Details

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample3.4s (40.7%)

Results

1.5s	2144×	body	2048	valid
1.4s	4538×	body	256	valid
397.0ms	1039×	body	1024	valid
146.0ms	535×	body	512	valid

preprocess22.0ms (0.3%)

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)

simplify32.0ms (0.4%)

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))

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

15.5b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	15.5b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	1.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0%)

Counts

2 → 8

Calls

6 calls:

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

rewrite62.0ms (0.7%)

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))))))))

simplify69.0ms (0.8%)

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))

eval18.0ms (0.2%)

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

prune8.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Error

14.2b

Counts

57 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	14.3b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	15.5b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	34.8b	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
▶	34.0b	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))

Compiler

Compiled 44 to 34 computations (22.7% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.6b	(cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3))
✓	1.0b	(pow.f64 (atan.f64 (+.f64 N 1)) 3)
✓	1.6b	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))

Compiler

Compiled 36 to 27 computations (25% saved)

series8.0ms (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)
1.0ms	N	@	0	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
1.0ms	N	@	-inf	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))

rewrite135.0ms (1.6%)

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

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

((#(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))))))

simplify172.0ms (2%)

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	274	240
6	735	240
7	1465	240
8	1659	240
9	1998	240
10	3207	240
11	3866	240
12	5688	240
13	7968	240

Stop Event

1×	node limit

Counts

191 → 168

Calls

Call 1

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

localize66.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.6b	(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3)
✓	1.0b	(cbrt.f64 (atan.f64 (+.f64 N 1)))
✓	33.8b	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))

Compiler

Compiled 35 to 26 computations (25.7% saved)

series18.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	N	@	inf	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
5.0ms	N	@	0	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
4.0ms	N	@	-inf	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
1.0ms	N	@	-inf	(cbrt.f64 (atan.f64 (+.f64 N 1)))
1.0ms	N	@	0	(cbrt.f64 (atan.f64 (+.f64 N 1)))

rewrite174.0ms (2.1%)

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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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 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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))))))

simplify261.0ms (3.1%)

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))

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 N (+.f64 N 1)))
✓	0.0b	(*.f64 N (+.f64 N 1))
✓	0.0b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	1.7b	(+.f64 N (-.f64 1 N))

Compiler

Compiled 39 to 26 computations (33.3% saved)

series8.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite141.0ms (1.7%)

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	43
1	210	37
2	3076	37

Stop Event

1×	node limit

Counts

4 → 240

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

simplify113.0ms (1.3%)

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	327
1	44	269
2	67	269
3	163	269
4	583	269
5	1634	269
6	3616	269
7	5643	269
8	7339	269

Stop Event

1×	node limit

Counts

288 → 253

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

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

eval344.0ms (4.1%)

Compiler: Compiled 10978 to 7103 computations (35.3% saved)

prune81.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	637	2	639
Fresh	0	0	0
Picked	0	1	1
Done	2	1	3
Total	639	4	643

Error

0.3b

Counts

643 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	14.3b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	15.5b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
▶	0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 41 to 30 computations (26.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (*.f64 N (+.f64 N 1)))
	0.0b	(*.f64 N (+.f64 N 1))
✓	0.3b	(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))))

rewrite100.0ms (1.2%)

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)))))))))

simplify78.0ms (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)))

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (fma.f64 N N N))
✓	0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 21 to 9 computations (57.1% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite100.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`pow1_binary64`
556×	`add-log-exp_binary64`
556×	`log1p-expm1-u_binary64`
556×	`expm1-log1p-u_binary64`
545×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	121	19
2	1493	19

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

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

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)))))))))

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

simplify186.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
902×	`fma-def_binary64`
572×	`cube-prod_binary64`
555×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	215
1	25	203
2	35	203
3	54	203
4	112	203
5	308	203
6	993	203
7	2246	203
8	2714	203
9	2930	203
10	3168	203
11	3531	203
12	3968	203
13	4474	203
14	5060	203
15	5785	203
16	6626	203
17	7018	203
18	7306	203
19	7585	203
20	7657	203
21	7691	203

Stop Event

1×	node limit

Counts

70 → 57

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

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

eval106.0ms (1.3%)

