Details

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25.7%	74.3%	0%	0%	0%	0
100%	25.7%	0%	74.3%	0%	0%	0%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample2.0s (36.6%)

Results

1.1s	6135×	body	256	valid
428.0ms	1063×	body	512	valid
379.0ms	1027×	body	1024	valid
14.0ms	31×	body	2048	valid

Bogosity

preprocess66.0ms (1.2%)

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)

simplify36.0ms (0.7%)

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
▶	0.0b	(*.f64 eps (fma.f64 2 x eps))
▶	17.1b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Compiler

Compiled 19 to 13 computations (31.6% saved)

localize6.0ms (0.1%)

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))

rewrite47.0ms (0.9%)

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))))))))

simplify164.0ms (3.1%)

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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x eps) 2)
✓	3.1b	(-.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))

rewrite97.0ms (1.8%)

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))))))))

simplify226.0ms (4.2%)

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))

eval61.0ms (1.1%)

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

prune49.0ms (0.9%)

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

Counts

97 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	10.3b	(pow.f64 (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))) 2)
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
▶	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
▶	18.9b	(*.f64 eps eps)
▶	25.0b	(.f64 eps (.f64 2 x))
▶	17.1b	(*.f64 (+.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x))

Compiler

Compiled 102 to 63 computations (38.2% saved)

localize20.0ms (0.4%)

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)

series4.0ms (0.1%)

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))
1.0ms	x	@	inf	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
0.0ms	x	@	-inf	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))

rewrite62.0ms (1.1%)

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))))))

simplify181.0ms (3.4%)

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)

localize5.0ms (0.1%)

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

localize29.0ms (0.5%)

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)
✓	5.2b	(-.f64 (+.f64 x eps) x)

Compiler

Compiled 28 to 6 computations (78.6% saved)

series6.0ms (0.1%)

Counts

3 → 72

Calls

18 calls:

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

rewrite217.0ms (4%)

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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simplify213.0ms (4%)

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))

localize51.0ms (1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 eps (fma.f64 2 x eps))
✓	0.1b	(pow.f64 (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))) 2)
✓	17.6b	(sqrt.f64 (*.f64 eps (fma.f64 2 x eps)))

Compiler

Compiled 31 to 18 computations (41.9% saved)

series10.0ms (0.2%)

Counts

2 → 24

Calls

12 calls:

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

rewrite85.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

632×	`pow1_binary64`
583×	`add-log-exp_binary64`
583×	`log1p-expm1-u_binary64`
583×	`expm1-log1p-u_binary64`
569×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	165	18
2	1634	18

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

Outputs

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

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

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-neg_binary64`
563×	`associate-/r/_binary64`
500×	`fma-def_binary64`
459×	`cancel-sign-sub-inv_binary64`
273×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	331
1	243	311
2	916	292
3	3869	284

