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 (62.8%)

Results

908.0ms	2173×	body	2048	valid
428.0ms	4234×	body	128	valid
338.0ms	1038×	body	1024	valid
171.0ms	538×	body	512	valid
47.0ms	273×	body	256	valid

preprocess20.0ms (0.7%)

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

17.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize12.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series2.0ms (0.1%)

Counts

2 → 8

Calls

6 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))
0.0ms	N	@	-inf	(atan.f64 (+.f64 N 1))
0.0ms	N	@	0	(atan.f64 (+.f64 N 1))

rewrite49.0ms (1.6%)

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	17
1	156	17
2	2202	17

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

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

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

simplify16.0ms (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	84
1	20	68
2	31	68
3	61	68
4	88	68
5	134	68
6	182	68
7	216	68
8	257	68
9	293	68
10	319	68
11	321	68

Stop Event

1×

saturated

Counts

64 → 60

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

prune72.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	4	61

Error

16.4b

Counts

61 → 4

Alt Table

Status	Error	Program
	33.5b	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
▶	16.7b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
	17.9b	(/.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)))))
	32.6b	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))

Compiler

Compiled 962 to 650 computations (32.4% 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))))
✓	3.2b	(+.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	@	0	(*.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	@	-inf	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite59.0ms (1.9%)

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

simplify32.0ms (1%)

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)

prune247.0ms (8.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	172	3	175

Error

0.4b

Counts

175 → 3

Alt Table

Status

Error

Program

31.6b

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

▶

0.4b

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

17.9b

(/.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)))))

Compiler

Compiled 3513 to 2267 computations (35.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 N (+.f64 N 1))
✓	0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

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

rewrite39.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

798×	`pow1_binary64`
742×	`log1p-expm1-u_binary64`
742×	`expm1-log1p-u_binary64`
78×	`add-sqr-sqrt_binary64`
76×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	152	11
2	2044	11

Stop Event

1×	node limit

Counts

1 → 18

Calls

Call 1

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

Outputs

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

simplify28.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
331×	`cancel-sign-sub-inv_binary64`
308×	`fma-def_binary64`
199×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	104
1	33	88
2	54	88
3	151	88
4	570	88
5	1588	88
6	3503	88

Stop Event

1×	node limit

Counts

26 → 21

Calls

Call 1

Inputs
(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)))))

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

prune97.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Error

0.4b

Counts

76 → 6

Alt Table

Status	Error	Program
	1.0b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
	12.4b	(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
✓	0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	0.7b	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))
	1.7b	(*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
	22.8b	(atan2.f64 1 (+.f64 1 (fma.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))) -1)))

Compiler

Compiled 1120 to 708 computations (36.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 N) N)
✓	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))
✓	0.6b	(cbrt.f64 N)
✓	0.6b	(pow.f64 (cbrt.f64 N) 2)

series9.0ms (0.3%)

Counts

4 → 12

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	N	@	-inf	(pow.f64 (cbrt.f64 N) 2)
1.0ms	N	@	0	(pow.f64 (cbrt.f64 N) 2)
1.0ms	N	@	-inf	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))
1.0ms	N	@	-inf	(cbrt.f64 N)
1.0ms	N	@	inf	(pow.f64 (cbrt.f64 N) 2)

rewrite47.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
98×	`add-sqr-sqrt_binary64`
94×	`pow1_binary64`
93×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	204	28
2	2392	28

