Details

analyze4.0ms (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
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample1.4s (84.2%)

Results

644.0ms	2780×	body	1024	valid
309.0ms	3139×	body	128	valid
242.0ms	1358×	body	512	valid
88.0ms	699×	body	256	valid
76.0ms	280×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 22 to 18 computations (18.2% saved)

preprocess28.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

848×	`fma-def_binary64`
569×	`distribute-rgt-in_binary64`
541×	`associate--r-_binary64`
489×	`distribute-lft-in_binary64`
372×	`fma-neg_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
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 10 to 8 computations (20% saved)

simplify16.0ms (1%)

Algorithm

1×	egg-herbie

Rules

848×	`fma-def_binary64`
569×	`distribute-rgt-in_binary64`
541×	`associate--r-_binary64`
489×	`distribute-lft-in_binary64`
372×	`fma-neg_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

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))

prune3.0ms (0.2%)

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

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.4%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(*.f64 x (+.f64 x 2))
1.0ms	x	@	-inf	(*.f64 x (+.f64 x 2))
1.0ms	x	@	inf	(*.f64 x (+.f64 x 2))

rewrite31.0ms (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`
58×	`add-sqr-sqrt_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 → 24

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

simplify56.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

471×	`fma-def_binary64`
464×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	102
1	13	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

Stop Event

1×	node limit

Counts

36 → 29

Calls

Call 1

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

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

prune20.0ms (1.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	1	30

Error

Counts

30 → 1

Alt Table

Status	Error	Program
▶	0b	(fma.f64 x x (*.f64 x 2))

Compiler

Compiled 291 to 187 computations (35.7% saved)

localize3.0ms (0.2%)

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Error

Counts

1 → 1

Alt Table

Status	Error	Program
✓	0b	(fma.f64 x x (*.f64 x 2))

Compiler

Compiled 7 to 4 computations (42.9% saved)

regimes59.0ms (3.6%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

21 → 1

Compiler

Compiled 772 to 568 computations (26.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	6	8

Stop Event

1×

saturated

Calls

Call 1

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

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

end27.0ms (1.7%)

Stop Event

1×

done

Compiler

Compiled 21 to 12 computations (42.9% saved)

Details

analyze4.0ms (0.2%)

sample1.4s (84.2%)

preprocess28.0ms (1.7%)

simplify16.0ms (1%)

prune3.0ms (0.2%)

localize3.0ms (0.2%)

series6.0ms (0.4%)

rewrite31.0ms (1.9%)

simplify56.0ms (3.4%)

prune20.0ms (1.2%)

localize3.0ms (0.2%)

prune1.0ms (0%)

regimes59.0ms (3.6%)

simplify2.0ms (0.1%)

end27.0ms (1.7%)

Profiling