Stop Event

1×	node limit

Counts

76 → 74

Calls

Call 1

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

Outputs
eps
(+.f64 eps x)
(+.f64 eps (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 x 2) eps)) x))
(+.f64 eps (fma.f64 -1/2 (/.f64 (*.f64 x x) eps) x))
(fma.f64 -1/2 (*.f64 (/.f64 x eps) x) (+.f64 eps x))
(+.f64 x (fma.f64 (/.f64 -1/2 eps) (*.f64 x x) eps))
(+.f64 eps (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 eps 2))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) eps)) x)))
(+.f64 eps (fma.f64 1/2 (/.f64 (pow.f64 x 3) (.f64 eps eps)) (fma.f64 -1/2 (/.f64 (.f64 x x) eps) x)))
(fma.f64 (/.f64 1/2 (.f64 eps eps)) (pow.f64 x 3) (fma.f64 -1/2 (.f64 (/.f64 x eps) x) (+.f64 eps x)))
(+.f64 eps (+.f64 x (.f64 (.f64 (/.f64 x eps) x) (+.f64 (/.f64 (*.f64 x 1/2) eps) -1/2))))
(.f64 -1 (.f64 eps (pow.f64 (sqrt.f64 -1) 2)))
eps
(+.f64 (.f64 -1 (.f64 eps (pow.f64 (sqrt.f64 -1) 2))) x)
(+.f64 eps x)
(+.f64 (.f64 -1 (.f64 eps (pow.f64 (sqrt.f64 -1) 2))) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) eps)))))
(+.f64 eps (fma.f64 -1/2 (/.f64 (*.f64 x x) eps) x))
(fma.f64 -1/2 (*.f64 (/.f64 x eps) x) (+.f64 eps x))
(+.f64 x (fma.f64 (/.f64 -1/2 eps) (*.f64 x x) eps))
(+.f64 (.f64 -1 (.f64 eps (pow.f64 (sqrt.f64 -1) 2))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)))) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) eps))))))
(+.f64 eps (fma.f64 1/2 (/.f64 (pow.f64 x 3) (.f64 eps eps)) (fma.f64 -1/2 (/.f64 (.f64 x x) eps) x)))
(fma.f64 (/.f64 1/2 (.f64 eps eps)) (pow.f64 x 3) (fma.f64 -1/2 (.f64 (/.f64 x eps) x) (+.f64 eps x)))
(+.f64 eps (+.f64 x (.f64 (.f64 (/.f64 x eps) x) (+.f64 (/.f64 (*.f64 x 1/2) eps) -1/2))))
eps
(+.f64 eps x)
(+.f64 eps (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 x 2) eps)) x))
(+.f64 eps (fma.f64 -1/2 (/.f64 (*.f64 x x) eps) x))
(fma.f64 -1/2 (*.f64 (/.f64 x eps) x) (+.f64 eps x))
(+.f64 x (fma.f64 (/.f64 -1/2 eps) (*.f64 x x) eps))
(+.f64 eps (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 eps 2))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) eps)) x)))
(+.f64 eps (fma.f64 1/2 (/.f64 (pow.f64 x 3) (.f64 eps eps)) (fma.f64 -1/2 (/.f64 (.f64 x x) eps) x)))
(fma.f64 (/.f64 1/2 (.f64 eps eps)) (pow.f64 x 3) (fma.f64 -1/2 (.f64 (/.f64 x eps) x) (+.f64 eps x)))
(+.f64 eps (+.f64 x (.f64 (.f64 (/.f64 x eps) x) (+.f64 (/.f64 (*.f64 x 1/2) eps) -1/2))))
(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 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 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 2 (.f64 eps x)) (+.f64 (/.f64 (pow.f64 x 3) eps) (+.f64 (pow.f64 x 2) (.f64 -1 (/.f64 (pow.f64 x 3) eps)))))))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 x 2)))
(*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2))
(*.f64 eps eps)
(+.f64 (.f64 -2 (.f64 eps (.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 x 2)))
(+.f64 (.f64 -2 (.f64 eps (.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (pow.f64 x 2) (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2)))))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 x 2)))
(+.f64 (.f64 -2 (.f64 eps (.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 2)) (.f64 -1 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 2)))) eps)) (+.f64 (pow.f64 x 2) (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 eps 2))))))
(+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x)))
(fma.f64 eps eps (.f64 eps (.f64 x 2)))
(.f64 eps (+.f64 eps (.f64 x 2)))
(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 x 2)))
(+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/2 eps) 2) (/.f64 1 (pow.f64 eps 2)))) (.f64 5/4 (/.f64 1 (pow.f64 eps 2)))) (pow.f64 x 4)) (+.f64 (pow.f64 eps 2) (.f64 2 (*.f64 eps x))))
(fma.f64 (fma.f64 -1 (+.f64 (pow.f64 (/.f64 -1/2 eps) 2) (/.f64 1 (.f64 eps eps))) (/.f64 5/4 (.f64 eps eps))) (pow.f64 x 4) (+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x))))
(fma.f64 (-.f64 (/.f64 (/.f64 5/4 eps) eps) (+.f64 (pow.f64 (/.f64 -1/2 eps) 2) (/.f64 1 (.f64 eps eps)))) (pow.f64 x 4) (fma.f64 eps eps (.f64 eps (*.f64 x 2))))
(fma.f64 (fma.f64 -1 (pow.f64 (/.f64 -1/2 eps) 2) (.f64 (/.f64 1 (.f64 eps eps)) 1/4)) (pow.f64 x 4) (.f64 eps (+.f64 eps (.f64 x 2))))
(fma.f64 (-.f64 (.f64 (/.f64 1 (.f64 eps eps)) 1/4) (/.f64 (/.f64 1/4 eps) eps)) (pow.f64 x 4) (.f64 eps (+.f64 eps (.f64 x 2))))
(+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/2 eps) 2) (/.f64 1 (pow.f64 eps 2)))) (.f64 5/4 (/.f64 1 (pow.f64 eps 2)))) (pow.f64 x 4)) (+.f64 (pow.f64 eps 2) (.f64 2 (*.f64 eps x))))
(fma.f64 (fma.f64 -1 (+.f64 (pow.f64 (/.f64 -1/2 eps) 2) (/.f64 1 (.f64 eps eps))) (/.f64 5/4 (.f64 eps eps))) (pow.f64 x 4) (+.f64 (.f64 eps eps) (.f64 2 (*.f64 eps x))))
(fma.f64 (-.f64 (/.f64 (/.f64 5/4 eps) eps) (+.f64 (pow.f64 (/.f64 -1/2 eps) 2) (/.f64 1 (.f64 eps eps)))) (pow.f64 x 4) (fma.f64 eps eps (.f64 eps (*.f64 x 2))))
(fma.f64 (fma.f64 -1 (pow.f64 (/.f64 -1/2 eps) 2) (.f64 (/.f64 1 (.f64 eps eps)) 1/4)) (pow.f64 x 4) (.f64 eps (+.f64 eps (.f64 x 2))))
(fma.f64 (-.f64 (.f64 (/.f64 1 (.f64 eps eps)) 1/4) (/.f64 (/.f64 1/4 eps) eps)) (pow.f64 x 4) (.f64 eps (+.f64 eps (.f64 x 2))))

