Details

analyze1.0ms (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)

sample2.9s (39.2%)

Results

1.1s	2267×	body	2048	valid
966.0ms	4465×	body	256	valid
517.0ms	1017×	body	1024	valid
272.0ms	507×	body	512	valid

preprocess48.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify12.0ms (0.2%)

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

16.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	16.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

localize45.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	1.0b	(-.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))

rewrite89.0ms (1.2%)

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

Outputs

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

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

simplify25.0ms (0.3%)

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))

eval20.0ms (0.3%)

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

15.1b

Counts

57 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	16.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	15.3b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	29.4b	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
▶	30.5b	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))

Compiler

Compiled 44 to 34 computations (22.7% saved)

localize58.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 36 to 27 computations (25% saved)

series4.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

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

rewrite225.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 163

Calls

Call 1

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

Outputs
((#(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 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 log1p.f64 (expm1.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)))))))
((#(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) 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Outputs

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

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

simplify107.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

191 → 170

Calls

Call 1

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

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

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.5b	(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3)
✓	1.0b	(cbrt.f64 (atan.f64 (+.f64 N 1)))
✓	29.0b	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))

Compiler

Compiled 35 to 26 computations (25.7% saved)

series33.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
25.0ms	N	@	inf	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
3.0ms	N	@	0	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
3.0ms	N	@	-inf	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))
0.0ms	N	@	-inf	(cbrt.f64 (atan.f64 (+.f64 N 1)))
0.0ms	N	@	0	(cbrt.f64 (atan.f64 (+.f64 N 1)))

rewrite91.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 174

Calls

Call 1

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

Outputs

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((#(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 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 log1p.f64 (expm1.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))))

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

simplify215.0ms (2.9%)

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))

localize59.0ms (0.8%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 39 to 26 computations (33.3% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
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	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite124.0ms (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	33
1	210	29
2	3076	29

Stop Event

1×	node limit

Counts

3 → 181

Calls

Call 1

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

Outputs

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

simplify111.0ms (1.5%)

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	240
1	44	198
2	67	198
3	163	198
4	583	198
5	1634	198
6	3616	198
7	5643	198
8	7339	198

Stop Event

1×	node limit

Counts

217 → 190

Calls

Call 1

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

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

eval490.0ms (6.6%)

Compiler: Compiled 9878 to 6492 computations (34.3% saved)

prune83.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	576	2	578
Fresh	0	0	0
Picked	0	1	1
Done	2	1	3
Total	578	4	582

Error

0.7b

Counts

582 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	16.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	15.3b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	15.3b	(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))
▶	0.7b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 48 to 35 computations (27.1% saved)

localize62.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
✓	0.0b	(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))
✓	0.5b	(pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)
	1.7b	(+.f64 N (-.f64 1 N))

Compiler

Compiled 63 to 34 computations (46% saved)

series7.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	N	@	inf	(pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)
1.0ms	N	@	0	(pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)
1.0ms	N	@	-inf	(pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)
0.0ms	N	@	-inf	(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))
0.0ms	N	@	0	(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))

rewrite115.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

833×	`prod-diff_binary64`
461×	`log-prod_binary64`
403×	`fma-def_binary64`
279×	`pow2_binary64`
194×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	54
1	246	54
2	3045	54

Stop Event

1×	node limit

Counts

3 → 70

Calls

Call 1

Inputs

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

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2) (*.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (*.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3/2) (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) 1) (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3)))))))

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

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

simplify235.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
676×	`cube-prod_binary64`
666×	`pow-sqr_binary64`
560×	`fabs-mul_binary64`
374×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	432
1	21	432
2	32	432
3	50	432
4	79	432
5	166	432
6	553	432
7	1227	432
8	1319	432
9	1453	432
10	1611	432
11	1845	432
12	2167	432
13	2589	432
14	3091	432
15	3693	432
16	4417	432
17	4738	432
18	5020	432
19	5244	432
20	5422	432
21	5506	432
22	6446	432
23	7420	432
24	7886	432

Stop Event

1×	node limit

Counts

106 → 51

Calls

Call 1

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

Outputs
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3)
(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

localize37.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 N (+.f64 N 1))
✓	0.7b	(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))))

rewrite80.0ms (1.1%)