Compiler: Compiled 2597 to 1524 computations (41.3% saved)

prune107.0ms (1.3%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	187	11	198
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	188	14	202

Error

0.2b

Counts

202 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	0.8b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
✓	14.3b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
	10.4b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
✓	15.5b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	34.5b	(atan2.f64 1 (+.f64 N 1))
	2.3b	(atan2.f64 1 (+.f64 1 (*.f64 N N)))
	1.4b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
✓	0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	35.5b	(atan2.f64 1 1)
	24.0b	(atan2.f64 1 (*.f64 N N))
▶	27.4b	(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
▶	0.5b	(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
▶	23.6b	(atan2.f64 1 (fma.f64 N N N))
	27.4b	(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))

Compiler

Compiled 264 to 194 computations (26.5% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (fma.f64 N N N))
✓	0.2b	(pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3)
✓	0.3b	(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
✓	18.2b	(cbrt.f64 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 41 to 21 computations (48.8% saved)

series37.0ms (0.4%)

Counts

3 → 20

Calls

9 calls:

Time	Variable		Point	Expression
25.0ms	N	@	inf	(cbrt.f64 (+.f64 1 (fma.f64 N N N)))
4.0ms	N	@	0	(cbrt.f64 (+.f64 1 (fma.f64 N N N)))
2.0ms	N	@	inf	(pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3)
1.0ms	N	@	0	(pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3)
1.0ms	N	@	-inf	(pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3)

rewrite94.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

761×	`pow1_binary64`
714×	`add-log-exp_binary64`
713×	`log1p-expm1-u_binary64`
713×	`expm1-log1p-u_binary64`
698×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	189	29
2	1974	29

Stop Event

1×	node limit

Counts

3 → 74

Calls

Call 1

Inputs
(cbrt.f64 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3)

Outputs

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

((#(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)))))))))

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

simplify182.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1103×	`sqr-pow_binary64`
802×	`fma-def_binary64`
524×	`pow-sqr_binary64`
518×	`cube-prod_binary64`
465×	`fabs-mul_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	256
1	75	190
2	164	190
3	419	184
4	1136	181
5	2315	181
6	2730	181
7	3060	181
8	3388	181
9	3791	181
10	4320	181
11	4983	181
12	5799	181
13	6178	181
14	6523	181
15	6776	181
16	7008	181
17	7152	181

Stop Event

1×	node limit

Counts

94 → 86

Calls

Call 1

Inputs
1
(+.f64 (*.f64 1/3 N) 1)
(+.f64 (.f64 1/3 N) (+.f64 (.f64 2/9 (pow.f64 N 2)) 1))
(+.f64 (.f64 1/3 N) (+.f64 (.f64 2/9 (pow.f64 N 2)) (+.f64 1 (*.f64 -13/81 (pow.f64 N 3)))))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
1
(+.f64 N 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))

Outputs
1
(+.f64 (*.f64 1/3 N) 1)
(fma.f64 1/3 N 1)
(+.f64 (.f64 1/3 N) (+.f64 (.f64 2/9 (pow.f64 N 2)) 1))
(fma.f64 1/3 N (fma.f64 2/9 (*.f64 N N) 1))
(fma.f64 1/3 N (fma.f64 N (*.f64 N 2/9) 1))
(fma.f64 N (fma.f64 N 2/9 1/3) 1)
(+.f64 (.f64 1/3 N) (+.f64 (.f64 2/9 (pow.f64 N 2)) (+.f64 1 (*.f64 -13/81 (pow.f64 N 3)))))
(fma.f64 1/3 N (+.f64 (fma.f64 2/9 (.f64 N N) 1) (.f64 -13/81 (pow.f64 N 3))))
(fma.f64 1/3 N (fma.f64 2/9 (*.f64 N N) (fma.f64 -13/81 (pow.f64 N 3) 1)))
(fma.f64 1/3 N (fma.f64 N (*.f64 N 2/9) (fma.f64 -13/81 (pow.f64 N 3) 1)))
(fma.f64 1/3 N (fma.f64 (*.f64 N N) (fma.f64 N -13/81 2/9) 1))
(fma.f64 N (fma.f64 N (fma.f64 N -13/81 2/9) 1/3) 1)
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (pow.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 1/3) 3))
(atan2.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))

localize5.0ms (0.1%)

