Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample3.4s (42.9%)

Results

1.8s	2176×	body	2048	valid
1.0s	4544×	body	256	valid
444.0ms	1033×	body	1024	valid
172.0ms	503×	body	512	valid

Bogosity

preprocess212.0ms (2.6%)

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	122	11
8	168	11
9	204	11
10	230	11
11	232	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 9 to 7 computations (22.2% saved)

simplify27.0ms (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	122	11
8	168	11
9	204	11
10	230	11
11	232	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))

eval1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	14.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

localize20.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	0.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series3.0ms (0%)

Counts

2 → 8

Calls

6 calls:

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

rewrite119.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

890×	`pow1_binary64`
828×	`log1p-expm1-u_binary64`
828×	`expm1-log1p-u_binary64`
827×	`add-log-exp_binary64`
810×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	156	17
2	2213	17

Stop Event

1×	node limit

Counts

2 → 52

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

simplify31.0ms (0.4%)

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	215	68
8	258	68
9	294	68
10	320	68
11	322	68

Stop Event

1×

saturated

Counts

60 → 56

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))

eval59.0ms (0.7%)

Compiler: Compiled 786 to 518 computations (34.1% saved)

prune11.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	4	57

Error

13.5b

Counts

57 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.1b	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
▶	13.6b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	14.0b	(cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))
▶	30.1b	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))

Compiler

Compiled 47 to 37 computations (21.3% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.0b	(cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))
✓	0.5b	(pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)
	0.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 39 to 26 computations (33.3% saved)

series4.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)
1.0ms	N	@	0	(pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)
1.0ms	N	@	inf	(pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)
0.0ms	N	@	0	(cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))
0.0ms	N	@	-inf	(cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))

rewrite105.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

688×	`prod-diff_binary64`
420×	`log-prod_binary64`
347×	`fma-def_binary64`
276×	`pow-prod-down_binary64`
254×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	223	25
2	2705	25

Stop Event

1×	node limit

Counts

2 → 139

Calls

Call 1

Inputs
(pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)
(cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (.f64 (neg.f64 (atan.f64 N)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (atan.f64 (+.f64 N 1))) (.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 5/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3/2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 5/2) (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) 1) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (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 (pow.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) 3) (pow.f64 (fma.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 3) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (fma.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))) (fma.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (-.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 sqrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 9))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 3 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 9)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3/2 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (.f64 (neg.f64 (atan.f64 N)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (atan.f64 (+.f64 N 1)) (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (neg.f64 (atan.f64 N))))))))
((#(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))) (cbrt.f64 (pow.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)) (+.f64 (neg.f64 (atan.f64 N)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 -1 (atan.f64 N) (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 (pow.f64 (atan.f64 N) 2))) (cbrt.f64 (atan.f64 N)) (atan.f64 N)))))) 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Outputs

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

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

752×	`unsub-neg_binary64`
578×	`distribute-neg-out_binary64`
402×	`distribute-rgt-in_binary64`
362×	`unswap-sqr_binary64`
360×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	196
1	35	188
2	62	188
3	181	188
4	524	188
5	2134	188
6	5416	188

Stop Event

1×	node limit

Counts

155 → 143

Calls

Call 1

Inputs
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)) 3)
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (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))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))

Outputs
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N)) 3)
(pow.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 3)
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (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 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 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 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.5b	(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))
✓	0.9b	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
✓	1.0b	(pow.f64 (atan.f64 (+.f64 N 1)) 3)

Compiler

Compiled 36 to 27 computations (25% saved)

series5.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	N	@	-inf	(pow.f64 (atan.f64 (+.f64 N 1)) 3)
1.0ms	N	@	0	(pow.f64 (atan.f64 (+.f64 N 1)) 3)
1.0ms	N	@	inf	(pow.f64 (atan.f64 (+.f64 N 1)) 3)
0.0ms	N	@	inf	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
0.0ms	N	@	0	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))

rewrite107.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`prod-diff_binary64`
401×	`log-prod_binary64`
304×	`exp-prod_binary64`
293×	`fma-def_binary64`
261×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	219	26
2	2534	26

