Details

analyze55.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
25%	50%	25.1%	7
31.2%	37.5%	31.3%	8
39%	24.2%	36.8%	9
42.9%	18.3%	38.7%	10
47.2%	11.9%	40.9%	11
49.4%	9.1%	41.6%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample1.1s (39.3%)

Results

1.1s	8256×	body	256	valid
34.0ms	332×	body	256	invalid

preprocess138.0ms (4.9%)

Algorithm

2×	egg-herbie

Rules

856×	`fma-def_binary64`
576×	`distribute-rgt-in_binary64`
560×	`unsub-neg_binary64`
508×	`fma-neg_binary64`
432×	`distribute-rgt-out--_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	25	20
2	47	20
3	103	20
4	273	20
5	821	20
6	2115	20
7	3862	20
8	5608	20
9	6168	20
10	6281	20
11	6395	20
12	6475	20
13	6475	20
14	7856	20
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(-.f64 (.f64 x x) (.f64 y y))
(-.f64 (.f64 y y) (.f64 x x))

Outputs
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(-.f64 (.f64 y y) (.f64 x x))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify127.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-def_binary64`
611×	`unsub-neg_binary64`
582×	`fma-neg_binary64`
443×	`distribute-rgt-out--_binary64`
409×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	15	10
2	27	10
3	56	10
4	133	10
5	382	10
6	832	10
7	1661	10
8	3915	10
9	5409	10
10	6280	10
11	6701	10
12	6947	10
13	7062	10
14	7062	10

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 y y))

Outputs
(-.f64 (.f64 x x) (.f64 y y))

eval0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 9 to 5 computations (44.4% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 17 to 5 computations (70.6% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite65.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`pow1_binary64`
684×	`add-log-exp_binary64`
684×	`log1p-expm1-u_binary64`
684×	`expm1-log1p-u_binary64`
667×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	139	10
2	1985	10

Stop Event

1×	node limit

Counts

1 → 46

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 y y))

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

Outputs

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

simplify59.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

897×	`fma-neg_binary64`
692×	`distribute-rgt-neg-in_binary64`
674×	`fma-def_binary64`
606×	`distribute-lft-neg-in_binary64`
486×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	228
1	21	210
2	42	210
3	87	210
4	223	210
5	763	210
6	1792	210
7	5169	210

Stop Event

1×	node limit

Counts

70 → 51

Calls

Call 1

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

Outputs
(*.f64 -1 (pow.f64 y 2))
(neg.f64 (*.f64 y y))
(*.f64 y (neg.f64 y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(*.f64 -1 (pow.f64 y 2))
(neg.f64 (*.f64 y y))
(*.f64 y (neg.f64 y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(*.f64 -1 (pow.f64 y 2))
(neg.f64 (*.f64 y y))
(*.f64 y (neg.f64 y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 -1 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y (neg.f64 y)))

eval22.0ms (0.8%)

Compiler: Compiled 777 to 233 computations (70% saved)

prune21.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Error

Counts

52 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.8b	(*.f64 x x)
▶	0.2b	(fma.f64 (+.f64 x y) (-.f64 x y) (fma.f64 (neg.f64 y) y (*.f64 y y)))
▶	27.6b	(*.f64 y (neg.f64 y))
▶	0.0b	(*.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 36 to 20 computations (44.4% saved)

localize7.0ms (0.2%)

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

localize12.0ms (0.4%)

Compiler: Compiled 9 to 4 computations (55.6% saved)

localize14.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 5 computations (70.6% saved)

series8.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(*.f64 (-.f64 x y) (+.f64 x y))
1.0ms	x	@	0	(*.f64 (-.f64 x y) (+.f64 x y))
1.0ms	x	@	inf	(*.f64 (-.f64 x y) (+.f64 x y))
1.0ms	y	@	inf	(*.f64 (-.f64 x y) (+.f64 x y))
1.0ms	y	@	0	(*.f64 (-.f64 x y) (+.f64 x y))

rewrite68.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

863×	`pow1_binary64`
807×	`add-log-exp_binary64`
807×	`log1p-expm1-u_binary64`
807×	`expm1-log1p-u_binary64`
788×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	140	10
2	2219	10