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 exp.f64 (log.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)))))))))

simplify76.0ms (1%)

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)))

eval148.0ms (2%)

Compiler: Compiled 4512 to 2744 computations (39.2% saved)

prune74.0ms (1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	223	8	231
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	224	11	235

Error

0.6b

Counts

235 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.1b	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
	1.5b	(atan2.f64 1 (+.f64 1 (*.f64 N N)))
✓	16.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	15.3b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	0.7b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	20.8b	(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
	1.3b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
▶	29.0b	(atan2.f64 1 (+.f64 1 N))
▶	2.0b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
	11.5b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3))
▶	0.8b	(atan2.f64 1 (+.f64 1 (fma.f64 (.f64 (cbrt.f64 N) N) (cbrt.f64 (.f64 N N)) N)))

Compiler

Compiled 224 to 162 computations (27.7% saved)

localize40.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 N) N)
✓	0.5b	(cbrt.f64 N)
✓	0.7b	(atan2.f64 1 (+.f64 1 (fma.f64 (.f64 (cbrt.f64 N) N) (cbrt.f64 (.f64 N N)) N)))
✓	30.2b	(cbrt.f64 (*.f64 N N))

Compiler

Compiled 52 to 13 computations (75% saved)

series12.0ms (0.2%)

Counts

4 → 12

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	N	@	0	(*.f64 (cbrt.f64 N) N)
2.0ms	N	@	0	(cbrt.f64 (*.f64 N N))
1.0ms	N	@	-inf	(cbrt.f64 N)
1.0ms	N	@	inf	(cbrt.f64 (*.f64 N N))
1.0ms	N	@	-inf	(*.f64 (cbrt.f64 N) N)

rewrite101.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

848×	`pow1_binary64`
789×	`add-log-exp_binary64`
788×	`log1p-expm1-u_binary64`
788×	`expm1-log1p-u_binary64`
769×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	198	28
2	2377	28

Stop Event

1×	node limit

Counts

4 → 74

Calls

Call 1

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

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

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

923×	`fma-def_binary64`
863×	`unswap-sqr_binary64`
678×	`unsub-neg_binary64`
411×	`fma-neg_binary64`
360×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	280
1	53	280
2	119	280
3	352	280
4	1331	272
5	2939	272
6	6258	272

Stop Event

1×	node limit

Counts

86 → 78

Calls

Call 1

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

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

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite92.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

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

Outputs

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

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

28 → 19

Calls

Call 1

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

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

localize87.0ms (1.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.7b	(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
✓	11.4b	(-.f64 (pow.f64 N 4) (*.f64 N N))
✓	33.9b	(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))

Compiler

Compiled 69 to 29 computations (58% saved)

series9.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms	N	@	-inf	(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms	N	@	inf	(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms	N	@	-inf	(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
1.0ms	N	@	inf	(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))

rewrite170.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`fma-def_binary64`
469×	`log-prod_binary64`
339×	`fma-neg_binary64`
256×	`pow2_binary64`
207×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	271	24
2	4027	24