Stop Event

1×	node limit

Counts

3 → 163

Calls

Call 1

Inputs
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan.f64 (+.f64 N 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))) (log.f64 (sqrt.f64 (exp.f64 (atan.f64 (+.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))) (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.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 (pow.f64 (atan.f64 (+.f64 N 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 6) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 9) 1/9)))) (#(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 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 3/2)))) (#(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)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/3) (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (atan.f64 (+.f64 N 1)))) 2)) (cbrt.f64 (log.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (atan.f64 (+.f64 N 1))))) (sqrt.f64 (log.f64 (atan.f64 (+.f64 N 1)))))))) (#(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 atan.f64 (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.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 exp.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) 1) 1/3))))))

simplify113.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1109×	`fma-def_binary64`
691×	`fma-neg_binary64`
419×	`neg-mul-1_binary64`
417×	`neg-sub0_binary64`
362×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	248
1	35	240
2	50	240
3	89	240
4	137	240
5	286	240
6	751	240
7	1476	240
8	1674	240
9	2013	240
10	3222	240
11	3881	240
12	5703	240
13	7983	240

Stop Event

1×	node limit

Counts

191 → 170

Calls

Call 1

Inputs
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (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))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 N 1))
(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
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (neg.f64 N))) 3)
(pow.f64 (atan.f64 (+.f64 1 N)) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (neg.f64 N))) 3)
(pow.f64 (atan.f64 (+.f64 1 N)) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (neg.f64 N))) 3)
(pow.f64 (atan.f64 (+.f64 1 N)) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (neg.f64 N))) 3)
(pow.f64 (atan.f64 (+.f64 1 N)) 3)
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (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 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 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 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 1 N))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 1 N))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 1 N))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 1 N))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 1 N))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 1 N))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 1 N))
(atan.f64 (+.f64 N 1))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 1 N))

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.5b	(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3)
✓	1.0b	(cbrt.f64 (atan.f64 (+.f64 N 1)))
✓	28.4b	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))

Compiler

Compiled 35 to 26 computations (25.7% saved)

series9.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	N	@	0	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
2.0ms	N	@	-inf	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
2.0ms	N	@	inf	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
0.0ms	N	@	-inf	(cbrt.f64 (atan.f64 (+.f64 N 1)))
0.0ms	N	@	0	(cbrt.f64 (atan.f64 (+.f64 N 1)))

rewrite156.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

631×	`prod-diff_binary64`
404×	`log-prod_binary64`
303×	`exp-prod_binary64`
300×	`fma-def_binary64`
265×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	220	25
2	2581	25

Stop Event

1×	node limit

Counts

3 → 174

Calls

Call 1

Inputs
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
(cbrt.f64 (atan.f64 (+.f64 N 1)))
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3)

Outputs

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(+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (fma.f64 (neg.f64 (atan.f64 N)) 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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))) (fma.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (pow.f64 (atan.f64 N) 2)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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 (neg.f64 (atan.f64 N)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (atan.f64 N) 2))) (cbrt.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 5/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 5/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (*.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1) (cbrt.f64 (atan.f64 (+.f64 N 1))) (*.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 2) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 2) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (*.f64 (neg.f64 (atan.f64 N)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/3) (log.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 2)) (cbrt.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))) (sqrt.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan.f64 (+.f64 N 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan.f64 (+.f64 N 1))))) (log.f64 (sqrt.f64 (exp.f64 (atan.f64 (+.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 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)) (*.f64 (cbrt.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 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (pow.f64 (atan.f64 (+.f64 N 1)) 5/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 5/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))) 2) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(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 atan.f64 (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.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 exp.f64 (*.f64 (*.f64 3 (log.f64 (atan.f64 (+.f64 N 1)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2/3 (log.f64 (atan.f64 (+.f64 N 1)))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (atan.f64 (+.f64 N 1))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 3/2) 2))))))

simplify214.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1292×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
625×	`cube-prod_binary64`
470×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	372
1	51	300
2	76	300
3	116	300
4	173	300
5	313	300
6	746	300
7	1433	300
8	1560	300
9	1732	300
10	1921	300
11	2162	300
12	2489	300
13	2915	300
14	3423	300
15	4027	300
16	4752	300
17	5075	300
18	5357	300
19	5581	300
20	5759	300
21	5841	300
22	6784	300
23	7761	300