Stop Event

1×	node limit

Counts

1 → 44

Calls

Call 1

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

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

Outputs

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

simplify61.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

451×	`distribute-rgt-out--_binary64`
441×	`unsub-neg_binary64`
324×	`difference-of-squares_binary64`
320×	`unswap-sqr_binary64`
310×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	300
1	79	192
2	272	180
3	478	180
4	1762	180
5	4428	180

Stop Event

1×	node limit

Counts

68 → 56

Calls

Call 1

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

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

localize23.0ms (0.8%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (+.f64 x y) (-.f64 x y) (fma.f64 (neg.f64 y) y (*.f64 y y)))
✓	41.3b	(fma.f64 (neg.f64 y) y (*.f64 y y))

Compiler

Compiled 36 to 8 computations (77.8% saved)

series10.0ms (0.4%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(fma.f64 (neg.f64 y) y (*.f64 y y))
2.0ms	y	@	inf	(fma.f64 (neg.f64 y) y (*.f64 y y))
1.0ms	y	@	0	(fma.f64 (neg.f64 y) y (*.f64 y y))
1.0ms	x	@	-inf	(fma.f64 (+.f64 x y) (-.f64 x y) (fma.f64 (neg.f64 y) y (*.f64 y y)))
1.0ms	x	@	0	(fma.f64 (+.f64 x y) (-.f64 x y) (fma.f64 (neg.f64 y) y (*.f64 y y)))

rewrite91.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

806×	`pow1_binary64`
749×	`add-log-exp_binary64`
748×	`log1p-expm1-u_binary64`
748×	`expm1-log1p-u_binary64`
732×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	198	14
2	2953	14

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

Inputs
(fma.f64 (neg.f64 y) y (*.f64 y y))
(fma.f64 (+.f64 x y) (-.f64 x y) (fma.f64 (neg.f64 y) y (*.f64 y y)))

Outputs

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

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

simplify75.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

690×	`unsub-neg_binary64`
516×	`sub-neg_binary64`
494×	`fma-def_binary64`
324×	`difference-of-squares_binary64`
309×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	324
1	118	204
2	461	192
3	756	192
4	2508	192
5	6142	192

Stop Event

1×	node limit

Counts

104 → 86

Calls

Call 1

Inputs
0
0
0
0
0
0
0
0
0
0
0
0
(+.f64 (pow.f64 y 2) (*.f64 -2 (pow.f64 y 2)))
(+.f64 (.f64 -2 (pow.f64 y 2)) (+.f64 (pow.f64 y 2) (.f64 (+.f64 y (*.f64 -1 y)) x)))
(+.f64 (.f64 -2 (pow.f64 y 2)) (+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (.f64 (+.f64 y (*.f64 -1 y)) x))))
(+.f64 (.f64 -2 (pow.f64 y 2)) (+.f64 (pow.f64 y 2) (+.f64 (pow.f64 x 2) (.f64 (+.f64 y (*.f64 -1 y)) x))))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 (+.f64 y (.f64 -1 y)) x))
(+.f64 (pow.f64 y 2) (+.f64 (.f64 -2 (pow.f64 y 2)) (+.f64 (pow.f64 x 2) (.f64 (+.f64 y (*.f64 -1 y)) x))))
(+.f64 (pow.f64 y 2) (+.f64 (.f64 -2 (pow.f64 y 2)) (+.f64 (pow.f64 x 2) (.f64 (+.f64 y (*.f64 -1 y)) x))))
(pow.f64 x 2)
(+.f64 (.f64 -1 (.f64 (+.f64 y (*.f64 -1 y)) x)) (pow.f64 x 2))
(+.f64 (.f64 -1 (.f64 (+.f64 y (.f64 -1 y)) x)) (+.f64 (pow.f64 y 2) (+.f64 (.f64 -2 (pow.f64 y 2)) (pow.f64 x 2))))
(+.f64 (.f64 -1 (.f64 (+.f64 y (.f64 -1 y)) x)) (+.f64 (pow.f64 y 2) (+.f64 (.f64 -2 (pow.f64 y 2)) (pow.f64 x 2))))
(pow.f64 x 2)
(+.f64 (.f64 y (+.f64 (.f64 -1 x) x)) (pow.f64 x 2))
(+.f64 (.f64 -1 (pow.f64 y 2)) (+.f64 (.f64 y (+.f64 (*.f64 -1 x) x)) (pow.f64 x 2)))
(+.f64 (.f64 -1 (pow.f64 y 2)) (+.f64 (.f64 y (+.f64 (*.f64 -1 x) x)) (pow.f64 x 2)))
(*.f64 -1 (pow.f64 y 2))
(+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 y (+.f64 (*.f64 -1 x) x)))
(+.f64 (.f64 -1 (pow.f64 y 2)) (+.f64 (.f64 y (+.f64 (*.f64 -1 x) x)) (pow.f64 x 2)))
(+.f64 (.f64 -1 (pow.f64 y 2)) (+.f64 (.f64 y (+.f64 (*.f64 -1 x) x)) (pow.f64 x 2)))
(*.f64 -1 (pow.f64 y 2))
(+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 -1 (.f64 y (+.f64 (.f64 -1 x) x))))
(+.f64 (.f64 -1 (pow.f64 y 2)) (+.f64 (.f64 -1 (.f64 y (+.f64 (.f64 -1 x) x))) (pow.f64 x 2)))
(+.f64 (.f64 -1 (pow.f64 y 2)) (+.f64 (.f64 -1 (.f64 y (+.f64 (.f64 -1 x) x))) (pow.f64 x 2)))