eval155.0ms (2.9%)

Compiler: Compiled 8035 to 3048 computations (62.1% saved)

prune183.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	451	2	453
Fresh	0	0	0
Picked	1	0	1
Done	3	2	5
Total	455	4	459

Error

Counts

459 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(.f64 eps (+.f64 eps (.f64 x 2)))
✓	18.9b	(*.f64 eps eps)
✓	25.0b	(.f64 eps (.f64 2 x))
▶	0.0b	(*.f64 (+.f64 (+.f64 x eps) x) eps)

Compiler

Compiled 30 to 19 computations (36.7% saved)

localize18.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite74.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	153	8
2	2092	8

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify201.0ms (3.7%)

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

47 → 28

Calls

Call 1

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

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

localize11.0ms (0.2%)

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)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite123.0ms (2.3%)

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)))))))))

simplify184.0ms (3.4%)

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))

eval55.0ms (1%)

Compiler: Compiled 1756 to 737 computations (58% saved)

prune68.0ms (1.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	130	4	134

Error

Counts

134 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(.f64 eps (+.f64 eps (.f64 x 2)))
✓	18.9b	(*.f64 eps eps)
✓	25.0b	(.f64 eps (.f64 2 x))
✓	0.0b	(*.f64 (+.f64 (+.f64 x eps) x) eps)

Compiler

Compiled 30 to 19 computations (36.7% saved)

regimes22.0ms (0.4%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	eps
5.0ms	x
3.0ms	(-.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))`

Compiler

Compiled 85 to 45 computations (47.1% saved)

regimes192.0ms (3.6%)

