Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.9s (67.7%)

Results

978.0ms	2147×	body	2048	valid
443.0ms	4297×	body	128	valid
330.0ms	1043×	body	1024	valid
135.0ms	508×	body	512	valid
44.0ms	261×	body	256	valid

preprocess25.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

prune2.0ms (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

13.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series1.0ms (0%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	N	@	0	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms	N	@	-inf	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms	N	@	inf	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite43.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`log1p-expm1-u_binary64`
828×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
82×	`*-un-lft-identity_binary64`
82×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	156	11
2	2202	11

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (atan.f64 N)) 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (pow.f64 (cbrt.f64 (atan.f64 N)) 2) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (/.f64 1 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (/.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))) (neg.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (neg.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (neg.f64 (atan.f64 N)) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N)))) (-.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (.f64 N (+.f64 N 1))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (*.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (atan.f64 N)) 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (pow.f64 (cbrt.f64 (atan.f64 N)) 2) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (/.f64 1 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (/.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))) (neg.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (neg.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (neg.f64 (atan.f64 N)) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (*.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N))) (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N)))) (-.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))))))

simplify15.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

52×	`fma-def_binary64`
43×	`fma-neg_binary64`
23×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
14×	`associate--r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	52
1	20	44
2	31	44
3	61	44
4	88	44
5	134	44
6	182	44
7	216	44
8	257	44
9	293	44
10	319	44
11	321	44

Stop Event

1×

saturated

Counts

42 → 40

Calls

Call 1

Inputs
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))

Outputs
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))

prune53.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	35	5	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	5	41

Error

13.0b

Counts

41 → 5

Alt Table

Status	Error	Program
	39.5b	(*.f64 (+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))))
	47.1b	(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))
▶	13.2b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
	30.4b	(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
	14.1b	(expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))

Compiler

Compiled 781 to 516 computations (33.9% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 N (+.f64 N 1))
✓	0.0b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	2.2b	(+.f64 N (-.f64 1 N))

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(*.f64 N (+.f64 N 1))
1.0ms	N	@	inf	(*.f64 N (+.f64 N 1))
0.0ms	N	@	inf	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms	N	@	0	(*.f64 N (+.f64 N 1))
0.0ms	N	@	-inf	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite60.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`fma-def_binary64`
297×	`fma-neg_binary64`
180×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`
146×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	210	29
2	3059	29