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

eval34.0ms (1.2%)

Compiler: Compiled 2132 to 814 computations (61.8% saved)

prune21.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	142	4	146

Error

Counts

146 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(*.f64 (-.f64 x y) (+.f64 x y))
▶	0.0b	(+.f64 (.f64 y (-.f64 x y)) (.f64 x (-.f64 x y)))
✓	28.8b	(*.f64 x x)
✓	27.6b	(*.f64 y (neg.f64 y))

Compiler

Compiled 33 to 18 computations (45.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 28 to 6 computations (78.6% saved)

series8.0ms (0.3%)

Counts

3 → 72

Calls

18 calls:

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

rewrite73.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

995×	`pow1_binary64`
928×	`add-log-exp_binary64`
928×	`log1p-expm1-u_binary64`
928×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	163	24
2	2565	24

Stop Event

1×	node limit

Counts

3 → 84

Calls

Call 1

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

Outputs

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

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

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

simplify74.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

417×	`unsub-neg_binary64`
353×	`fma-def_binary64`
348×	`difference-of-squares_binary64`
322×	`sub-neg_binary64`
320×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	764
1	104	588
2	296	498
3	530	498
4	2152	498
5	5350	498

Stop Event

1×	node limit

Counts

156 → 105

Calls

Call 1

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

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

eval21.0ms (0.8%)

Compiler: Compiled 1678 to 489 computations (70.9% saved)

prune15.0ms (0.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	105	4	109

Error

Counts

109 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(*.f64 (-.f64 x y) (+.f64 x y))
✓	0.0b	(+.f64 (.f64 y (-.f64 x y)) (.f64 x (-.f64 x y)))
✓	28.8b	(*.f64 x x)
✓	27.6b	(*.f64 y (neg.f64 y))

Compiler

Compiled 33 to 18 computations (45.5% saved)

regimes33.0ms (1.2%)

Counts

6 → 1

Calls

Call 1

Inputs
(*.f64 x x)
(*.f64 y (neg.f64 y))
(*.f64 (-.f64 x y) (+.f64 x y))
(-.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 y (-.f64 x y)) (.f64 x (-.f64 x y)))
(fma.f64 (+.f64 x y) (-.f64 x y) (fma.f64 (neg.f64 y) y (*.f64 y y)))

Outputs
(*.f64 (-.f64 x y) (+.f64 x y))

Calls

7 calls:

6.0ms	y
5.0ms	x
5.0ms	(-.f64 (.f64 x x) (.f64 y y))
4.0ms	(*.f64 y y)
4.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 83 to 36 computations (56.6% saved)

regimes222.0ms (8%)

Accuracy

Total -48.0b remaining (-656.7%)

Threshold costs -48.0b (-656.7%)

Counts

2 → 7

Calls

Call 1

Inputs
(*.f64 x x)
(*.f64 y (neg.f64 y))

Outputs
(*.f64 x x)
(*.f64 y (neg.f64 y))
(*.f64 x x)
(*.f64 y (neg.f64 y))
(*.f64 x x)
(*.f64 y (neg.f64 y))
(*.f64 x x)

Calls

3 calls:

193.0ms	x
19.0ms	y
9.0ms	(*.f64 x x)