Stop Event

1×	node limit

Counts

3 → 272

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N)) (neg.f64 (/.f64 N (/.f64 (fma.f64 N N N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (fma.f64 N N N) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N)) (/.f64 N (/.f64 (fma.f64 N N N) N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 N N 0) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (+.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 2) (/.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 (fma.f64 N N N) (*.f64 (fma.f64 N N N) (/.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 (cbrt.f64 (fma.f64 N N N)) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (neg.f64 (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4) (*.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (neg.f64 (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 N N N)) (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4)) (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4) 1) (pow.f64 (cbrt.f64 (fma.f64 N N N)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) -2) (/.f64 (pow.f64 (fma.f64 N N N) 2) (cbrt.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) -1/2) (pow.f64 (fma.f64 N N N) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4) (hypot.f64 N (sqrt.f64 N))) (/.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 6) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 N (sqrt.f64 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 N N N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1 (fma.f64 N N N)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (+.f64 1 (expm1.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (pow.f64 (exp.f64 N) N) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (pow.f64 (exp.f64 N) N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (+.f64 1 (expm1.f64 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (+.f64 1 (expm1.f64 (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (exp.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 N) N) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 N N))) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N N N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N 1 (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N -1 (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 4) (/.f64 1 (fma.f64 N N N)) (neg.f64 (/.f64 N (/.f64 (fma.f64 N N N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N N) 1 N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (fma.f64 N N N) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N N)) (neg.f64 (/.f64 N (/.f64 (fma.f64 N N N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (fma.f64 N N N) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) (pow.f64 (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) 2) (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (pow.f64 (cbrt.f64 N) 4) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (neg.f64 (cbrt.f64 N)) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 N) (pow.f64 (cbrt.f64 N) 2) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 4) (pow.f64 (cbrt.f64 N) 2) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 4) (neg.f64 (pow.f64 (cbrt.f64 N) 2)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (sqrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (neg.f64 (sqrt.f64 N)) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (/.f64 1 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) 1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (+.f64 (fma.f64 N N N) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (sqrt.f64 N)) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N))) 2) (cbrt.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N))) (neg.f64 (/.f64 N (/.f64 (fma.f64 N N N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 N) 8)) (sqrt.f64 (pow.f64 (cbrt.f64 N) 4)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N))) (sqrt.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N N))) (neg.f64 (/.f64 N (/.f64 (fma.f64 N N N) N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 N) 4)) (sqrt.f64 (pow.f64 (cbrt.f64 N) 2)) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 4)) (pow.f64 (cbrt.f64 N) 2) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 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fma.f64 (pow.f64 (fma.f64 N N N) 3) (/.f64 1 (fma.f64 N N N)) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 3) (/.f64 1 (fma.f64 N N N)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 4) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 N N) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (pow.f64 (fma.f64 N N N) 2) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 4) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 4) (pow.f64 (/.f64 1 (fma.f64 N N N)) 2) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 4) (pow.f64 (/.f64 1 (fma.f64 N N N)) 2) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 4) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 4) (pow.f64 (fma.f64 N N N) -2) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 4) (pow.f64 (fma.f64 N N N) -2) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 4) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (sqrt.f64 N)) (sqrt.f64 N) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 3/2) (hypot.f64 N (sqrt.f64 N)) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 3/2) (hypot.f64 N (sqrt.f64 N)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 4) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 2))) 2) (cbrt.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 N) 8)) (sqrt.f64 (pow.f64 (cbrt.f64 N) 4)) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (fma.f64 N N N)) (hypot.f64 1 (fma.f64 N N N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 4)) (pow.f64 (cbrt.f64 N) 2) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4)) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 4)) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 4) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N 1) (*.f64 N N) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N 1) (*.f64 N N) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 4) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 N N N) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (cbrt.f64 (fma.f64 N N N)) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 N N N) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (cbrt.f64 (fma.f64 N N N)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (pow.f64 (cbrt.f64 N) 4) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 N N) (pow.f64 (cbrt.f64 N) 4)) (pow.f64 (cbrt.f64 N) 2) (*.f64 N N))))))

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

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

824×	`associate-/r*_binary64`
749×	`fma-def_binary64`
681×	`associate-l_binary64`
377×	`associate-*l/_binary64`
256×	`associate-/r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	593
1	57	566
2	101	566
3	280	434
4	1636	374

Stop Event

1×	node limit

Counts

308 → 284

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

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
✓	0.7b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	13.4b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

Compiler

Compiled 42 to 22 computations (47.6% saved)

series30.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
21.0ms	N	@	-inf	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
2.0ms	N	@	-inf	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
2.0ms	N	@	inf	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
2.0ms	N	@	0	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
1.0ms	N	@	0	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)

rewrite124.0ms (1.7%)

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	35
1	188	35
2	1976	35

Stop Event

1×	node limit

Counts

3 → 63

Calls

Call 1

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

Outputs

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

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

simplify240.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1290×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
625×	`cube-prod_binary64`
558×	`fabs-mul_binary64`
373×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	420
1	27	420
2	41	420
3	61	420
4	93	420
5	190	420
6	586	420
7	1263	420
8	1360	420
9	1499	420
10	1662	420
11	1901	420
12	2228	420
13	2656	420
14	3163	420
15	3770	420
16	4497	420
17	4818	420
18	5102	420
19	5324	420
20	5502	420
21	5584	420
22	6527	420
23	7504	420
24	7970	420