Stop Event

1×	node limit

Counts

3 → 162

Calls

Call 1

Inputs
(+.f64 N (-.f64 1 N))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(*.f64 N (+.f64 N 1))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 N (-.f64 1 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 N N) (+.f64 (+.f64 N -1) N)) (/.f64 (pow.f64 (-.f64 1 N) 2) (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 N (-.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 N (-.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) (sqrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (/.f64 1 (fma.f64 N N (.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 N N) (pow.f64 (-.f64 1 N) 2)) (/.f64 1 (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (hypot.f64 1 (sqrt.f64 N)) (sqrt.f64 N)) (-.f64 (hypot.f64 1 (sqrt.f64 N)) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 N N (.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N))) (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 N -1) N) (-.f64 (.f64 N N) (pow.f64 (-.f64 1 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (fma.f64 N N (.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (+.f64 (pow.f64 (-.f64 1 N) 2) (-.f64 (.f64 N N) (.f64 N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 N N) (pow.f64 (-.f64 1 N) 2)) (+.f64 (+.f64 N -1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))) (neg.f64 (fma.f64 N N (.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 N N) (pow.f64 (-.f64 1 N) 2))) (neg.f64 (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 N 1) 3) (pow.f64 N 3)) (+.f64 (pow.f64 (+.f64 N 1) 2) (fma.f64 N N (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 N 1) 2) (.f64 N N)) (+.f64 (+.f64 N 1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 1 N) 2) (.f64 N N)) (-.f64 (-.f64 1 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 N (-.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (+.f64 N 1)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 N)) (exp.f64 (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 N) (+.f64 1 (expm1.f64 (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 N)) (+.f64 1 (expm1.f64 (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (-.f64 1 N))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (-.f64 1 N)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (-.f64 1 N))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (+.f64 N 1)) (exp.f64 (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (exp.f64 (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (+.f64 N 1)) (/.f64 1 (exp.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (+.f64 N 1))) (/.f64 1 (exp.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 N (-.f64 1 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N 1 (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 N (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 N (-.f64 1 N)) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 N (-.f64 1 N)) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 N (-.f64 1 N)) (fma.f64 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 N 1) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 N) 1 N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 N (-.f64 1 N)) 1 (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 N (-.f64 1 N)) 1 (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 N (-.f64 1 N)) 1 (fma.f64 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 N 1) 1 (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (fma.f64 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule 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(+.f64 N (-.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) (sqrt.f64 (+.f64 N (-.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) (sqrt.f64 (+.f64 N (-.f64 1 N))) (fma.f64 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (sqrt.f64 N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (.f64 (sqrt.f64 N) 1) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (sqrt.f64 N)) (hypot.f64 1 (sqrt.f64 N)) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 N)) (sqrt.f64 (-.f64 1 N)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 N 3)) (/.f64 1 (+.f64 1 (fma.f64 N N N))) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (/.f64 1 (fma.f64 N N (.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N)))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (/.f64 1 (fma.f64 N N (.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N)))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (/.f64 1 (fma.f64 N N (.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N)))) (fma.f64 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 N 3)) (/.f64 1 (-.f64 (fma.f64 N N 1) N)) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (.f64 N N)) (/.f64 1 (+.f64 N 1)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (.f64 N N) (pow.f64 (-.f64 1 N) 2)) (/.f64 1 (+.f64 (+.f64 N -1) N)) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (.f64 N N) (pow.f64 (-.f64 1 N) 2)) (/.f64 1 (+.f64 (+.f64 N -1) N)) (fma.f64 (neg.f64 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 N N) 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 N N) 3) (pow.f64 N 3)) (fma.f64 (.f64 N N) (.f64 N N) (-.f64 (.f64 N N) (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 N N) (.f64 N N)) (.f64 N N)) (-.f64 (.f64 N N) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 N N -1) N) (+.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 N (fma.f64 N N -1)) (+.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 N (sqrt.f64 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 N) (exp.f64 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 N)) (exp.f64 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 N N)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (.f64 (log1p.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N N N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N 1 (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 N (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (fma.f64 N N N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (fma.f64 N N N)) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 N N) 1 N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 2) (cbrt.f64 (+.f64 1 (fma.f64 N N N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 N) (pow.f64 (cbrt.f64 N) 2) (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 N) (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (.f64 (cbrt.f64 N) 1) (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (.f64 (cbrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 N (hypot.f64 1 (sqrt.f64 N))) (hypot.f64 N (hypot.f64 1 (sqrt.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (sqrt.f64 N) (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (.f64 (sqrt.f64 N) 1) (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (.f64 (sqrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (/.f64 1 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) 1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 N (sqrt.f64 N)) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 (cbrt.f64 N) 2) (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 2) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 N N N)) 1))))))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 1))))))

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

simplify33.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
334×	`cancel-sign-sub-inv_binary64`
329×	`fma-def_binary64`
192×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	240
1	44	198
2	67	198
3	163	198
4	578	198
5	1574	198
6	3510	198

Stop Event

1×	node limit

Counts

198 → 171

Calls

Call 1

Inputs
1
1
1
1
1
1
1
1
1
1
1
1
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))

Outputs
1
1
1
1
1
1
1
1
1
1
1
1
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)

prune167.0ms (5.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	173	3	176

Error

0.5b

Counts

176 → 3

Alt Table

Status	Error	Program
✓	13.2b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
	14.1b	(expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
▶	0.5b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

Compiler

Compiled 3431 to 2209 computations (35.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 N (fma.f64 N N 1))
✓	0.5b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

series2.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	N	@	inf	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
0.0ms	N	@	0	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
0.0ms	N	@	-inf	(+.f64 N (fma.f64 N N 1))
0.0ms	N	@	-inf	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
0.0ms	N	@	0	(+.f64 N (fma.f64 N N 1))

rewrite41.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`pow1_binary64`
596×	`add-log-exp_binary64`
596×	`log1p-expm1-u_binary64`
596×	`expm1-log1p-u_binary64`
63×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	122	19
2	1586	19

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(+.f64 N (fma.f64 N N 1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))))

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

simplify27.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

993×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
330×	`cancel-sign-sub-inv_binary64`
297×	`fma-def_binary64`
226×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	127
1	35	115
2	57	115
3	149	115
4	516	115
5	1494	115
6	3364	115

Stop Event

1×	node limit

Counts

67 → 62

Calls

Call 1

Inputs
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
1
(+.f64 N 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))

Outputs
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (fma.f64 N N 1))
(+.f64 1 (fma.f64 N N N))

prune60.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	61	4	65

Error

0.5b

Counts

65 → 4

Alt Table

Status	Error	Program
	1.7b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)
▶	1.1b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))
✓	13.2b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	0.5b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

