Details

analyze9.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample1.3s (63.3%)

Results

603.0ms	2728×	body	1024	valid
420.0ms	3839×	body	256	valid
212.0ms	1378×	body	512	valid
88.0ms	311×	body	2048	valid
0.0ms	1×	body	256	invalid

preprocess68.0ms (3.2%)

Algorithm

2×	egg-herbie

Rules

891×	`fma-neg_binary64`
852×	`fma-def_binary64`
584×	`distribute-neg-in_binary64`
565×	`distribute-rgt-in_binary64`
563×	`associate--r-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	22	10
2	55	7
3	134	7
4	571	7
5	1967	7
6	5410	7
7	7894	7
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)

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

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify54.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

891×	`fma-neg_binary64`
852×	`fma-def_binary64`
584×	`distribute-neg-in_binary64`
565×	`distribute-rgt-in_binary64`
563×	`associate--r-_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	22	10
2	55	7
3	134	7
4	571	7
5	1967	7
6	5410	7
7	7894	7

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)

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

eval1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite41.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

593×	`pow1_binary64`
557×	`add-log-exp_binary64`
556×	`log1p-expm1-u_binary64`
556×	`expm1-log1p-u_binary64`
548×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	114	7
2	1488	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

Outputs

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

simplify163.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
481×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	14	75
2	28	75
3	50	75
4	109	75
5	311	75
6	1042	75
7	2192	75
8	2539	75
9	2731	75
10	2941	75
11	3251	75
12	3660	75
13	4145	75
14	4717	75
15	5413	75
16	6261	75
17	6654	75
18	6942	75
19	7218	75
20	7290	75
21	7326	75

Stop Event

1×	node limit

Counts

33 → 26

Calls

Call 1

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

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

eval5.0ms (0.2%)

Compiler: Compiled 248 to 156 computations (37.1% saved)

prune4.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	23	3	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	4	27

Error

Counts

27 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(*.f64 x (+.f64 x 2))
▶	0.0b	(+.f64 (.f64 x x) (.f64 x 2))
▶	42.8b	(*.f64 x x)
▶	18.4b	(*.f64 2 x)

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize2.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize2.0ms (0.1%)

Compiler: Compiled 5 to 2 computations (60% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 8 computations (50% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite47.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

683×	`pow1_binary64`
641×	`add-log-exp_binary64`
640×	`log1p-expm1-u_binary64`
640×	`expm1-log1p-u_binary64`
627×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	133	7
2	1793	7

Stop Event

1×	node limit

Counts

1 → 39

Calls

Call 1

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

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

Outputs

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

simplify161.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
481×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	14	75
2	28	75
3	50	75
4	109	75
5	311	75
6	1042	75
7	2192	75
8	2539	75
9	2731	75
10	2941	75
11	3251	75
12	3660	75
13	4145	75
14	4717	75
15	5413	75
16	6261	75
17	6654	75
18	6942	75
19	7218	75
20	7290	75
21	7326	75

Stop Event

1×	node limit

Counts

51 → 44

Calls

Call 1

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

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

eval10.0ms (0.5%)

Compiler: Compiled 501 to 332 computations (33.7% saved)

prune6.0ms (0.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	44	4	48

Error

Counts

48 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(*.f64 x (+.f64 x 2))
✓	0.0b	(+.f64 (.f64 x x) (.f64 x 2))
✓	42.8b	(*.f64 x x)
✓	18.4b	(*.f64 2 x)

Compiler

Compiled 22 to 14 computations (36.4% saved)

regimes12.0ms (0.6%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 x x)
(*.f64 2 x)
(*.f64 x (+.f64 x 2))
(+.f64 (.f64 x x) (.f64 x 2))
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)

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

Calls

4 calls:

4.0ms	x
3.0ms	(+.f64 x 1)
2.0ms	(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
2.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)`
0.0b	1	`(*.f64 (+.f64 x 1) (+.f64 x 1))`
0.0b	1	`(+.f64 x 1)`

Compiler

Compiled 52 to 35 computations (32.7% saved)

regimes9.0ms (0.4%)

Accuracy

Total -59.6b remaining (-7635.5%)

Threshold costs -59.6b (-7635.5%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
0.8b	3	`x`

Compiler

Compiled 9 to 5 computations (44.4% saved)

bsearch29.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
14.0ms	9.346374982514411e-7	1505765794.3420343
15.0ms	-32597.845920558284	-2.518210312236727e-20

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	17	35

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(*.f64 x (+.f64 x 2))
(if (<=.f64 x -4480213828763035/137438953472) (.f64 x x) (if (<=.f64 x 2206850397687871/2361183241434822606848) (.f64 2 x) (*.f64 x x)))
(*.f64 x x)

Outputs
(*.f64 x (+.f64 x 2))
(if (<=.f64 x -4480213828763035/137438953472) (.f64 x x) (if (<=.f64 x 2206850397687871/2361183241434822606848) (.f64 2 x) (*.f64 x x)))
(if (<=.f64 x -4480213828763035/137438953472) (.f64 x x) (if (<=.f64 x 2206850397687871/2361183241434822606848) (.f64 x 2) (*.f64 x x)))
(*.f64 x x)

Compiler

Compiled 28 to 16 computations (42.9% saved)

soundness115.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

891×	`fma-neg_binary64`
852×	`fma-def_binary64`
584×	`distribute-neg-in_binary64`
565×	`distribute-rgt-in_binary64`
563×	`associate--r-_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	22	10
2	55	7
3	134	7
4	571	7
5	1967	7
6	5410	7
7	7894	7

Stop Event

1×	node limit

Compiler

Compiled 80 to 64 computations (20% saved)

end21.0ms (1%)

Compiler: Compiled 26 to 13 computations (50% saved)

Details

analyze9.0ms (0.4%)

sample1.3s (63.3%)

preprocess68.0ms (3.2%)

simplify54.0ms (2.6%)

eval1.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite41.0ms (1.9%)

simplify163.0ms (7.7%)

eval5.0ms (0.2%)

prune4.0ms (0.2%)

localize2.0ms (0.1%)

localize2.0ms (0.1%)

localize7.0ms (0.3%)

series1.0ms (0.1%)

rewrite47.0ms (2.2%)

simplify161.0ms (7.6%)

eval10.0ms (0.5%)

prune6.0ms (0.3%)

regimes12.0ms (0.6%)

regimes9.0ms (0.4%)

bsearch29.0ms (1.4%)

simplify3.0ms (0.1%)

soundness115.0ms (5.4%)

end21.0ms (1%)

Profiling