Details

analyze56.0ms (3.3%)

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)

sample848.0ms (50.3%)

Results

795.0ms	8256×	body	256	valid
28.0ms	329×	body	256	invalid

preprocess167.0ms (9.9%)

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)

simplify137.0ms (8.1%)

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))

eval1.0ms (0%)

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

prune1.0ms (0.1%)

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)

localize14.0ms (0.8%)

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)

series5.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

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

rewrite72.0ms (4.3%)

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)))))))

simplify54.0ms (3.2%)

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)))

eval11.0ms (0.6%)

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

prune8.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	4	52

Error

Counts

52 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.3b	(+.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))))
✓	0.0b	(-.f64 (.f64 x x) (.f64 y y))
▶	30.3b	(*.f64 x x)
▶	24.5b	(*.f64 y (neg.f64 y))

Compiler

Compiled 45 to 21 computations (53.3% saved)

localize3.0ms (0.2%)

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

localize4.0ms (0.2%)

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

localize16.0ms (0.9%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x x) (.f64 y y))
✓	39.9b	(fma.f64 (neg.f64 y) y (*.f64 y y))

Compiler

Compiled 64 to 9 computations (85.9% saved)

series3.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

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

rewrite50.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

374×	`pow1_binary64`
361×	`add-sqr-sqrt_binary64`
354×	`*-un-lft-identity_binary64`
346×	`add-log-exp_binary64`
345×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	103	7
2	1292	7