Accuracy

Total -38.0b remaining (-854.8%)

Threshold costs -38.0b (-854.8%)

Counts

2 → 3

Calls

Call 1

Inputs
(*.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:

178.0ms	x
13.0ms	eps

Results

Error	Segments	Branch
4.4b	3	`x`
9.9b	3	`eps`

Compiler

Compiled 16 to 10 computations (37.5% saved)

bsearch90.0ms (1.7%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
26.0ms	4.500055914425196e-97	1.5399830380439365e-92
64.0ms	-4.749882866018889e-102	-4.4223816535702896e-102

Compiler

Compiled 16 to 12 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	21	44

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

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

(if (<=.f64 x -5988957251808775/1260864198284623334792929283204595641762551656654894293374345388935863096687910739565256520156317300505812095689818112) (*.f64 eps (*.f64 2 x)) (if (<=.f64 x 8657774952358555/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (*.f64 eps eps) (*.f64 eps (*.f64 2 x))))

(*.f64 eps eps)

Outputs
(.f64 eps (+.f64 eps (.f64 x 2)))
(if (<=.f64 x -5988957251808775/1260864198284623334792929283204595641762551656654894293374345388935863096687910739565256520156317300505812095689818112) (.f64 eps (.f64 2 x)) (if (<=.f64 x 8657774952358555/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (.f64 eps eps) (.f64 eps (*.f64 2 x))))
(if (<=.f64 x -5988957251808775/1260864198284623334792929283204595641762551656654894293374345388935863096687910739565256520156317300505812095689818112) (.f64 eps (.f64 x 2)) (if (<=.f64 x 8657774952358555/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (.f64 eps eps) (.f64 eps (*.f64 x 2))))
(*.f64 eps eps)

Compiler

Compiled 37 to 24 computations (35.1% saved)

soundness206.0ms (3.8%)

Algorithm

2×	egg-herbie

Rules

564×	`fma-neg_binary64`
563×	`associate-/r/_binary64`
563×	`distribute-rgt-in_binary64`
513×	`cancel-sign-sub-inv_binary64`
510×	`fma-neg_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
0	79	331
1	243	311
2	916	292
3	3869	284

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 265 to 164 computations (38.1% saved)

end84.0ms (1.6%)

Compiler: Compiled 33 to 19 computations (42.4% saved)

Details

analyze1.0ms (0%)

sample2.0s (36.6%)

preprocess66.0ms (1.2%)

simplify36.0ms (0.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite47.0ms (0.9%)

simplify164.0ms (3.1%)

localize9.0ms (0.2%)

series6.0ms (0.1%)

rewrite97.0ms (1.8%)

simplify226.0ms (4.2%)

eval61.0ms (1.1%)

prune49.0ms (0.9%)

localize20.0ms (0.4%)

series4.0ms (0.1%)

rewrite62.0ms (1.1%)

simplify181.0ms (3.4%)

localize3.0ms (0%)

localize5.0ms (0.1%)

localize29.0ms (0.5%)

series6.0ms (0.1%)

rewrite217.0ms (4%)

simplify213.0ms (4%)

localize51.0ms (1%)

series10.0ms (0.2%)

rewrite85.0ms (1.6%)

simplify58.0ms (1.1%)

eval155.0ms (2.9%)

prune183.0ms (3.4%)

localize18.0ms (0.3%)

series3.0ms (0.1%)

rewrite74.0ms (1.4%)

simplify201.0ms (3.7%)

localize11.0ms (0.2%)

series3.0ms (0.1%)

rewrite123.0ms (2.3%)

simplify184.0ms (3.4%)

eval55.0ms (1%)

prune68.0ms (1.3%)

regimes22.0ms (0.4%)

regimes192.0ms (3.6%)

bsearch90.0ms (1.7%)

simplify4.0ms (0.1%)

soundness206.0ms (3.8%)

end84.0ms (1.6%)

Profiling