Compiler

Compiled 917 to 622 computations (32.2% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 N (fma.f64 N N 1))
	0.5b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
✓	0.6b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))
✓	15.1b	(sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))

series2.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))
0.0ms	N	@	-inf	(sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))
0.0ms	N	@	inf	(sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))
0.0ms	N	@	inf	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))
0.0ms	N	@	-inf	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))

rewrite43.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

721×	`pow1_binary64`
672×	`add-log-exp_binary64`
671×	`log1p-expm1-u_binary64`
671×	`expm1-log1p-u_binary64`
73×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	163	24
2	1853	24

Stop Event

1×	node limit

Counts

2 → 37

Calls

Call 1

Inputs
(sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))) (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1/4) (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2)) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2) 1/2) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))

simplify18.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

123×	`fma-neg_binary64`
92×	`fma-def_binary64`
28×	`cancel-sign-sub-inv_binary64`
28×	`unsub-neg_binary64`
24×	`associate--r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	192
1	23	184
2	36	184
3	92	184
4	245	184
5	454	184
6	592	184
7	606	184

Stop Event

1×

saturated

Counts

53 → 41

Calls

Call 1

Inputs
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))

Outputs
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N))))
(sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N))))
(sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N))))
(sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N))))
(sqrt.f64 (atan2.f64 1 (-.f64 (fma.f64 N N 1) (neg.f64 N))))
(sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (fma.f64 N N 1) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

prune230.0ms (8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	186	7	193

Error

0.5b

Counts

193 → 7

Alt Table

Status	Error	Program
	1.9b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (pow.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))) 3))
	1.7b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)
	1.4b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)))
✓	1.1b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))
✓	13.2b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
	1.1b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N 1)) 2) (cbrt.f64 (fma.f64 N N 1)) N))))
✓	0.5b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

Compiler

Compiled 4457 to 3133 computations (29.7% saved)

regimes48.0ms (1.7%)

Accuracy

Total -60.0b remaining (-11732.1%)

Threshold costs -60.0b (-11732.1%)

Counts

32 → 1

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (.f64 N N))))
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (fma.f64 N N N))))
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3))))
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N 1)) 2) (cbrt.f64 (fma.f64 N N 1)) N))))
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)))
(expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (pow.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))) 3))
(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2)) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2)
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))
(*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2))
(atan2.f64 1 (fma.f64 N N N))
(atan2.f64 1 (pow.f64 N 2))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)
(/.f64 1 (/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))))
(*.f64 (+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))))
(.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (/.f64 1 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))
(*.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))
(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))
(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (pow.f64 (cbrt.f64 (atan.f64 N)) 2) (atan.f64 N)))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Outputs
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

Results

18.0ms	0.5b	`N`
4.0ms	0.5b	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`
4.0ms	0.5b	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 507 to 346 computations (31.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	9	11

Stop Event

1×

saturated

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

Outputs
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

end16.0ms (0.6%)

Stop Event

1×

fuel

Compiler

Compiled 18 to 12 computations (33.3% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11
0	1	1

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Iter	Nodes	Cost
0	9	52
1	20	44
2	31	44
3	61	44
4	88	44
5	134	44
6	182	44
7	216	44
8	257	44
9	293	44
10	319	44
11	321	44

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11
0	1	1

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Iter	Nodes	Cost
0	9	52
1	20	44
2	31	44
3	61	44
4	88	44
5	134	44
6	182	44
7	216	44
8	257	44
9	293	44
10	319	44
11	321	44

Details

analyze0.0ms (0%)

sample1.9s (67.7%)

preprocess25.0ms (0.9%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite43.0ms (1.5%)

simplify15.0ms (0.5%)

prune53.0ms (1.9%)

localize8.0ms (0.3%)

series4.0ms (0.1%)

rewrite60.0ms (2.1%)

simplify33.0ms (1.2%)

prune167.0ms (5.8%)

localize5.0ms (0.2%)

series2.0ms (0.1%)

rewrite41.0ms (1.4%)

simplify27.0ms (0.9%)

prune60.0ms (2.1%)

localize7.0ms (0.3%)

series2.0ms (0.1%)

rewrite43.0ms (1.5%)

simplify18.0ms (0.6%)

prune230.0ms (8%)

regimes48.0ms (1.7%)

simplify2.0ms (0.1%)

end16.0ms (0.6%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11
0	1	1

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Iter	Nodes	Cost
0	9	52
1	20	44
2	31	44
3	61	44
4	88	44
5	134	44
6	182	44
7	216	44
8	257	44
9	293	44
10	319	44
11	321	44