Stop Event

1×	node limit

Counts

210 → 182

Calls

Call 1

Inputs
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N))))
(.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N))))
(.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N))))
(.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N))))

Outputs
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 N -1)) (atan.f64 N))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(cbrt.f64 (atan.f64 (-.f64 N -1)))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1)))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N))))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N))))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N))))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))
(.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N))))
(*.f64 1 (atan.f64 (+.f64 1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 N -1))

localize17.0ms (0.2%)

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))))
✓	2.4b	(+.f64 N (-.f64 1 N))

Compiler

Compiled 39 to 26 computations (33.3% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	N	@	0	(*.f64 N (+.f64 N 1))
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	@	-inf	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite141.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`fma-def_binary64`
473×	`log-prod_binary64`
352×	`pow-prod-down_binary64`
297×	`fma-neg_binary64`
270×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	210	29
2	3076	29

Stop Event

1×	node limit

Counts

3 → 181

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 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 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 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)) (-.f64 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 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 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 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 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 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)) 2) 1/2)))) (#(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 pow.f64 (/.f64 (fma.f64 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N)) (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (+.f64 N -1) N) (-.f64 (*.f64 N N) (pow.f64 (-.f64 1 N) 2))) -1)))) (#(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 (+.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 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 exp.f64 (*.f64 (*.f64 3 (log1p.f64 (-.f64 N N))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (-.f64 N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (-.f64 N N))) 2))))) (#(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)) (cbrt.f64 (*.f64 N N)) 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)) (cbrt.f64 (*.f64 N N)) 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)) (cbrt.f64 (*.f64 N N)) 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)) (cbrt.f64 (*.f64 N 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 -1 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 N) (cbrt.f64 (*.f64 N N)) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (cbrt.f64 N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (*.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)) (cbrt.f64 (*.f64 N 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 -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 (sqrt.f64 (+.f64 N 1)) (sqrt.f64 (+.f64 N 1)) (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 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 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 (-.f64 1 N) (-.f64 (-.f64 1 N) N) (*.f64 N N))) (fma.f64 (neg.f64 (cbrt.f64 N)) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(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))) 2) 1/2)))) (#(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 exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.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 exp.f64 (*.f64 (log.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 +.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 N 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 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N 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 N 6) (pow.f64 N 3)) (+.f64 (pow.f64 N 4) (-.f64 (*.f64 N N) (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 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 (pow.f64 (fma.f64 N N N) 2) 1/2)))) (#(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 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 exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 N (sqrt.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 N N N))) 1/3))))) (#(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) (cbrt.f64 (*.f64 N N)) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (cbrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (*.f64 (cbrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 N N)) (*.f64 (cbrt.f64 N) 1) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 1 (hypot.f64 N (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) (pow.f64 N 3/2) 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 (+.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 (cbrt.f64 N) N) (cbrt.f64 (*.f64 N N)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))))

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
447×	`distribute-rgt-neg-in_binary64`
354×	`cancel-sign-sub-inv_binary64`
329×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	240
1	44	198
2	67	198
3	163	198
4	583	198
5	1634	198
6	3616	198
7	5643	198
8	7339	198

Stop Event

1×	node limit

Counts

217 → 190

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

eval439.0ms (5.5%)

Compiler: Compiled 13438 to 8837 computations (34.2% saved)

prune104.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	775	2	777
Fresh	0	0	0
Picked	1	0	1
Done	3	0	3
Total	779	2	781

Error

0.5b

Counts

781 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	13.7b	(exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 25 to 18 computations (28% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
✓	0.2b	(exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
✓	0.8b	(log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
	2.4b	(+.f64 N (-.f64 1 N))