Results

Error	Segments	Branch
7.3b	7	`x`
11.0b	5	`y`
8.9b	4	`(*.f64 x x)`

Compiler

Compiled 20 to 12 computations (40% saved)

bsearch279.0ms (10%)

Algorithm

6×	binary-search

Steps

Time	Left	Right
16.0ms	2.750773054450256e+20	3.4815279712742246e+21
45.0ms	1.8182797219656897e-17	1.7340035137776547e-16
17.0ms	1.4545134939914696e-46	2.1213998457649413e-43
41.0ms	-2.7205698542016622e-90	-4.296766235824699e-102
17.0ms	-1.211790202385206e-55	-1.100006324835641e-56
143.0ms	-4.18143352514134e-12	-2.999971457011718e-18

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	84
1	38	84
2	43	84
3	46	84
4	47	84

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(*.f64 (-.f64 x y) (+.f64 x y))

(if (<=.f64 x -331287294872491328/79228162514264337593543950336) (*.f64 x x) (if (<=.f64 x -6690774881910955/55213970774324510299478046898216203619608871777363092441300193790394368) (*.f64 y (neg.f64 y)) (if (<=.f64 x -24958492781263292/9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496) (*.f64 x x) (if (<=.f64 x 7479401822025481/51422017416287688817342786954917203280710495801049370729644032) (*.f64 y (neg.f64 y)) (if (<=.f64 x 5900655055187519/324518553658426726783156020576256) (*.f64 x x) (if (<=.f64 x 36054932579290396986703872/131072) (*.f64 y (neg.f64 y)) (*.f64 x x)))))))

(*.f64 x x)

Outputs
(*.f64 (-.f64 x y) (+.f64 x y))
(if (<=.f64 x -331287294872491328/79228162514264337593543950336) (.f64 x x) (if (<=.f64 x -6690774881910955/55213970774324510299478046898216203619608871777363092441300193790394368) (.f64 y (neg.f64 y)) (if (<=.f64 x -24958492781263292/9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496) (.f64 x x) (if (<=.f64 x 7479401822025481/51422017416287688817342786954917203280710495801049370729644032) (.f64 y (neg.f64 y)) (if (<=.f64 x 5900655055187519/324518553658426726783156020576256) (.f64 x x) (if (<=.f64 x 36054932579290396986703872/131072) (.f64 y (neg.f64 y)) (*.f64 x x)))))))
(if (<=.f64 x -5176363982382677/1237940039285380274899124224) (.f64 x x) (if (<=.f64 x -6690774881910955/55213970774324510299478046898216203619608871777363092441300193790394368) (.f64 y (neg.f64 y)) (if (<=.f64 x -6239623195315823/2293498615990071511610820895302086940796564989168281123737588839386922876088484808070018553110125686554624) (.f64 x x) (if (<=.f64 x 7479401822025481/51422017416287688817342786954917203280710495801049370729644032) (.f64 y (neg.f64 y)) (if (<=.f64 x 5900655055187519/324518553658426726783156020576256) (.f64 x x) (if (<=.f64 x 275077305445025611776) (.f64 y (neg.f64 y)) (*.f64 x x)))))))
(*.f64 x x)

Compiler

Compiled 64 to 31 computations (51.6% saved)

soundness0.0ms (0%)

end31.0ms (1.1%)

Compiler: Compiled 60 to 26 computations (56.7% saved)

Details

analyze55.0ms (2%)

sample1.1s (39.3%)

preprocess138.0ms (4.9%)

simplify127.0ms (4.5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite65.0ms (2.3%)

simplify59.0ms (2.1%)

eval22.0ms (0.8%)

prune21.0ms (0.7%)

localize7.0ms (0.2%)

localize12.0ms (0.4%)

localize14.0ms (0.5%)

series8.0ms (0.3%)

rewrite68.0ms (2.4%)

simplify61.0ms (2.2%)

localize23.0ms (0.8%)

series10.0ms (0.4%)

rewrite91.0ms (3.3%)

simplify75.0ms (2.7%)

eval34.0ms (1.2%)

prune21.0ms (0.8%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite73.0ms (2.6%)

simplify74.0ms (2.6%)

eval21.0ms (0.8%)

prune15.0ms (0.6%)

regimes33.0ms (1.2%)

regimes222.0ms (8%)

bsearch279.0ms (10%)

simplify8.0ms (0.3%)

soundness0.0ms (0%)

end31.0ms (1.1%)

Profiling