Stop Event

1×	node limit

Counts

99 → 49

Calls

Call 1

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

Outputs
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 1/3)
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (pow.f64 1 1/3) (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(*.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) (pow.f64 1 1/3))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)
	0.5b	(cbrt.f64 N)
✓	0.6b	(pow.f64 (cbrt.f64 N) 5)
✓	0.7b	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))

Compiler

Compiled 40 to 21 computations (47.5% saved)

series8.0ms (0.1%)

Counts

3 → 18

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	N	@	-inf	(pow.f64 (cbrt.f64 N) 5)
2.0ms	N	@	0	(pow.f64 (cbrt.f64 N) 5)
1.0ms	N	@	inf	(pow.f64 (cbrt.f64 N) 5)
1.0ms	N	@	-inf	(fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)
0.0ms	N	@	-inf	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))

rewrite129.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

871×	`pow1_binary64`
820×	`add-log-exp_binary64`
819×	`log1p-expm1-u_binary64`
819×	`expm1-log1p-u_binary64`
801×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	187	30
2	2221	30

Stop Event

1×	node limit

Counts

3 → 52

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(pow.f64 (cbrt.f64 N) 5)
(fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (cbrt.f64 N) 5)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (cbrt.f64 N) 5))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 N) 5) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 N) 5)) (cbrt.f64 (pow.f64 (cbrt.f64 N) 10)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 N) 10)) (cbrt.f64 (pow.f64 (cbrt.f64 N) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 N 5/6) (pow.f64 N 5/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 N)) 2) 5) (pow.f64 (cbrt.f64 (cbrt.f64 N)) 5))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 N 1/6) 5) (pow.f64 (pow.f64 N 1/6) 5))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 N) 10))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 N) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 N) 5) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 N) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 5 (log.f64 (cbrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 N) 5)))))))

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

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Rules

958×	`fma-def_binary64`
381×	`sqr-pow_binary64`
362×	`*-commutative_binary64`
361×	`distribute-rgt-neg-in_binary64`
351×	`swap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	222
1	44	186
2	90	186
3	238	138
4	878	138
5	1850	138
6	2504	138
7	4124	138
8	6354	138

Stop Event

1×	node limit

Counts

70 → 56

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 5) (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 5) (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 5) (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 5) (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) N)))
N
N
N
N
N
N

Outputs
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 (pow.f64 (pow.f64 N 1/3) 5) (pow.f64 N 1/3) N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 5) (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 5) (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 5) (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) 5) (.f64 (pow.f64 (.f64 N -1) 1/3) (cbrt.f64 -1)) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(atan2.f64 1 (+.f64 1 (+.f64 N (pow.f64 (cbrt.f64 N) 6))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
N
N
N
N
N
N

eval273.0ms (3.7%)

Compiler: Compiled 9516 to 5197 computations (45.4% saved)

prune74.0ms (1%)

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	521	7	528
Fresh	2	1	3
Picked	1	0	1
Done	2	5	7
Total	526	13	539

Error

0.6b

Counts

539 → 13

Alt Table

Click to see full alt table

Status	Error	Program
	1.1b	(atan2.f64 1 (+.f64 1 (+.f64 (pow.f64 (cbrt.f64 N) 6) N)))
✓	16.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	15.3b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
	1.3b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 N 1)))) 2)
	2.0b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 N 1)))) 3)
	2.4b	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) 3)
	11.5b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3))
	1.0b	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (.f64 N (cbrt.f64 N))) 3) (cbrt.f64 (.f64 N N)) N)))
	1.5b	(atan2.f64 1 (+.f64 1 (*.f64 N N)))
✓	29.0b	(atan2.f64 1 (+.f64 1 N))
✓	0.7b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	0.8b	(atan2.f64 1 (+.f64 1 (fma.f64 (.f64 (cbrt.f64 N) N) (cbrt.f64 (.f64 N N)) N)))
	21.4b	(atan2.f64 1 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))))