Compiler

Compiled 60 to 31 computations (48.3% saved)

series85.0ms (1.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
33.0ms	N	@	0	(log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
31.0ms	N	@	inf	(log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
19.0ms	N	@	-inf	(log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
0.0ms	N	@	0	(exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
0.0ms	N	@	inf	(exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))

rewrite77.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

833×	`prod-diff_binary64`
600×	`unpow-prod-down_binary64`
430×	`log-prod_binary64`
398×	`fma-def_binary64`
258×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	53
1	203	53
2	2749	53

Stop Event

1×	node limit

Counts

3 → 97

Calls

Call 1

Inputs

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

(exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(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 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(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) 1/2)))) (#(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 pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2))) (cbrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (sqrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(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 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 +.f64 0 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(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 *.f64 (pow.f64 1 1/3) (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (E.f64)) 2) (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (pow.f64 (cbrt.f64 (E.f64)) (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (E.f64)) (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (pow.f64 (sqrt.f64 (E.f64)) (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)) 1/3) (pow.f64 (sqrt.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 *.f64 (pow.f64 (*.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)) 1/3) (cbrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1/3) (cbrt.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2) 3) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 3) (pow.f64 (sqrt.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 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(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))) 2) 1/2)))) (#(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 pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2))) (cbrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (sqrt.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(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)))))))))

simplify32.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
6×	`+-commutative_binary64`
4×	`distribute-lft-in_binary64`
3×	`distribute-rgt1-in_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	420
1	12	420
2	18	420
3	27	420
4	35	420
5	39	420
6	51	420
7	64	420
8	69	420
9	70	420

Stop Event

1×

saturated

Counts

133 → 69

Calls

Call 1

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

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

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

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))))

rewrite60.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

798×	`pow1_binary64`
742×	`log1p-expm1-u_binary64`
742×	`expm1-log1p-u_binary64`
741×	`add-log-exp_binary64`
727×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	152	11
2	2057	11

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (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 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 log1p.f64 (expm1.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)))))))))

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
451×	`distribute-rgt-neg-in_binary64`
353×	`cancel-sign-sub-inv_binary64`
312×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	104
1	33	88
2	54	88
3	151	88
4	575	88
5	1638	88
6	3627	88
7	5662	88
8	7359	88

Stop Event

1×	node limit

Counts

24 → 19

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

eval156.0ms (1.9%)

Compiler: Compiled 4897 to 2949 computations (39.8% saved)

prune37.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	243	6	249
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	244	7	251

Error

0.4b

Counts

251 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	22.8b	(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
▶	1.7b	(exp.f64 (log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))))
▶	1.5b	(atan2.f64 1 (+.f64 1 (*.f64 N N)))
▶	1.0b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
	1.7b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
▶	29.2b	(atan2.f64 1 (+.f64 1 N))

Compiler

Compiled 146 to 110 computations (24.7% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	0.6b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
✓	14.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

Compiler

Compiled 42 to 22 computations (47.6% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
1.0ms	N	@	0	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
1.0ms	N	@	inf	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
1.0ms	N	@	0	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
0.0ms	N	@	inf	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite110.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

735×	`pow1_binary64`
684×	`add-log-exp_binary64`
683×	`log1p-expm1-u_binary64`
683×	`expm1-log1p-u_binary64`
669×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	186	35
2	1924	35

Stop Event

1×	node limit

Counts

3 → 58

Calls

Call 1

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

Outputs

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

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

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
6×	`+-commutative_binary64`
4×	`distribute-lft-in_binary64`
3×	`distribute-rgt1-in_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	420
1	12	420
2	18	420
3	27	420
4	35	420
5	39	420
6	51	420
7	64	420
8	69	420
9	70	420

Stop Event

1×

saturated

Counts

94 → 45

Calls

Call 1

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

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite56.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`pow1_binary64`
482×	`add-sqr-sqrt_binary64`
460×	`add-log-exp_binary64`
460×	`log1p-expm1-u_binary64`
460×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	101	7
2	1243	7

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

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

Outputs

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

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

13×	`fma-def_binary64`
11×	`fma-neg_binary64`
7×	`cancel-sign-sub-inv_binary64`
6×	`associate--r+_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	84
1	19	84
2	25	84
3	48	84
4	67	84
5	97	84
6	112	84
7	116	84