Stop Event

1×	node limit

Counts

4 → 77

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (cbrt.f64 N) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 N) (cbrt.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 N) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (cbrt.f64 N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 N)) 2) (cbrt.f64 (.f64 N (cbrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 N (cbrt.f64 N))) (pow.f64 (cbrt.f64 (cbrt.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 N) (pow.f64 N 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N 1/6) (sqrt.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N 1/6) (.f64 (pow.f64 N 1/6) (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 N (cbrt.f64 N)) 2))) (sqrt.f64 (cbrt.f64 (.f64 N (cbrt.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 N) (pow.f64 (cbrt.f64 (cbrt.f64 N)) 2)) (cbrt.f64 (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 N (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (cbrt.f64 N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cbrt.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (cbrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 2 (log.f64 (cbrt.f64 N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 N) 2)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (cbrt.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 N)) 2) (cbrt.f64 (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 (cbrt.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N 1/6) (pow.f64 N 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (.f64 N (cbrt.f64 N)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (cbrt.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 N) 1/3) (pow.f64 (sqrt.f64 N) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 N 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 N) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 N)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 N 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 N) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 N)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (.f64 N N))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (+.f64 N (*.f64 N N))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 N (cbrt.f64 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 N 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 N) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 N) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 N (cbrt.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 N 3) N) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 N (cbrt.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 N (cbrt.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 N) (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 N (cbrt.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 N 3) N))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 N (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 N (cbrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 N (cbrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 N (cbrt.f64 N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 N (cbrt.f64 N))))))))

simplify39.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-def_binary64`
460×	`unswap-sqr_binary64`
349×	`neg-sub0_binary64`
349×	`neg-mul-1_binary64`
343×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	312
1	60	308
2	148	308
3	564	308
4	1397	300
5	2871	300
6	4366	300

Stop Event

1×	node limit

Counts

89 → 81

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 2) (.f64 -1 (.f64 (pow.f64 (pow.f64 N 4) 1/3) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 2) (.f64 -1 (.f64 (pow.f64 (pow.f64 N 4) 1/3) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 2) (.f64 -1 (.f64 (pow.f64 (pow.f64 N 4) 1/3) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 2) (.f64 -1 (.f64 (pow.f64 (pow.f64 N 4) 1/3) (cbrt.f64 -1))) N)))

Outputs
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (pow.f64 N 1/3) 2) (pow.f64 (pow.f64 N 4) 1/3) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 2) (.f64 -1 (.f64 (pow.f64 (pow.f64 N 4) 1/3) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 N -1)) (cbrt.f64 -1)) 2) (neg.f64 (*.f64 (cbrt.f64 (pow.f64 N 4)) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2) (.f64 (cbrt.f64 (pow.f64 N 4)) (neg.f64 (cbrt.f64 -1))) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2) (.f64 (cbrt.f64 -1) (neg.f64 (cbrt.f64 (pow.f64 N 4)))) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 N (.f64 (cbrt.f64 -1) (.f64 (cbrt.f64 (pow.f64 N 4)) (pow.f64 (*.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2))))))
(atan2.f64 1 (-.f64 N (fma.f64 (cbrt.f64 -1) (.f64 (cbrt.f64 (pow.f64 N 4)) (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2)) -1)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 2) (.f64 -1 (.f64 (pow.f64 (pow.f64 N 4) 1/3) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 N -1)) (cbrt.f64 -1)) 2) (neg.f64 (*.f64 (cbrt.f64 (pow.f64 N 4)) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2) (.f64 (cbrt.f64 (pow.f64 N 4)) (neg.f64 (cbrt.f64 -1))) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2) (.f64 (cbrt.f64 -1) (neg.f64 (cbrt.f64 (pow.f64 N 4)))) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 N (.f64 (cbrt.f64 -1) (.f64 (cbrt.f64 (pow.f64 N 4)) (pow.f64 (*.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2))))))
(atan2.f64 1 (-.f64 N (fma.f64 (cbrt.f64 -1) (.f64 (cbrt.f64 (pow.f64 N 4)) (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2)) -1)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 2) (.f64 -1 (.f64 (pow.f64 (pow.f64 N 4) 1/3) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 N -1)) (cbrt.f64 -1)) 2) (neg.f64 (*.f64 (cbrt.f64 (pow.f64 N 4)) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2) (.f64 (cbrt.f64 (pow.f64 N 4)) (neg.f64 (cbrt.f64 -1))) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2) (.f64 (cbrt.f64 -1) (neg.f64 (cbrt.f64 (pow.f64 N 4)))) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 N (.f64 (cbrt.f64 -1) (.f64 (cbrt.f64 (pow.f64 N 4)) (pow.f64 (*.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2))))))
(atan2.f64 1 (-.f64 N (fma.f64 (cbrt.f64 -1) (.f64 (cbrt.f64 (pow.f64 N 4)) (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2)) -1)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 2) (.f64 -1 (.f64 (pow.f64 (pow.f64 N 4) 1/3) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 N -1)) (cbrt.f64 -1)) 2) (neg.f64 (*.f64 (cbrt.f64 (pow.f64 N 4)) (cbrt.f64 -1))) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2) (.f64 (cbrt.f64 (pow.f64 N 4)) (neg.f64 (cbrt.f64 -1))) N)))
(atan2.f64 1 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2) (.f64 (cbrt.f64 -1) (neg.f64 (cbrt.f64 (pow.f64 N 4)))) (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 N (.f64 (cbrt.f64 -1) (.f64 (cbrt.f64 (pow.f64 N 4)) (pow.f64 (*.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2))))))
(atan2.f64 1 (-.f64 N (fma.f64 (cbrt.f64 -1) (.f64 (cbrt.f64 (pow.f64 N 4)) (pow.f64 (.f64 (cbrt.f64 (neg.f64 N)) (cbrt.f64 -1)) 2)) -1)))