Compiler: Compiled 5 to 5 computations (0% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

series2.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite61.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

486×	`pow1_binary64`
473×	`add-sqr-sqrt_binary64`
465×	`*-un-lft-identity_binary64`
452×	`log1p-expm1-u_binary64`
452×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1249	7

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

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

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))))))))

simplify23.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	36
1	16	28
2	24	28
3	47	28
4	66	28
5	96	28
6	111	28
7	115	28

Stop Event

1×

saturated

Counts

20 → 18

Calls

Call 1

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

localize14.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(atan2.f64 1 (fma.f64 N N N))

Compiler

Compiled 13 to 5 computations (61.5% saved)

series2.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite66.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

394×	`pow1_binary64`
378×	`add-sqr-sqrt_binary64`
373×	`*-un-lft-identity_binary64`
360×	`add-log-exp_binary64`
360×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	91	8
2	969	8

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 1 (fma.f64 N N N))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.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 1 (fma.f64 N N N)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N N))) (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N N))) 2) (cbrt.f64 (atan2.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N N))) (sqrt.f64 (atan2.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (atan2.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N N)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N N)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (atan2.f64 1 (fma.f64 N N N)) (cbrt.f64 (atan2.f64 1 (fma.f64 N N N)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N N)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (atan2.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 1 (fma.f64 N N N)))) 2) 3) (cbrt.f64 (atan2.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N N)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N N)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (fma.f64 N N N))))))))

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

26 → 26

Calls

Call 1

Inputs

Outputs

localize89.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 N N 1) N)
✓	0.0b	(*.f64 (+.f64 1 (pow.f64 N 3)) N)
✓	0.3b	(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
✓	23.6b	(/.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)

series14.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	N	@	-inf	(*.f64 (+.f64 1 (pow.f64 N 3)) N)
2.0ms	N	@	-inf	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
2.0ms	N	@	0	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
2.0ms	N	@	inf	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) 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))))

rewrite163.0ms (1.9%)

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

simplify118.0ms (1.4%)

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))

eval423.0ms (5%)

Compiler: Compiled 8390 to 5702 computations (32% saved)

prune136.0ms (1.6%)

Pruning

15 alts after pruning (9 fresh and 6 done)

	Pruned	Kept	Total
New	402	8	410
Fresh	5	1	6
Picked	1	0	1
Done	1	6	7
Total	409	15	424

Error

0.2b

Counts

424 → 15

Alt Table

Click to see full alt table

Status	Error	Program
✓	14.3b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
	24.2b	(atan2.f64 1 (pow.f64 (cbrt.f64 (*.f64 N N)) 3))
✓	15.5b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
	33.7b	(cbrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N N)) 3))
✓	34.5b	(atan2.f64 1 (+.f64 N 1))
	23.7b	(pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N N))) 2)
✓	0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	35.5b	(atan2.f64 1 1)
	23.9b	(pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N N))) 3)
	27.4b	(atan2.f64 1 (+.f64 1 (/.f64 (.f64 (+.f64 1 (pow.f64 N 3)) N) (+.f64 (.f64 N N) (-.f64 1 N)))))
	24.0b	(atan2.f64 1 (*.f64 N N))
	29.0b	(atan2.f64 1 (+.f64 1 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N))))
	25.1b	(atan2.f64 1 (+.f64 1 (*.f64 (/.f64 (+.f64 1 (pow.f64 N 3)) 1) (/.f64 N (fma.f64 N N (-.f64 1 N))))))
	2.3b	(atan2.f64 1 (+.f64 1 (*.f64 N N)))
✓	23.6b	(atan2.f64 1 (fma.f64 N N N))

Compiler

Compiled 158 to 117 computations (25.9% saved)

regimes202.0ms (2.4%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

162.0ms	N
6.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
5.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
0.3b	1	`N`
0.3b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`
0.3b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 276 to 183 computations (33.7% saved)

regimes31.0ms (0.4%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

19.0ms	N
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
0.3b	1	`N`
0.3b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`
0.3b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 81 to 56 computations (30.9% saved)

regimes31.0ms (0.4%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

1 calls:

29.0ms

Results

Error	Segments	Branch
2.3b	1	`N`

Compiler

Compiled 30 to 20 computations (33.3% saved)

regimes19.0ms (0.2%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

1 calls:

17.0ms

Results

Error	Segments	Branch
1.8b	3	`N`

Compiler

Compiled 16 to 12 computations (25% saved)

bsearch171.0ms (2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
90.0ms	0.007115602309660742	472.01743582695923
80.0ms	-141.95970556005847	-0.5352218021411645

Compiler

Compiled 12 to 9 computations (25% saved)

regimes9.0ms (0.1%)

Accuracy

Total -1.0b remaining (-3%)

Threshold costs -1.0b (-3%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
34.5b	1	`N`

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	78
1	30	78

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(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 N)))
(if (<=.f64 N -2497381551023065/17592186044416) (atan2.f64 1 (.f64 N N)) (if (<=.f64 N 4101865460519009/576460752303423488) (atan2.f64 1 (+.f64 N 1)) (atan2.f64 1 (.f64 N N))))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 1)

Outputs
(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 1 (*.f64 N N)))
(if (<=.f64 N -2497381551023065/17592186044416) (atan2.f64 1 (.f64 N N)) (if (<=.f64 N 4101865460519009/576460752303423488) (atan2.f64 1 (+.f64 N 1)) (atan2.f64 1 (.f64 N N))))
(if (<=.f64 N -2497381551023065/17592186044416) (atan2.f64 1 (.f64 N N)) (if (<=.f64 N 4101865460519009/576460752303423488) (atan2.f64 1 (+.f64 1 N)) (atan2.f64 1 (.f64 N N))))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 1)

Compiler

Compiled 61 to 45 computations (26.2% saved)

soundness467.0ms (5.5%)

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	327
1	44	269
2	67	269
3	163	269
4	583	269
5	1634	269
6	3616	269
7	5643	269
8	7339	269

Stop Event

1×	node limit

Compiler

Compiled 41 to 30 computations (26.8% saved)

end86.0ms (1%)

Compiler: Compiled 56 to 39 computations (30.4% 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 (40.7%)

preprocess22.0ms (0.3%)

simplify32.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize10.0ms (0.1%)

series2.0ms (0%)

rewrite62.0ms (0.7%)

simplify69.0ms (0.8%)

eval18.0ms (0.2%)

prune8.0ms (0.1%)

localize30.0ms (0.3%)

series8.0ms (0.1%)

rewrite135.0ms (1.6%)

simplify172.0ms (2%)

localize66.0ms (0.8%)

series18.0ms (0.2%)

rewrite174.0ms (2.1%)

simplify261.0ms (3.1%)

localize30.0ms (0.4%)

series8.0ms (0.1%)

rewrite141.0ms (1.7%)

simplify113.0ms (1.3%)

eval344.0ms (4.1%)

prune81.0ms (1%)

localize11.0ms (0.1%)

series1.0ms (0%)

rewrite100.0ms (1.2%)

simplify78.0ms (0.9%)

localize9.0ms (0.1%)

series2.0ms (0%)

rewrite100.0ms (1.2%)

simplify186.0ms (2.2%)

eval106.0ms (1.3%)

prune107.0ms (1.3%)

localize33.0ms (0.4%)

series37.0ms (0.4%)

rewrite94.0ms (1.1%)

simplify182.0ms (2.2%)

localize5.0ms (0.1%)

localize10.0ms (0.1%)

series2.0ms (0%)

rewrite61.0ms (0.7%)

simplify23.0ms (0.3%)

localize14.0ms (0.2%)

series2.0ms (0%)

rewrite66.0ms (0.8%)

simplify14.0ms (0.2%)

localize89.0ms (1.1%)

series14.0ms (0.2%)

rewrite163.0ms (1.9%)

simplify118.0ms (1.4%)

eval423.0ms (5%)

prune136.0ms (1.6%)

regimes202.0ms (2.4%)

regimes31.0ms (0.4%)

regimes31.0ms (0.4%)

regimes19.0ms (0.2%)

bsearch171.0ms (2%)

regimes9.0ms (0.1%)

simplify13.0ms (0.2%)

soundness467.0ms (5.5%)

end86.0ms (1%)

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