Stop Event

1×

saturated

Counts

28 → 19

Calls

Call 1

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

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

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite88.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

563×	`pow1_binary64`
525×	`add-log-exp_binary64`
524×	`log1p-expm1-u_binary64`
524×	`expm1-log1p-u_binary64`
513×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	121	8
2	1482	8

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

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

Outputs

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

simplify161.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1366×	`sqr-pow_binary64`
695×	`pow-sqr_binary64`
617×	`cube-prod_binary64`
613×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	120
1	14	96
2	21	96
3	32	96
4	61	96
5	160	96
6	581	96
7	1449	96
8	1633	96
9	1817	96
10	2025	96
11	2318	96
12	2713	96
13	3196	96
14	3762	96
15	4448	96
16	5283	96
17	5681	96
18	5971	96
19	6251	96
20	6325	96
21	6361	96
22	7302	96

Stop Event

1×	node limit

Counts

28 → 18

Calls

Call 1

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

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

localize80.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 N N 1) N)
✓	0.1b	(*.f64 (+.f64 1 (pow.f64 N 3)) N)
✓	0.5b	(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
✓	19.6b	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))

Compiler

Compiled 77 to 52 computations (32.5% saved)

series7.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
1.0ms	N	@	0	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
1.0ms	N	@	inf	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
1.0ms	N	@	-inf	(*.f64 (+.f64 1 (pow.f64 N 3)) N)
1.0ms	N	@	inf	(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))

rewrite119.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

661×	`fma-def_binary64`
652×	`log-prod_binary64`
350×	`pow2_binary64`
264×	`fma-neg_binary64`
240×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	64
1	275	64
2	3904	58

Stop Event

1×	node limit

Counts

4 → 224

Calls

Call 1

Inputs
(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
(*.f64 (+.f64 1 (pow.f64 N 3)) N)
(-.f64 (fma.f64 N N 1) N)

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

simplify207.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

451×	`associate-/l*_binary64`
396×	`fma-neg_binary64`
382×	`fma-def_binary64`
350×	`div-sub_binary64`
301×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	561
1	78	477
2	143	477
3	360	477
4	1393	477
5	4958	477

Stop Event

1×	node limit

Counts

272 → 241

Calls

Call 1

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

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

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
✓	1.3b	(exp.f64 (log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))))
✓	15.4b	(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))

Compiler

Compiled 40 to 20 computations (50% saved)

series48.0ms (0.6%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
42.0ms	N	@	inf	(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
3.0ms	N	@	0	(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
0.0ms	N	@	0	(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
0.0ms	N	@	-inf	(log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
0.0ms	N	@	inf	(exp.f64 (log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))))

rewrite59.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`pow1_binary64`
609×	`log1p-expm1-u_binary64`
609×	`expm1-log1p-u_binary64`
608×	`add-log-exp_binary64`
595×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	35
1	146	35
2	1683	35

Stop Event

1×	node limit

Counts

3 → 58

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (log.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)) (log.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (pow.f64 (cbrt.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) (cbrt.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.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 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))))

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

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

simplify24.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
6×	`+-commutative_binary64`
4×	`distribute-lft-in_binary64`
3×	`distribute-rgt1-in_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	132
1	11	132
2	17	132
3	26	132
4	34	132
5	38	132
6	50	132
7	63	132
8	68	132
9	69	132

Stop Event

1×

saturated

Counts

70 → 40

Calls

Call 1

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

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

eval414.0ms (5.2%)

Compiler: Compiled 7542 to 5248 computations (30.4% saved)

prune259.0ms (3.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	357	6	363
Fresh	1	0	1
Picked	0	1	1
Done	2	3	5
Total	360	10	370