Stop Event

1×	node limit

Counts

1 → 55

Calls

Call 1

Inputs
(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 y (+.f64 y y)) (.f64 y (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (+.f64 y y)) (fma.f64 (neg.f64 (.f64 (cbrt.f64 y) y)) (pow.f64 (cbrt.f64 y) 2) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (+.f64 y y)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) y) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (+.f64 y y)) (fma.f64 (neg.f64 (.f64 y (sqrt.f64 y))) (sqrt.f64 y) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (+.f64 y y)) (fma.f64 (neg.f64 (sqrt.f64 y)) (.f64 y (sqrt.f64 y)) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 y (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (+.f64 y y)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (+.f64 y y))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 y y (neg.f64 (.f64 (.f64 y y) -1))) (fma.f64 (.f64 y y) -1 (.f64 (.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 y y) 1 (neg.f64 (.f64 (.f64 y y) -1))) (fma.f64 (.f64 y y) -1 (.f64 (.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (.f64 y y) (neg.f64 (.f64 (.f64 y y) -1))) (fma.f64 (.f64 y y) -1 (.f64 (.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) y) (neg.f64 (.f64 (.f64 y y) -1))) (fma.f64 (.f64 y y) -1 (.f64 (.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (cbrt.f64 y) y) (pow.f64 (cbrt.f64 y) 2) (neg.f64 (.f64 (.f64 y y) -1))) (fma.f64 (.f64 y y) -1 (.f64 (.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 y) (.f64 y (sqrt.f64 y)) (neg.f64 (.f64 (.f64 y y) -1))) (fma.f64 (.f64 y y) -1 (.f64 (.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1 (.f64 y y) (neg.f64 (.f64 (.f64 y y) -1))) (fma.f64 (.f64 y y) -1 (.f64 (.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 y (sqrt.f64 y)) (sqrt.f64 y) (neg.f64 (.f64 (.f64 y y) -1))) (fma.f64 (.f64 y y) -1 (.f64 (.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 y (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (neg.f64 (.f64 (.f64 y y) -1))) (fma.f64 (.f64 y y) -1 (.f64 (.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 y y (neg.f64 (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 y (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 y y) 1 (neg.f64 (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 y (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (.f64 y y) (neg.f64 (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 y (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) y) (neg.f64 (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 y (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (cbrt.f64 y) y) (pow.f64 (cbrt.f64 y) 2) (neg.f64 (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 y (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 y) (.f64 y (sqrt.f64 y)) (neg.f64 (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 y (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1 (.f64 y y) (neg.f64 (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 y (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 y (sqrt.f64 y)) (sqrt.f64 y) (neg.f64 (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 y (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 y (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (neg.f64 (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (.f64 y (pow.f64 (cbrt.f64 y) 2)) (.f64 (cbrt.f64 y) (.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(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))) (cbrt.f64 (pow.f64 (hypot.f64 y y) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (hypot.f64 y y) 4)) (cbrt.f64 (.f64 y (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 y y) (hypot.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (.f64 y (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (pow.f64 (hypot.f64 y y) 6)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (hypot.f64 y y) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 y y) 4) (cbrt.f64 (pow.f64 (hypot.f64 y y) 4))) 1/3) (cbrt.f64 (cbrt.f64 (.f64 y (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 y y) 4) (hypot.f64 y y)) 1/3) (cbrt.f64 (hypot.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 y (+.f64 y y)))) 2) 3) (cbrt.f64 (.f64 y (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (cbrt.f64 (.f64 y (+.f64 y y)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (.f64 y (+.f64 y y)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 6) (pow.f64 y 6)) (+.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 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 (hypot.f64 y y) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 y y) 6) 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 (hypot.f64 y y) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 y y) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (pow.f64 (exp.f64 y) y) (pow.f64 (exp.f64 y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 y y) 6))))) (#(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))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y y) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (+.f64 y y)) (*.f64 y (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (+.f64 y y)) (fma.f64 (neg.f64 (*.f64 (cbrt.f64 y) y)) (pow.f64 (cbrt.f64 y) 2) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (+.f64 y y)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) y) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (+.f64 y y)) (fma.f64 (neg.f64 (*.f64 y (sqrt.f64 y))) (sqrt.f64 y) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (+.f64 y y)) (fma.f64 (neg.f64 (sqrt.f64 y)) (*.f64 y (sqrt.f64 y)) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 y (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (+.f64 y y)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (+.f64 y y))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 y y (neg.f64 (*.f64 (*.f64 y y) -1))) (fma.f64 (*.f64 y y) -1 (*.f64 (*.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 y y) 1 (neg.f64 (*.f64 (*.f64 y y) -1))) (fma.f64 (*.f64 y y) -1 (*.f64 (*.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (*.f64 y y) (neg.f64 (*.f64 (*.f64 y y) -1))) (fma.f64 (*.f64 y y) -1 (*.f64 (*.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) y) (neg.f64 (*.f64 (*.f64 y y) -1))) (fma.f64 (*.f64 y y) -1 (*.f64 (*.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 (cbrt.f64 y) y) (pow.f64 (cbrt.f64 y) 2) (neg.f64 (*.f64 (*.f64 y y) -1))) (fma.f64 (*.f64 y y) -1 (*.f64 (*.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 y) (*.f64 y (sqrt.f64 y)) (neg.f64 (*.f64 (*.f64 y y) -1))) (fma.f64 (*.f64 y y) -1 (*.f64 (*.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1 (*.f64 y y) (neg.f64 (*.f64 (*.f64 y y) -1))) (fma.f64 (*.f64 y y) -1 (*.f64 (*.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 y (sqrt.f64 y)) (sqrt.f64 y) (neg.f64 (*.f64 (*.f64 y y) -1))) (fma.f64 (*.f64 y y) -1 (*.f64 (*.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (neg.f64 (*.f64 (*.f64 y y) -1))) (fma.f64 (*.f64 y y) -1 (*.f64 (*.f64 y y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 y y (neg.f64 (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 y y) 1 (neg.f64 (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (*.f64 y y) (neg.f64 (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) y) (neg.f64 (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 (cbrt.f64 y) y) (pow.f64 (cbrt.f64 y) 2) (neg.f64 (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 y) (*.f64 y (sqrt.f64 y)) (neg.f64 (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1 (*.f64 y y) (neg.f64 (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 y (sqrt.f64 y)) (sqrt.f64 y) (neg.f64 (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (neg.f64 (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2))))) (fma.f64 (neg.f64 (cbrt.f64 y)) (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (*.f64 (cbrt.f64 y) (*.f64 y (pow.f64 (cbrt.f64 y) 2)))))))) (#(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))) (cbrt.f64 (pow.f64 (hypot.f64 y y) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 y y) 4)) (cbrt.f64 (*.f64 y (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 y y) (hypot.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (*.f64 y (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (hypot.f64 y y) 6)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (hypot.f64 y y) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 y y) 4) (cbrt.f64 (pow.f64 (hypot.f64 y y) 4))) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 y (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 y y) 4) (hypot.f64 y y)) 1/3) (cbrt.f64 (hypot.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (+.f64 y y)))) 2) 3) (cbrt.f64 (*.f64 y (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 y (+.f64 y y)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (*.f64 y (+.f64 y y)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 6) (pow.f64 y 6)) (+.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 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 (hypot.f64 y y) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 y y) 6) 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 (hypot.f64 y y) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 y y) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (pow.f64 (exp.f64 y) y) (pow.f64 (exp.f64 y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 y y) 6))))) (#(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))))))))