Compiler

Compiled 168 to 125 computations (25.6% saved)

regimes27.0ms (0.4%)

Counts

21 → 1

Calls

Call 1

Inputs
(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 2) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) 3)
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (.f64 N (cbrt.f64 N))) 3) (cbrt.f64 (.f64 N N)) N)))
(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))
(cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))
(atan2.f64 1 (+.f64 1 (fma.f64 (.f64 (cbrt.f64 N) N) (cbrt.f64 (.f64 N N)) N)))
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3))
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1)) 3))
(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 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 (pow.f64 N 4) (fma.f64 N N (neg.f64 N)))))
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 N 1)))) 2)
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 (*.f64 N N) (+.f64 N 1)))) 3)
(atan2.f64 1 (+.f64 1 (+.f64 (pow.f64 (cbrt.f64 N) 6) N)))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 1 N))

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

Calls

2 calls:

13.0ms	N
7.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
0.7b	1	`N`
0.7b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 263 to 171 computations (35% saved)

regimes4.0ms (0.1%)

Accuracy

Total -27.9b remaining (-1878.5%)

Threshold costs -27.9b (-1878.5%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
1.5b	1	`N`

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	18	30

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 24 to 19 computations (20.8% saved)

soundness0.0ms (0%)

end83.0ms (1.1%)

Compiler: Compiled 22 to 17 computations (22.7% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11
0	1	1

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11

Iter	Nodes	Cost
0	9	84
1	20	68
2	31	68
3	61	68
4	88	68
5	134	68
6	182	68
7	215	68
8	258	68
9	294	68
10	320	68
11	322	68

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11
0	1	1

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11

Iter	Nodes	Cost
0	9	84
1	20	68
2	31	68
3	61	68
4	88	68
5	134	68
6	182	68
7	215	68
8	258	68
9	294	68
10	320	68
11	322	68

Details

analyze1.0ms (0%)

sample2.9s (39.2%)

preprocess48.0ms (0.6%)

simplify12.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize45.0ms (0.6%)

series2.0ms (0%)

rewrite89.0ms (1.2%)

simplify25.0ms (0.3%)

eval20.0ms (0.3%)

prune8.0ms (0.1%)

localize58.0ms (0.8%)

series4.0ms (0.1%)

rewrite225.0ms (3%)

simplify107.0ms (1.4%)

localize23.0ms (0.3%)

series33.0ms (0.4%)

rewrite91.0ms (1.2%)

simplify215.0ms (2.9%)

localize59.0ms (0.8%)

series6.0ms (0.1%)

rewrite124.0ms (1.7%)

simplify111.0ms (1.5%)

eval490.0ms (6.6%)

prune83.0ms (1.1%)

localize62.0ms (0.8%)

series7.0ms (0.1%)

rewrite115.0ms (1.6%)

simplify235.0ms (3.2%)

localize37.0ms (0.5%)

series1.0ms (0%)

rewrite80.0ms (1.1%)

simplify76.0ms (1%)

eval148.0ms (2%)

prune74.0ms (1%)

localize40.0ms (0.5%)

series12.0ms (0.2%)

rewrite101.0ms (1.4%)

simplify83.0ms (1.1%)

localize13.0ms (0.2%)

series2.0ms (0%)

rewrite92.0ms (1.2%)

simplify28.0ms (0.4%)

localize87.0ms (1.2%)

series9.0ms (0.1%)

rewrite170.0ms (2.3%)

simplify59.0ms (0.8%)

localize17.0ms (0.2%)

series30.0ms (0.4%)

rewrite124.0ms (1.7%)

simplify240.0ms (3.2%)

localize18.0ms (0.2%)

series8.0ms (0.1%)

rewrite129.0ms (1.7%)

simplify73.0ms (1%)

eval273.0ms (3.7%)

prune74.0ms (1%)

regimes27.0ms (0.4%)

regimes4.0ms (0.1%)

simplify4.0ms (0.1%)

soundness0.0ms (0%)

end83.0ms (1.1%)

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