Error

0.4b

Counts

370 → 10

Alt Table

Click to see full alt table

Status	Error	Program
	19.7b	(atan2.f64 1 (+.f64 1 (.f64 (+.f64 1 (pow.f64 N 3)) (.f64 N (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))
	2.1b	(pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 2)
	5.2b	(pow.f64 (cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3/2)) 2)
✓	29.2b	(atan2.f64 1 (+.f64 1 N))
✓	1.7b	(exp.f64 (log.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))))
✓	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	1.5b	(atan2.f64 1 (+.f64 1 (*.f64 N N)))
	1.9b	(pow.f64 (*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) 2)
	2.8b	(pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N 1))) 3)
	22.8b	(atan2.f64 1 (+.f64 1 (/.f64 (.f64 (+.f64 1 (pow.f64 N 3)) N) (+.f64 (.f64 N N) (-.f64 1 N)))))

Compiler

Compiled 133 to 101 computations (24.1% saved)

regimes48.0ms (0.6%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

20.0ms	N
8.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
6.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
0.5b	1	`N`
0.5b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`
0.5b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 246 to 172 computations (30.1% saved)

regimes9.0ms (0.1%)

Accuracy

Total -28.0b remaining (-1821.4%)

Threshold costs -28.0b (-1821.4%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
1.5b	1	`N`

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	18	30

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 24 to 19 computations (20.8% saved)

soundness0.0ms (0%)

end57.0ms (0.7%)

Compiler: Compiled 22 to 17 computations (22.7% 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	122	11
8	168	11
9	204	11
10	230	11
11	232	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	122	11
8	168	11
9	204	11
10	230	11
11	232	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	215	68
8	258	68
9	294	68
10	320	68
11	322	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	122	11
8	168	11
9	204	11
10	230	11
11	232	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	122	11
8	168	11
9	204	11
10	230	11
11	232	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	215	68
8	258	68
9	294	68
10	320	68
11	322	68

Details

analyze0.0ms (0%)

sample3.4s (42.9%)

preprocess212.0ms (2.6%)

simplify27.0ms (0.3%)

eval1.0ms (0%)

prune2.0ms (0%)

localize20.0ms (0.2%)

series3.0ms (0%)

rewrite119.0ms (1.5%)

simplify31.0ms (0.4%)

eval59.0ms (0.7%)

prune11.0ms (0.1%)

localize25.0ms (0.3%)

series4.0ms (0.1%)

rewrite105.0ms (1.3%)

simplify60.0ms (0.7%)

localize25.0ms (0.3%)

series5.0ms (0.1%)

rewrite107.0ms (1.3%)

simplify113.0ms (1.4%)

localize22.0ms (0.3%)

series9.0ms (0.1%)

rewrite156.0ms (2%)

simplify214.0ms (2.7%)

localize17.0ms (0.2%)

series6.0ms (0.1%)

rewrite141.0ms (1.8%)

simplify87.0ms (1.1%)

eval439.0ms (5.5%)

prune104.0ms (1.3%)

localize31.0ms (0.4%)

series85.0ms (1.1%)

rewrite77.0ms (1%)

simplify32.0ms (0.4%)

localize12.0ms (0.2%)

series1.0ms (0%)

rewrite60.0ms (0.7%)

simplify76.0ms (0.9%)

eval156.0ms (1.9%)

prune37.0ms (0.5%)

localize16.0ms (0.2%)

series4.0ms (0.1%)

rewrite110.0ms (1.4%)

simplify62.0ms (0.8%)

localize6.0ms (0.1%)

series1.0ms (0%)

rewrite56.0ms (0.7%)

simplify13.0ms (0.2%)

localize7.0ms (0.1%)

series1.0ms (0%)

rewrite88.0ms (1.1%)

simplify161.0ms (2%)

localize80.0ms (1%)

series7.0ms (0.1%)

rewrite119.0ms (1.5%)

simplify207.0ms (2.6%)

localize21.0ms (0.3%)

series48.0ms (0.6%)

rewrite59.0ms (0.7%)

simplify24.0ms (0.3%)

eval414.0ms (5.2%)

prune259.0ms (3.2%)

regimes48.0ms (0.6%)

regimes9.0ms (0.1%)

simplify9.0ms (0.1%)

soundness0.0ms (0%)

end57.0ms (0.7%)

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	122	11
8	168	11
9	204	11
10	230	11
11	232	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	122	11
8	168	11
9	204	11
10	230	11
11	232	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	215	68
8	258	68
9	294	68
10	320	68
11	322	68