Details

analyze3.0ms (0.2%)

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)

sample1.2s (70.3%)

Results

559.0ms	2741×	body	1024	valid
302.0ms	3876×	body	256	valid
190.0ms	1345×	body	512	valid
167.0ms	294×	body	2048	valid

preprocess47.0ms (2.7%)

Algorithm

2×	egg-herbie

Rules

891×	`fma-neg_binary64`
848×	`fma-def_binary64`
580×	`distribute-neg-in_binary64`
569×	`distribute-rgt-in_binary64`
541×	`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	1936	7
6	5291	7
7	7713	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)

simplify37.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

891×	`fma-neg_binary64`
848×	`fma-def_binary64`
580×	`distribute-neg-in_binary64`
569×	`distribute-rgt-in_binary64`
541×	`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	1936	7
6	5291	7
7	7713	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 2 expressions with local error:

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

rewrite35.0ms (2%)

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	1485	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 fma.f64 x 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 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))))))))

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 fma.f64 x 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 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))))))))

simplify122.0ms (7%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
561×	`cube-prod_binary64`
557×	`fabs-mul_binary64`
536×	`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	110	75
5	297	75
6	987	75
7	2137	75
8	2484	75
9	2676	75
10	2886	75
11	3182	75
12	3591	75
13	4071	75
14	4638	75
15	5334	75
16	6178	75
17	6573	75
18	6863	75
19	7139	75
20	7215	75
21	7251	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 (0.3%)

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 (.f64 x 2) (.f64 x x))
✓	0.0b	(*.f64 x (+.f64 x 2))
▶	44.6b	(*.f64 x x)
▶	17.6b	(*.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)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

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

rewrite39.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

677×	`pow1_binary64`
634×	`add-log-exp_binary64`
633×	`log1p-expm1-u_binary64`
633×	`expm1-log1p-u_binary64`
620×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	133	7
2	1780	7

Stop Event

1×	node limit

Counts

1 → 39

Calls

Call 1

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

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

simplify122.0ms (7%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
561×	`cube-prod_binary64`
557×	`fabs-mul_binary64`
536×	`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	110	75
5	297	75
6	987	75
7	2137	75
8	2484	75
9	2676	75
10	2886	75
11	3182	75
12	3591	75
13	4071	75
14	4638	75
15	5334	75
16	6178	75
17	6573	75
18	6863	75
19	7139	75
20	7215	75
21	7251	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))

eval11.0ms (0.6%)

Compiler: Compiled 501 to 335 computations (33.1% 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 (.f64 x 2) (.f64 x x))
✓	0.0b	(*.f64 x (+.f64 x 2))
✓	44.6b	(*.f64 x x)
✓	17.6b	(*.f64 2 x)

Compiler

Compiled 22 to 14 computations (36.4% saved)

regimes5.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 21 to 11 computations (47.6% saved)

regimes9.0ms (0.5%)

Accuracy

Total -58.7b remaining (-3356.3%)

Threshold costs -58.7b (-3356.3%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
1.7b	3	`x`

Compiler

Compiled 9 to 5 computations (44.4% saved)

bsearch29.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
14.0ms	0.39211478482209317	24.519932271271855
14.0ms	-6.624102134832562	-0.05713687744897332

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify2.0ms (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×

saturated

Calls

Call 1

Inputs
(*.f64 x (+.f64 x 2))
(if (<=.f64 x -932259497065501/140737488355328) (.f64 x x) (if (<=.f64 x 7233241083130843136/18446744073709551616) (.f64 2 x) (*.f64 x x)))
(*.f64 2 x)

Outputs
(*.f64 x (+.f64 x 2))
(if (<=.f64 x -932259497065501/140737488355328) (.f64 x x) (if (<=.f64 x 7233241083130843136/18446744073709551616) (.f64 2 x) (*.f64 x x)))
(if (<=.f64 x -932259497065501/140737488355328) (.f64 x x) (if (<=.f64 x 1765927998811241/4503599627370496) (.f64 x 2) (*.f64 x x)))
(*.f64 2 x)
(*.f64 x 2)

end23.0ms (1.3%)

Stop Event

1×

done

Compiler

Compiled 54 to 32 computations (40.7% saved)

Details

analyze3.0ms (0.2%)

sample1.2s (70.3%)

preprocess47.0ms (2.7%)

simplify37.0ms (2.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite35.0ms (2%)

simplify122.0ms (7%)

eval5.0ms (0.3%)

prune4.0ms (0.2%)

localize2.0ms (0.1%)

localize2.0ms (0.1%)

localize6.0ms (0.3%)

series1.0ms (0.1%)

rewrite39.0ms (2.2%)

simplify122.0ms (7%)

eval11.0ms (0.6%)

prune6.0ms (0.3%)

regimes5.0ms (0.3%)

regimes9.0ms (0.5%)

bsearch29.0ms (1.6%)

simplify2.0ms (0.1%)

end23.0ms (1.3%)

Profiling