.4%)

Counts

13 → 1

Calls

Call 1

Inputs
0
(*.f64 eps eps)
(.f64 eps (.f64 2 x))
(.f64 (+.f64 (.f64 2 x) eps) eps)
(*.f64 (+.f64 (+.f64 x eps) x) eps)
(+.f64 (.f64 (+.f64 x eps) eps) (.f64 x eps))
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(.f64 (+.f64 (.f64 2 x) eps) (-.f64 (+.f64 x eps) x))
(*.f64 (+.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x))
(+.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (neg.f64 x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x (neg.f64 x)))
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

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

Calls

4 calls:

7.0ms	eps
7.0ms	x
4.0ms	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
4.0ms	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`eps`
0.0b	1	`(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))`
0.0b	1	`(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))`

Compiler

Compiled 130 to 62 computations (52.3% saved)

regimes129.0ms (1.9%)

Counts

4 → 1

Calls

Call 1

Inputs
0
(*.f64 eps eps)
(.f64 eps (.f64 2 x))
(.f64 (+.f64 (.f64 2 x) eps) eps)

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

Calls

2 calls:

4.0ms	x
4.0ms	eps

Results

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

Compiler

Compiled 24 to 15 computations (37.5% saved)

regimes22.0ms (0.3%)

Counts

3 → 3

Calls

Call 1

Inputs
0
(*.f64 eps eps)
(.f64 eps (.f64 2 x))

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

Calls

2 calls:

11.0ms	eps
10.0ms	x

Results

Error	Segments	Branch
5.0b	3	`x`
6.9b	3	`eps`

Compiler

Compiled 17 to 11 computations (35.3% saved)

bsearch323.0ms (4.7%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
217.0ms	6.817229610759429e-70	5.695531299368639e-68
106.0ms	-4.0296518625625745e-68	-1.6495160141182313e-72

Compiler

Compiled 16 to 12 computations (25% saved)

regimes7.0ms (0.1%)

Accuracy

Total -24.2b remaining (-193.8%)

Threshold costs -24.2b (-193.8%)

Counts

2 → 1

Calls

Call 1

Inputs
0
(*.f64 eps eps)

Outputs
(*.f64 eps eps)

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

Error	Segments	Branch
12.5b	1	`x`
12.5b	1	`eps`

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	55
1	27	55

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 (+.f64 (+.f64 x eps) x) eps)
(.f64 (+.f64 (.f64 2 x) eps) eps)
(if (<=.f64 x -1223168643734341/30354201441027016733116592294117482916287606860189680019559568902170379456331382784) (.f64 eps (.f64 2 x)) (if (<=.f64 x 5297447958392983/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 eps eps) (.f64 eps (*.f64 2 x))))
(*.f64 eps eps)
0

Outputs
(*.f64 (+.f64 (+.f64 x eps) x) eps)
(*.f64 eps (+.f64 x (+.f64 x eps)))
(.f64 (+.f64 (.f64 2 x) eps) eps)
(.f64 eps (+.f64 eps (.f64 x 2)))
(if (<=.f64 x -1223168643734341/30354201441027016733116592294117482916287606860189680019559568902170379456331382784) (.f64 eps (.f64 2 x)) (if (<=.f64 x 5297447958392983/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 eps eps) (.f64 eps (*.f64 2 x))))
(if (<=.f64 x -1223168643734341/30354201441027016733116592294117482916287606860189680019559568902170379456331382784) (.f64 eps (.f64 x 2)) (if (<=.f64 x 5297447958392983/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 eps eps) (.f64 eps (*.f64 x 2))))
(*.f64 eps eps)
0

Compiler

Compiled 49 to 32 computations (34.7% saved)

soundness0.0ms (0%)

end31.0ms (0.5%)

Compiler: Compiled 41 to 23 computations (43.9% saved)

Details

analyze1.0ms (0%)

sample2.1s (31.1%)

preprocess137.0ms (2%)

simplify34.0ms (0.5%)

eval1.0ms (0%)

prune1.0ms (0%)

localize21.0ms (0.3%)

series4.0ms (0.1%)

rewrite193.0ms (2.8%)

simplify155.0ms (2.3%)

localize9.0ms (0.1%)

series6.0ms (0.1%)

rewrite126.0ms (1.9%)

simplify316.0ms (4.6%)

eval24.0ms (0.4%)

prune19.0ms (0.3%)

localize10.0ms (0.1%)

series3.0ms (0%)

rewrite54.0ms (0.8%)

simplify157.0ms (2.3%)

localize3.0ms (0%)

localize8.0ms (0.1%)

localize8.0ms (0.1%)

series8.0ms (0.1%)

rewrite122.0ms (1.8%)

simplify198.0ms (2.9%)

localize21.0ms (0.3%)

series4.0ms (0.1%)

rewrite75.0ms (1.1%)

simplify85.0ms (1.2%)

eval321.0ms (4.7%)

prune183.0ms (2.7%)

localize11.0ms (0.2%)

series2.0ms (0%)

rewrite120.0ms (1.8%)

simplify325.0ms (4.8%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite49.0ms (0.7%)

simplify182.0ms (2.7%)

localize9.0ms (0.1%)

series3.0ms (0%)

rewrite170.0ms (2.5%)

simplify197.0ms (2.9%)

eval152.0ms (2.2%)

prune56.0ms (0.8%)

localize8.0ms (0.1%)

series21.0ms (0.3%)

rewrite53.0ms (0.8%)

simplify158.0ms (2.3%)

localize11.0ms (0.2%)

series4.0ms (0.1%)

rewrite58.0ms (0.9%)

simplify145.0ms (2.1%)

eval53.0ms (0.8%)

prune40.0ms (0.6%)

regimes25.0ms (0.4%)

regimes129.0ms (1.9%)

regimes22.0ms (0.3%)

bsearch323.0ms (4.7%)

regimes7.0ms (0.1%)

simplify6.0ms (0.1%)

soundness0.0ms (0%)

end31.0ms (0.5%)

Profiling