prune144.0ms (4.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	103	7	110

Error

0.4b

Counts

110 → 7

Alt Table

Status	Error	Program
	7.9b	(atan2.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 (pow.f64 N 4)) (+.f64 1 N)))
	1.0b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
	12.4b	(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
✓	0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	0.7b	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))
	1.7b	(*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
	0.9b	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 N)) 2) (cbrt.f64 (cbrt.f64 N))) 2) (.f64 (cbrt.f64 N) N) N)))

Compiler

Compiled 1854 to 1089 computations (41.3% saved)

regimes51.0ms (1.7%)

Accuracy

Total -11.2b remaining (-3126.8%)

Threshold costs -11.2b (-3126.8%)

Counts

40 → 1

Compiler

Compiled 623 to 408 computations (34.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	11	11
2	12	11

Stop Event

1×

saturated

Calls

Call 1

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

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

end138.0ms (4.5%)

Stop Event

1×

fuel

Compiler

Compiled 119 to 77 computations (35.3% 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	84
1	20	68
2	31	68
3	61	68
4	88	68
5	134	68
6	182	68
7	216	68
8	257	68
9	293	68
10	319	68
11	321	68

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	84
1	20	68
2	31	68
3	61	68
4	88	68
5	134	68
6	182	68
7	216	68
8	257	68
9	293	68
10	319	68
11	321	68

Details

analyze0.0ms (0%)

sample1.9s (62.8%)

preprocess20.0ms (0.7%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize12.0ms (0.4%)

series2.0ms (0.1%)

rewrite49.0ms (1.6%)

simplify16.0ms (0.5%)

prune72.0ms (2.3%)

localize8.0ms (0.3%)

series4.0ms (0.1%)

rewrite59.0ms (1.9%)

simplify32.0ms (1%)

prune247.0ms (8.1%)

localize5.0ms (0.2%)

series1.0ms (0%)

rewrite39.0ms (1.3%)

simplify28.0ms (0.9%)

prune97.0ms (3.2%)

localize9.0ms (0.3%)

series9.0ms (0.3%)

rewrite47.0ms (1.5%)

simplify39.0ms (1.3%)

prune144.0ms (4.7%)

regimes51.0ms (1.7%)

simplify2.0ms (0.1%)

end138.0ms (4.5%)

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	84
1	20	68
2	31	68
3	61	68
4	88	68
5	134	68
6	182	68
7	216	68
8	257	68
9	293	68
10	319	68
11	321	68