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12

Stop Event

1×

saturated

Counts

67 → 56

Calls

Call 1

Inputs
0
0
0
0
0
0
0
0
0
0
0
0

Outputs
0
0
0
0
0
0
0
0
0
0
0
0

eval46.0ms (2.7%)

Compiler: Compiled 5305 to 1243 computations (76.6% saved)

prune24.0ms (1.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	163	4	167

Error

Counts

167 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.3b	(+.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))))
✓	0.0b	(-.f64 (.f64 x x) (.f64 y y))
✓	30.3b	(*.f64 x x)
✓	24.5b	(*.f64 y (neg.f64 y))

Compiler

Compiled 45 to 21 computations (53.3% saved)

regimes24.0ms (1.4%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	(-.f64 (.f64 x x) (.f64 y y))
4.0ms	x
4.0ms	y
3.0ms	(*.f64 y y)
3.0ms	(*.f64 x x)

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 y y)`

Compiler

Compiled 64 to 25 computations (60.9% saved)

regimes41.0ms (2.4%)

Accuracy

Total -45.1b remaining (-490%)

Threshold costs -45.1b (-490%)

Counts

2 → 5

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)

Calls

3 calls:

18.0ms	x
12.0ms	y
9.0ms	(*.f64 x x)

Results

Error	Segments	Branch
9.2b	5	`x`
10.2b	3	`y`
9.5b	4	`(*.f64 x x)`

Compiler

Compiled 20 to 12 computations (40% saved)

bsearch61.0ms (3.6%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
15.0ms	9.656345218715828e+21	1.5124378584854208e+33
15.0ms	2.5872514117791137e-76	8.139678074880758e-71
16.0ms	1.850980348804523e-98	2.537290848452074e-98
15.0ms	-5.731263211366129e-29	-4.3115544138891145e-39

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-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	21	62
1	30	62
2	35	62
3	38	62
4	39	62

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

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

(if (<=.f64 x -319528601355971/5575186299632655785383929568162090376495104) (*.f64 x x) (if (<=.f64 x 5697838997890643/307828173409331868845930000782371982852185463050511302093346042220669701339821957901673955116288403443801781174272) (*.f64 y (neg.f64 y)) (if (<=.f64 x 8432518728985991/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016) (*.f64 x x) (if (<=.f64 x 9656345218715828092928) (*.f64 y (neg.f64 y)) (*.f64 x x)))))

(*.f64 x x)

Outputs

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

(if (<=.f64 x -319528601355971/5575186299632655785383929568162090376495104) (*.f64 x x) (if (<=.f64 x 5697838997890643/307828173409331868845930000782371982852185463050511302093346042220669701339821957901673955116288403443801781174272) (*.f64 y (neg.f64 y)) (if (<=.f64 x 8432518728985991/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016) (*.f64 x x) (if (<=.f64 x 9656345218715828092928) (*.f64 y (neg.f64 y)) (*.f64 x x)))))

(*.f64 x x)

Compiler

Compiled 49 to 25 computations (49% saved)

soundness0.0ms (0%)

end27.0ms (1.6%)

Compiler: Compiled 45 to 19 computations (57.8% saved)

Details

analyze56.0ms (3.3%)

sample848.0ms (50.3%)

preprocess167.0ms (9.9%)

simplify137.0ms (8.1%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize14.0ms (0.8%)

series5.0ms (0.3%)

rewrite72.0ms (4.3%)

simplify54.0ms (3.2%)

eval11.0ms (0.6%)

prune8.0ms (0.5%)

localize3.0ms (0.2%)

localize4.0ms (0.2%)

localize16.0ms (0.9%)

series3.0ms (0.2%)

rewrite50.0ms (2.9%)

simplify9.0ms (0.5%)

eval46.0ms (2.7%)

prune24.0ms (1.4%)

regimes24.0ms (1.4%)

regimes41.0ms (2.4%)

bsearch61.0ms (3.6%)

simplify6.0ms (0.4%)

soundness0.0ms (0%)

end27.0ms (1.6%)

Profiling